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MATHS M.C.Q. [1 Marks Each]

Practical Geometry · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 167 questions.

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M.C.Q. [1 Marks Each]

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167 questions · auto-graded multiple-choice test.

MCQ 11 Mark
An angle of $75^\circ $ is drawn using a pair of compass and ruler by bisecting ___.
  • A
    $60^\circ $
  • ✓
    $60^\circ $ and $90^\circ $
  • C
    $0^\circ $ and $90^\circ $
  • D
    $120^\circ $ and $180^\circ $
Answer
Correct option: B.
$60^\circ $ and $90^\circ $
$60^\circ $ and $90^\circ $
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MCQ 21 Mark
Lines $a, b, p, q, m, n$ and $x$ have $a$ point $P$ common to all of them. What is the name of $P?$
  • ✓
    Point of concurrence
  • B
    Point of intersection
  • C
    Common point
  • D
    Distinct point
Answer
Correct option: A.
Point of concurrence
A point common to multiple lines is called a point of concurrence as the lines are concurrent lines.
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MCQ 31 Mark
Rohan thinks he knows how to bisect angles and follows following steps to construct $45^\circ $ angle.
Step $1$: Construct an angle of $90^\circ $
Step $2$: Bisect the $90^\circ $ angle.
Step $3$: Bisect one of the angles obtained in step $2$.
  • A
    Step $1$
  • B
    Step $2$
  • ✓
    Step $3$
  • D
    Step $2$ and $3$
Answer
Correct option: C.
Step $3$
Step $3$
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MCQ 41 Mark
If $O$ is a point on the circle and $P$ is a point in the exterior of the circle. Length of $\overline{\text{OP}}=7.5$cm and radius of the circle is $5.5\ cm$. What will be the length of $\overline{\text{OP}},$ if $Q$ is the centre?
  • A
    $5.5\ cm$
  • ✓
    $3\ cm$
  • C
    $7.5\ cm$
  • D
    $13.5\ cm$
Answer
Correct option: B.
$3\ cm$
$OQ + OP = 5.5 + 7.5 = 13\ cm$
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MCQ 51 Mark
Identify the condition when a triangle can be constructed?
  • ✓
    One side and two acute angles are given.
  • B
    A side and an acute angle are given.
  • C
    Two obtuse angles are given.
  • D
    All given sides are equal.
Answer
Correct option: A.
One side and two acute angles are given.
One side and two acute angles are given.
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MCQ 61 Mark
Mark $(\checkmark)$ against the correct answer in the following:
$\frac{3}{2}$ right angles = .......
  • A
    $115^\circ $
  • ✓
    $135^\circ $
  • C
    $230^\circ $
  • D
    $270^\circ $
Answer
Correct option: B.
$135^\circ $

$32$ right angles $= 32 \times 90^\circ = 135^\circ $
$32$ right angles $= 32 \times 90^\circ = 135^\circ $

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MCQ 71 Mark
To construct a perpendicular to a line $(L)$ from a point $(P)$ outside the line, steps are given in jumbled form. Identify the fourth step from the following
$(1)$ Draw line $PQ$
$(2)$Draw a line $L$ and consider point $P$ outside the line
$(3)$Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively
$(4)$Taking $A$ and $B$ as a center one by one and keeping the same distance in compass
draw the arcs on other side of the line. The point where these arcs intersect name that point as $Q$
  • A
    $4$
  • B
    $3$
  • C
    $2$
  • ✓
    $1$
Answer
Correct option: D.
$1$
The correct sequence is: Step
$(1)$ Draw a line $L$ and consider a point $P$ outside the line.
$(2)$ Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
$(3)$ Taking $A$ and $B$ as centres one by one and keeping the same distance in compass, draw the arcs on other side of the line .
$(4)$ The point where these arcs intersect name that as $Q$
$(5)$ Draw line $PQ$ So the fourth step is $1$
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MCQ 81 Mark
With the help of a ruler and a compass, it is possible to construct an angle of:
  • A
    $37.5^\circ$
  • B
    $40^\circ$
  • ✓
    $22.5^\circ$
  • D
    $67.5^\circ$
Answer
Correct option: C.
$22.5^\circ$
Using a ruler and compass it is possible to construct an angle of $22.5^\circ$
Step $1$: construct an angle of $90^\circ$
Step $2$: Draw angle bisector to get an angle of $45^\circ$
Step $3$: Again draw angle bisector to get an angle of $22.5^\circ$So option $C$ is correct.
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MCQ 91 Mark
A few lines in a plane have a point in common. What type of lines can they be?
  • A
    Intersecting lines
  • B
    Parallel lines
  • C
    Concurrent lines
  • ✓
    Either $[a]$ or $[c]$
Answer
Correct option: D.
Either $[a]$ or $[c]$
If the lines are only two, then they are intersecting lines.
If there are more than two lines, then they are concurrent lines.
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MCQ 101 Mark
Identify the uses of a ruler.
  • A
    To draw a line segment of a given length
  • B
    To draw a copy of a given segment.
  • C
    To draw a diameter of a circle.
  • ✓
    All the above.
Answer
Correct option: D.
All the above.

A ruler is used to draw a line segment of a given length, to draw the copy of a given segment, and to draw a diameter of a circle.
Thus, all the given options are correct.

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MCQ 121 Mark
The steps of construction of an $\angle\text{AOB}=45^\circ$ is given in jumbled order below:
$1.$ Place compass on intersection point.
$2.$ Place ruler on start point and where arc intersects perpendicular line.
$3.$ Adjust compass width to reach start point.
$4.$ Construct a perpendicular line.
$5.$ Draw $45$ degree line.
$6.$ Draw an arc that intersects perpendicular line.
$7.$ The third step in process is:
  • A
    $2$
  • ✓
    $3$
  • C
    $4$
  • D
    $5$
Answer
Correct option: B.
$3$
Correct sequence is:
$1.$ Construct a perpendicular line
$2.$ Draw an arc that intersect the perpendicular line.
$3.$ Adjust the compass width to reach the start point .
$4.$ Place compass on intersection point.
$5.$ Place ruler on start point and where the arc intersects the perpendicular line.
$6.$ Draw $45$ degree line.
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MCQ 131 Mark
$P$ and $Q$ are the end points of a line segment $\overline{\text{PQ}}.$ If $R$ is any point on $\overline{\text{PQ}}.$ which of the given statements may be true?
  • A
    $PR = QR$
  • B
    $PR$ $QR$
  • C
    $PR$ $QR$
  • ✓
    All the above
Answer
Correct option: D.
All the above

Given that $R$ is any point on $\overline{\text{PQ}},$ $R$ may be Icoser to $P$ or $Q$ or exactly in between $P$ and $Q.$
Hence $PR = QR$ or $PR < QR$ or $PR > QR$ may be true.
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MCQ 141 Mark
Choose the correct option in which a triangle $CANNOT$ be constructed with the given lengths of sides.
  • A
    $3\ cm, 13\ cm, 15\ cm$
  • B
    $6\ cm, 6\ cm, 6\ cm$
  • ✓
    $9\ cm, 6\ cm, 2\ cm$
  • D
    $13\ cm, 6\ cm, 8\ cm$
Answer
Correct option: C.
$9\ cm, 6\ cm, 2\ cm$
Difference of $2$ sides,
$[9 − 6 = 3]$
is greater than third side, whereas it should be lesser.
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MCQ 151 Mark
If $\angle{\text{ABC}}=60^\circ$ and $\angle{\text{ABX}}=30^\circ$ in what ratio does $\overrightarrow{\text{BX}}$ divide $\angle{\text{ABC}}$?
  • A
    $1:2$
  • ✓
    $1:1$
  • C
    $2:1$
  • D
    $1:3$
Answer
Correct option: B.
$1:1$
$\angle{\text{ABC}}=60^\circ$ and $\angle{\text{ABX}}=30^\circ\Rightarrow\overrightarrow{\text{BX}}$ is the bisector of $\angle{\text{ABC}}\Rightarrow\overrightarrow{\text{BX}}$ divides $\angle{\text{ABC}}$ in the ratio $1:1$.
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MCQ 161 Mark
Through a line in a plane, number of lines that can be drawn is______.
  • A
    $1$
  • B
    $2$
  • C
    $0$
  • ✓
    Infinite
Answer
Correct option: D.
Infinite
Infinite
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MCQ 171 Mark
With the help of a ruler and a compass it is not possible to construct an angle of.
  • A
    $37.5^\circ$
  • ✓
    $40^\circ$
  • C
    $22.5^\circ$
  • D
    $67.5^\circ$
Answer
Correct option: B.
$40^\circ$
$\rightarrow $$37.5^\circ$ can be constructed by bisecting $150^\circ$ twice which can be done by compass.
$\rightarrow $$\angle $$22.5^\circ$ is the bisector of $90^\circ$ which can be also constructed using compass.
$\rightarrow $$\angle $$67.5^\circ$ is the bisector of $135^\circ$ whcih can also be drawn using compass.
But $40^\circ$​​​​​​​ can not be drawn using ruler and compass.
So option $B$ is correct.
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MCQ 181 Mark
Which of the following is an obtuse angle?
  • A
    $30^\circ $
  • B
    $60^\circ $
  • C
    $87^\circ $
  • ✓
    $123^\circ $
Answer
Correct option: D.
$123^\circ $
$123^\circ $
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MCQ 191 Mark
Which property has been used to construct the triangle in $Q$ $33$?
  • A
    $RHS$ property
  • B
    $SSS$ property
  • C
    $SAS$ property
  • ✓
    $ASA$ property
Answer
Correct option: D.
$ASA$ property
It is important to identify the segments on which angle can be constructed.
Since given angle is $\angle{\text{C}}$ hence the segment will be $BC$.
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MCQ 201 Mark
With the help of ruler and compass, it is not possible to construct an angle of:
  • A
    $60^\circ$
  • B
    $15^\circ$
  • ✓
    $38^\circ$
  • D
    $135^\circ$
Answer
Correct option: C.
$38^\circ$
$60^\circ$ can be easily constructed by making a single arc on a supplementary angle using a compass.
$15^\circ$​​​​​​​ can be constructed by bisecting $60^\circ$​​​​​​​ twice.
$135^\circ$ can be constructed by first drawing an angle of $90^\circ$ and bisecting its obtuse side.
So $38^\circ$​​​​​​​ can not be constructed using rule and compass.
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MCQ 211 Mark
 
$\angle{\text{PQR}}=\angle{\text{XYZ}}.$ If $\overrightarrow{\text{QM}}$ bisects $\angle{\text{PQR}},$ $\overrightarrow{\text{YN}}$ bisects $\angle{\text{XYZ}},$ which of the following statements are true?
$I.\ \angle{\text{PQM}}+\angle{\text{NYZ}}=\angle{\text{PQR}}$
$II.\ \angle{\text{MQR}}+\text{XYN}=\angle{\text{XYZ}}$
$III.\ \angle{\text{PQM}}=2\angle{\text{PQR}}$
$IV.\ \angle{\text{XYZ}}=2\angle{\text{MQR}}$
 
  • A
    $(i)$ and $(ii)$ only
  • B
    $(i)$ and $(iv)$ only
  • C
    $(ii)$ and $(iii)$ only
  • ✓
    $(i), (ii)$ and $(iv)$ only
Answer
Correct option: D.
$(i), (ii)$ and $(iv)$ only

Given $\angle{\text{PQR}}=\angle{\text{XYZ}},\overrightarrow{\text{QM}}$ bisects $\angle{\text{PQR}},$ and $\overrightarrow{\text{YN}}$ bisects $\angle{\text{XYZ}},$ respectively.
$\Rightarrow\angle{\text{PQM}}+\angle{\text{MQR}}=\angle{\text{XYN}}=\angle{\text{NYZ}}$
$\Rightarrow\angle{\text{PQM}}+\angle{\text{MQR}}=\angle{\text{PQR}}$ s true.
$\angle{\text{MQR}}=\angle{\text{XYN}}=\angle{\text{XYZ}}$ is true $\angle{\text{PQM}}=2\angle{\text{PQR}}$ is false as $\angle{\text{PQM}}=\frac{1}{2}\angle{\text{PQR}}$.
$\angle{\text{XYZ}}=2\angle{\text{MQR}}$ is true since $2\angle{\text{MQR}}=\angle{\text{PQR}}=\angle{\text{XYZ}}$
Hence $(i), (ii)$ and $(iv)$ are true.
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MCQ 221 Mark
$\text{p}|\text{q}$ $C$ and $D$ are two points on $p$ and $M$ and $N$ are two points on $q$, such that $M$ and $N$ are exactly opposite to $C$ and $D$ respectively. Identify the true statement.
  • A
    $CDNM$ forms a rectangle.
  • B
    $ \overline{\text{CM}}=\overline{\text{DN}}$
  • ✓
    Both $[a]$ and $[b]$
  • D
    Neither $[a]$ nor $[b]$
Answer
Correct option: C.
Both $[a]$ and $[b]$


From the figure and the given data, clearly, $CDNM$ is a rectangle.
Also $ \overline{\text{CM}}=\overline{\text{DN}}$ as the distance between two parallel lines is the same throughout.

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MCQ 231 Mark
A perpendicular is drawn to a line segment $\overline{\text{MN}}$ at $N$ using protractor and point $P$ is marked on perpendicular, then _______.
  • A
    $\overline{\text{MP}}\perp\overline{\text{NP}}$
  • B
    $\overline{\text{MN}}\parallel\overline{\text{NP}}$
  • C
    $\overline{\text{MN}}\parallel\overline{MP}$
  • ✓
    $\overline{\text{MN}}\perp\overline{\text{Np}}$
Answer
Correct option: D.
$\overline{\text{MN}}\perp\overline{\text{Np}}$

$\therefore \overline{\text{MN}}\perp\overline{\text{NP}}$
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MCQ 241 Mark
Sumit constructed an angle of $90^\circ $ and trisected it. Measure of two angles taken together will be:
  • A
    $20^\circ $
  • B
    $40^\circ $
  • ✓
    $60^\circ $
  • D
    None of these
Answer
Correct option: C.
$60^\circ $
$60^\circ $
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MCQ 251 Mark
In Fig. $\angle\text{XYZ}$ cannot be written as:
  • A
    $\angle\text{Y}$
  • ✓
    $\angle\text{XYZ}$
  • C
    $\angle\text{ZYX}$
  • D
    $\angle\text{XYP}$
Answer
Correct option: B.
$\angle\text{XYZ}$

Since, $\angle\text{XYZ}$ can be written as $\angle\text{Y},\angle\text{ZYX},\angle\text{XYP}$ and $\angle\text{PYX.}$
So, $\angle\text{XYZ}$ cannot be written as $\angle\text{ZXY}.$

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MCQ 261 Mark
Lines $p$ and $q$ have a point $M$ in common. Identify the correct statement.
  • ✓
    $\angle1=−3$
  • B
    $\angle2=−3$
  • C
    $\angle3=\angle4$
  • D
    $\angle1=\angle2$
Answer
Correct option: A.
$\angle1=−3$


From the given figure and data, it is clear that $p$ and $q$ are intersecting lines.
So, the vertically opposite angles are equal.
Hence $ \angle1=\angle3.$

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MCQ 271 Mark
How many lines can be drawn passing through a given point?
  • A
    One only
  • B
    Two
  • C
    Three
  • ✓
    Infinitely many
Answer
Correct option: D.
Infinitely many
Infinitely many points can be drawn passing through a given point.
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MCQ 281 Mark
$\text{l}\parallel\text{m}$ $P$ and $Q$ are points on land m respectively such that ${\text{PQ}}\perp{\text{l}}$. $R$ is a point on a line n in the same plane such that $\overline{\text{PQ}}=\overline{\text{QR}}$. Which of the following is true?
  • A
    ${\text{l}}\parallel{\text{n}}$
  • B
    ${\text{m}}\parallel{\text{n}}$
  • ✓
    Both $[a]$ and $[b]$
  • D
    Neither $[a]$ nor $[b]$
Answer
Correct option: C.
Both $[a]$ and $[b]$

Clearly, from the given data and the figure, ${\text{l}}\parallel{\text{n}}\text{ and}{\text{ m}}\parallel{\text{n}}$
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MCQ 291 Mark
To construct a perpendicular to a line $(L)$ from a point $(P)$ outside the line, steps are given in jumbled form.Identify the third step from the following.
$1)$ Draw line $PQ.$
$2)$ Draw a line $L$ and consider point $P$ outside the line.
$3)$ Take $P$ as a center, draw $2$ arcs on line L and name it as points $A$ and $B$ respectively.
$4)$ Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.
  • ✓
    $4$
  • B
    $3$
  • C
    $2$
  • D
    $1$
Answer
Correct option: A.
$4$
The correct sequence is:
Step $1$. Draw a line $L$ and consider a point $P$ outside the line.
Step $2$. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step $3$.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step $4$. Draw line $P$Q So the third step is $4$ Option $A$ is correct.
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MCQ 301 Mark
The last step in the process is:
  • ✓
    $1$
  • B
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: A.
$1$
Correct sequence is :
$1.$ Draw a line $PQ$ and take a point $A$ anywhere outside the line.
$2.$ Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.
$3.$ From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S$.
$4.$ Join $R − S$ passing through $A$.
So the last step is $1$.
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MCQ 311 Mark
Given $PQ = 6\ cm, QR = 55\ cm$ and $RP = 55\ cm$, what type of a triangle can be constructed?
  • ✓
    An acute angled triangle.
  • B
    An obtuse angled triangle
  • C
    An equilateral triangle
  • D
    A right angle triangle
Answer
Correct option: A.
An acute angled triangle.
Since $QR = RP \Rightarrow $ it is isosceles $\triangle\text{le} $ and an isosceles $\triangle\text{le}$ is always acute $\angle\text{led}$
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MCQ 321 Mark
To draw an angle of $150^\circ$ using a pair of compass and ruler_____ .
  • ✓
    Bisect angle between $120^\circ$ and $180^\circ$
  • B
    Bisect angle between $60^\circ$ and $120^\circ$
  • C
    Bisect angle between $0^\circ$ and $160^\circ$
  • D
    None of these
Answer
Correct option: A.
Bisect angle between $120^\circ$ and $180^\circ$
$\Rightarrow $ To draw an angle of $150^\circ$ using a pair of compass and Bisect angle between $120^\circ$and $180^\circ$.
$\Rightarrow $ The difference angle between $120^\circ$ and $180^\circ$ is $60^\circ$.
So, when we bisect angle of $60^\circ$ we get $30^\circ$ angles each.
$\Rightarrow $ So, $120^\circ$ + $30^\circ$= $150^\circ$
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MCQ 331 Mark
In the adjoining figure line $L\ ||$ line $M$ and line $N$ is the transversal. Which of the following line is one of the pairs of alternative angles?
  • A
    $\angle{\text{a }}\text{&}\angle{\text{e}}$
  • ✓
    $\angle{\text{d }}\text{&}\angle{\text{F}}$
  • C
    $\angle{\text{b }}\text{&}\angle{\text{f}}$
  • D
    $\angle{\text{d }}\text{&}\angle{\text{e}}$
Answer
Correct option: B.
$\angle{\text{d }}\text{&}\angle{\text{F}}$

$\angle{\text{d }}$ and $\angle{\text{F}}$

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MCQ 341 Mark
To construct a perpendicular to a line $(L)$ from a point $(P)$ outside the line, steps are given in jumbled form.Identify the first step from the following.
$1)$ Draw line $PQ.$
$2)$ Draw a line $L$ and consider point $P$ outside the line.
$3)$Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
$4)$Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.
  • A
    $4$
  • B
    $3$
  • ✓
    $2$
  • D
    $1$
Answer
Correct option: C.
$2$
The correct sequence is:
Step $1$. Draw a line $L$ and consider a point $P$ outside the line.
Step $2$. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step $3$.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step $4$. Draw line $PQ$ So the first step is $2$ Option $C$ is correct.
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MCQ 351 Mark
Measures of the two angles between hour and minute hands of a clock at $9\ O’$ clock are:
  • A
    $60^\circ , 300^\circ $
  • ✓
    $270^\circ , 90^\circ $
  • C
    $75^\circ , 285^\circ $
  • D
    $30^\circ , 330^\circ $
Answer
Correct option: B.
$270^\circ , 90^\circ $
The positions of hour and minute hands of a clock at $9\ O’$ clock are represented in the following figure.

Clearly, $\angle1=90^\circ$
And $\angle2=\ \text{Reflex}\ \text{of}\ \angle1=360^\circ-90^\circ=270^\circ$
Note: A reflex angle is more than $180^\circ $ but less than $360^\circ $. For any acute angle $\theta,$ its reflex angle is $(360^\circ-\theta).$
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MCQ 361 Mark
Mark $(\checkmark)$ against the correct answer in the following:
Two planes intersect:
  • A
    At a point.
  • ✓
    In a line.
  • C
    In a plane.
  • D
    None os these.
Answer
Correct option: B.
In a line.
When the common points of two planes intersect, they form a line.
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MCQ 371 Mark
$X$ is the midpoint of $\overline{\text{AB}}.$If $\overline{\text{AX}}=9.3\text{cm}$ what is the measure of $\overline{\text{AB}}$?
  • A
    $4.65\ cm$
  • ✓
    $18.6\ cm$
  • C
    $9.3\ cm$
  • D
    $18\ cm$
Answer
Correct option: B.
$18.6\ cm$
$18.6\ cm$
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MCQ 381 Mark
Identify the pair of parallel lines.
$i.$ Lines $m$ and $n$ have two points in common.
$ii.$ Lines $p$ and $q$ do not have any point in common.
$iii.$ Lines $p$ and $q$ have a point $X$ in common.
  • A
    $(i)$ and $(ii)$ only
  • ✓
    $(ii)$ only
  • C
    $(ii)$ and $(iii)$ only
  • D
    $(i), (ii)$ and $(iii)$
Answer
Correct option: B.
$(ii)$ only
Parallel lines do not have any point in common.
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MCQ 391 Mark
The third step in the process will be:
  • ✓
    $1$
  • B
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: A.
$1$
Correct sequence of steps is :
Step $1$: Draw segment $AB$ and take a point $P$ on it.
Step $2$: From point $P$, mark two equidistant points from $P$ on line $AB$, and name them $C$ and $D$
Step $3$ : From points $C$ and $D$ mark two intersecting arcs on either side of the line $AB$.
Name the intersection point as $E$
Step $4$: Join $E$ and $P. EP$ is the required perpendicular.
So the third step is !!So option $A$ is correct.
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MCQ 401 Mark
Which of the following is done to draw an angle of $150^\circ $ using compasses and a ruler?
  • ✓
    Bisecting $120^\circ $ and $180^\circ $ angles.
  • B
    Bisecting $60^\circ $ and $120^\circ $ angles.
  • C
    Bisecting $0^\circ $ and $60^\circ $ angles.
  • D
    Bisecting a $360^\circ$ angle.
Answer
Correct option: A.
Bisecting $120^\circ $ and $180^\circ $ angles.
Bisecting $120^\circ $ and $180^\circ $ angles.
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MCQ 411 Mark
$\overrightarrow{\text{BA}}\perp\overrightarrow{\text{XY}}$ Which of the following statements are incorrect?
$i.\ \angle{\text{ABX}}+\angle{\text{ABY}}=180^\circ$
$ii.\ \angle{\text{ABX}}=2{\text{right angle}}$
$iii\ \angle{\text{ABY}}=90^\circ$
$iv.\ \angle{\text{XBY}}=90^\circ$
  • A
    $(i)$ and $(ii)$ only
  • ✓
    $(ii)$ and $(iv)$ only
  • C
    $(ii)$ and $(iii)$ only
  • D
    $(i)$ and $(iv)$ only
Answer
Correct option: B.
$(ii)$ and $(iv)$ only

Since $\overrightarrow{\text{BA}}\perp\overrightarrow{\text{XY}}$
$\angle{\text{ABY}}=90^\circ$ and $\angle{\text{XBY}}=90^\circ$
$\therefore\angle{\text{ABX}}+\angle{\text{ABY}}=180^\circ$ is true.
$\angle{\text{ABX}}=90^\circ\Rightarrow\angle{\text{ABX}}=2$ right angles is false. $\angle{\text{ABY}}=90^\circ$ is true.
$\angle{\text{XBY}}=90^\circ$ is false since $\angle{\text{ABY}}=\angle{\text{XBA}}+\angle{\text{ABY}}=180^\circ$.
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MCQ 421 Mark
$\triangle\text{PQR}$ is constructed with all its angles measuring $60^\circ $ each. Which of the following is correct?
  • ✓
    $\triangle\text{PQR}$ is an equilateral triangle.
  • B
    $\triangle\text{PQR}$ is isosceles triangle.
  • C
    $\triangle\text{PQR}$ is a scalene triangle.
  • D
    $\triangle\text{PQR} $ is a right angled triangle.
Answer
Correct option: A.
$\triangle\text{PQR}$ is an equilateral triangle.
$\triangle\text{PQR}$ is an equilateral triangle.
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MCQ 431 Mark
Given $AB = 3\ cm, AC = 5.2\ cm$, and $\angle\text{B} = 35^∘.$ $\angle\text{ABC}$ cannot be uniquely constructed, with $AC$ as base, why?
  • A
    Two sides and included angle are given.
  • B
    The other two angles are not given.
  • C
    The vertex $B$ cannot be uniquely located.
  • ✓
    The vertex $A$ coincides with the vertex $C$.
Answer
Correct option: D.
The vertex $A$ coincides with the vertex $C$.
Use $RHS$ property to Contruct the Ale as. Shown:
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MCQ 441 Mark
A triangle$ \triangle\text{PQR}$ with $ \angle\text{Q} = 90^∘,$$QR = 4\ cm$ and $PR = 5cm$ is constructed. What would be the measure of $PQ$?
  • ✓
    $2\ cm$
  • B
    $6\ cm$
  • C
    $7\ cm$
  • D
    $3\ cm$
Answer
Correct option: A.
$2\ cm$
$2\ cm$
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MCQ 451 Mark
There is a rectangular sheet of dimension $\big(2\text{m-1}\big)\times\big(2\text{n-1}\big),$ (where $m > 0, n > 0$). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length?
  • A
    $\big(\text{m+n+1}\big)^2$
  • B
    $\text{mn}\big(\text{m+1}\big)\big(\text{n+1}\big)$
  • C
    $4^\text{m+n-2}$
  • ✓
    $\text{m}^2\text{n}^2$
Answer
Correct option: D.
$\text{m}^2\text{n}^2$
Total no. of horizontal line $= 2m$ Total no. of vertical lines $= 2n$ $($$\because$ Each line is at unit distance and hence, total no. of lines = Distance/lenght $+1).$
To form a square from three lines,we mustselect one even and one odd numbered horizontal and vertical line
$\therefore$ Ways possible of selecting such squares $=(\text{c}_{1}^\text{m})\times(\text{c}_{1}^\text{m})\times$ $(\text{c}_{1}^\text{n}\times\text{c}_{1}^\text{n})=$ $\text{c}_{1}^\text{m}\times\text{c}_{1}^\text{m}\times\text{c}_{1}^\text{n}\times\text{c}_{1}^\text{n}=$ $\text{m}^2\times\text{n}^2=\text{m}^2\text{n}^2$
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MCQ 461 Mark
Which of the following steps is $INCORRECT$ while constructing an angle of $60^\circ $?
Step $1:$ Draw a line $EF$ and mark a point $O$ on it.
Step $2:$ Place the pointer of the compass at $O$ and draw an arc of convenient radius which cuts the line $EF$ at point $P$.
Step $3:$ With the pointer at $A$ (as centre) now draw an arc that passes through $O$.
Step $4:$ Let the two arcs intersect at $Q$. Join $OQ$. We get $\angle{\text{QOP}}$ whose measure is $60^\circ $ .
  • A
    Only Step - $1$
  • B
    Both Step - $2$ and Step - $3$
  • ✓
    Only Step - $3$
  • D
    Both Step - $3$ and Step - $4$
Answer
Correct option: C.
Only Step - $3$
Step-3 is incorrect it should be written as: with the pointer at $P$ (as centre) now draw an arc that passes through $0$.
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MCQ 471 Mark
$\overrightarrow{\text{MN}}$ is the perpendicular bisector of $\overleftrightarrow{\text{AB}}$ Which of the given statements is correct?
$i.\ \angle{\text{ANM}}+\angle{\text{MNB}}=90^\circ$
$ii.\ \overline{\text{AN}}=\overline{\text{NB}}$
$iii.\ \overline{\text{AN}}=2\overline{\text{NB}}$
$iv.\ \angle{\text{MNB}}=\frac{1}{2}\angle{\text{ANM}}$
 
  • A
    $(i)$ and $(iii)$ only
  • B
    $(ii)$ and $(iv)$ only
  • ✓
    $(i)$ and $(ii)$ only
  • D
    $(ii)$ and $(iii)$ only
Answer
Correct option: C.
$(i)$ and $(ii)$ only
$\overrightarrow{\text{NM}}\perp\overleftrightarrow{\text{AB}}$ and $\overrightarrow{\text{NM}}$ divides $\overleftrightarrow{\text{AB}}$ into two congruent parts.

Clearly $\angle{\text{ANM}}+\angle{\text{MNB}}=90^\circ$ is true.
$\overline{\text{AN}}=\overline{\text{NB}}$ is true since $\overrightarrow{\text{NM}}\perp\overleftrightarrow{\text{AB}}$ $\overline{\text{AN}}=2\overline{\text{NB}}$ is false, and $\angle{\text{MNB}}=\frac{1}{2}\angle{\text{ANM}}$ is false.
Thus, only $(i)$ and $(ii)$ are correct.
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MCQ 481 Mark
How do you draw a $90^\circ $ angle?
  • ✓
    By drawing a perpendicular to a line from a point lying on it.
  • B
    By bisecting a $120^\circ $ angle.
  • C
    By bisecting a $60^\circ $ angle.
  • D
    By drawing multiples of $45^\circ $ angle.
Answer
Correct option: A.
By drawing a perpendicular to a line from a point lying on it.
By drawing a perpendicular to a line from a point lying on it.
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MCQ 491 Mark
If the sum of two angles is greater than $180^\circ  $, then which of the following is not possible for the two angles?
  • A
    One obtuse angle and one acute angle.
  • B
    One reflex angle and one acute angle.
  • C
    Two obtuse angles.
  • ✓
    Two right angles.
Answer
Correct option: D.
Two right angles.
Because sum of two right angles is equal to $180^\circ .$
Note:
An acute angle is less than $90^\circ .$
A right angle is equal to $90^\circ .$
An obtuse angle is more than $90^\circ $ but less than $180^\circ .$
A reflex angle is more than $180^\circ $ but less than $360^\circ .$
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MCQ 501 Mark
If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
  • A
    One obtuse angle and one acute angle.
  • B
    One right angle and one acute angle.
  • C
    wo acute angles.
  • ✓
    Two right angles.
Answer
Correct option: D.
Two right angles.

Because sum of two right angles is equal to $180^\circ $.

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MCQ 511 Mark
The steps of construction of an $\angle AOB = 45^\circ$ is given in jumbled order below:
$1.$ Place compass on intersection point.
$2.$ Place ruler on start point and where arc intersects perpendicular line.
$3.$ Adjust compass width to reach start point.
$4.$ Construct a perpendicular line.
$5.$ Draw $45$ degree line.
$6.$ Draw an arc that intersects perpendicular line.
Which step comes last ?
  • A
    $2$
  • B
    $3$
  • C
    $4$
  • ✓
    $5$
Answer
Correct option: D.
$5$
Correct sequence is:
$1.$ Construct a perpendicular line.
$2.$ Draw an arc that intersect the perpendicular line.
$3.$ Adjust the compass width to reach the start point.
$4.$ Place compass on intersection point.
$5.$ Place ruler on start point and where the arc intersects the perpendicular line.
$6.$ Draw $45$ degree line. So the last step is $5$ Option $D$ is correct.
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MCQ 521 Mark
A quadrilateral is a rhombus but not a square if:
  • A
    its diagonals do not bisect each other
  • B
    its diagonals are not perpendicular
  • C
    opposite angles are not equal
  • ✓
    the length of diagonals are not equal
Answer
Correct option: D.
the length of diagonals are not equal
The length of diagnols are not equal
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MCQ 531 Mark
In $\triangle\text{XYZ},$ $a, b, c$ denote the three sides, which of the following is incorrect?
  • ✓
    $a − b > c$
  • B
    $a + c > b$
  • C
    $a − b < c$
  • D
    $a + b > c$
Answer
Correct option: A.
$a − b > c$
Actually, $a − b < c\ ∀ a, b, c$ $($the symbol$, ∀ a, b, c$ means for all $a, b, c)$ This implies that $b − c < a; c − a < b$
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MCQ 541 Mark
With the help of ruler and compass, it is not possible to construct an angle of:
  • A
    $37.5^\circ $
  • ✓
    $40^\circ $
  • C
    $22.5^\circ $
  • D
    $67.5^\circ $
Answer
Correct option: B.
$40^\circ $
With the help of a ruler and a compass, we can construct the angels, $90^\circ , 60^\circ , 45^\circ , 22.5^\circ , 30^\circ ,$
etc.i.e., the multiples of $15^\circ $ and its bisector of an angle.
So, it is not possible to construct an angle of $40^\circ $
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MCQ 551 Mark
The number of angles in Fig. is:
  • A
    $3$
  • B
    $4$
  • C
    $5$
  • ✓
    $6$
Answer
Correct option: D.
$6$
Angles shown in the figure are $40^\circ , 20^\circ , 30^\circ , 60^\circ , 50^\circ $ and $90^\circ $. Therefore, there are $6$ angles,
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MCQ 561 Mark
A perpendicular is drawn using:
  • A
    scale
  • ✓
    scale protractor
  • C
    set square
  • D
    divider
Answer
Correct option: B.
scale protractor
A perpendicular is drawn using scale, protractor as well as set squares.
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MCQ 571 Mark
A triangle $\triangle\text{PQR}$ with $ \angle\text{Q}=90^∘,$ $QR = 4\ cm$ and $PR = 5\ cm$ is constructed. What would be the measure of $PQ$?
  • ✓
    $2\ cm$
  • B
    $6\ cm$
  • C
    $7\ cm$
  • D
    $3\ cm$
Answer
Correct option: A.
$2\ cm$
$2\ cm$
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MCQ 581 Mark
In $\triangle\text{ABC},$ $\overline{\text{AB}}>\overline{\text{BC}}>\overline{\text{CA}}$ which of the following is the smallest angle?
  • A
    $\angle{\text{A}}$
  • ✓
    $\angle{\text{B}}$
  • C
    $\angle{\text{C}}$
  • D
    $ \angle{\text{A}} =\angle{\text{B}} = \angle{\text{C}}$
Answer
Correct option: B.
$\angle{\text{B}}$
$\angle{\text{B}}$
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MCQ 591 Mark
With the help of a ruler and a compass, it is possible to construct an angle of:
  • A
    $35^\circ$
  • B
    $40^\circ$
  • ✓
    $37.5^\circ$
  • D
    $47.5^\circ$
Answer
Correct option: C.
$37.5^\circ$
Using ruler and compass it is possible to construct $37.5^\circ$
Step $1$: Construct angle of $150^\circ$
Step $2$: Bisect the angle to get $75^\circ$
Step $3$: Again bisect the angle to get $37.5^\circ$
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MCQ 601 Mark
$X$ and $Y$ are two distinct points in a plane. How many lines can be drawn passing through both $X$ and $Y$?
  • A
    $0$
  • ✓
    $1$
  • C
    Only $2$
  • D
    Infinitely many
Answer
Correct option: B.
$1$
$1$
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MCQ 611 Mark
Mark $(\checkmark)$ against the correct answer in the following:
Where does the vertex of an angle lie?
  • A
    In its interior.
  • B
    In its exterior.
  • ✓
    On the angle.
  • D
    None os these.
Answer
Correct option: C.
On the angle.
The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.
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MCQ 621 Mark
Into what type of parts is a figure divided by bisecting it?
  • ✓
    Equa
  • B
    Equal
  • C
    Triangular
  • D
    Perpendicular
Answer
Correct option: A.
Equa
Equa
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MCQ 631 Mark
Number of lines passing through five points such that no three of them are collinear is:
  • ✓
    $10$
  • B
    $5$
  • C
    $20$
  • D
    $8$
Answer
Correct option: A.
$10$
$10$
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MCQ 641 Mark
The number of diagonals in a septagon is:
  • A
    $21$
  • B
    $42$
  • C
    $7$
  • ✓
    $14$
Answer
Correct option: D.
$14$
We know that, if a polygon has n sides, then Number of diagonals $=\frac{\text{n}(3-2)}{2}$
A septagon is a polygon having seven sides, i.e. $n = 7$
Number of diagonals in septagon $=\frac{7(7-3)}{2}=14$
Note: A diagonal is a line segment joining two non-consecutive vertices of a polygon.
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MCQ 651 Mark
In which of the following figures the adjacent sides are not necessarily be equal?
  • ✓
    Parallelogram
  • B
    Rhombus
  • C
    Rectangle
  • D
    Square
Answer
Correct option: A.
Parallelogram
$(a)$ & $(c)$ Both parallelogram and rectangle.
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MCQ 661 Mark
The steps for constructing a perpendicular from point $A$ to line $P$ $Q$ is given in jumbled order as follows: $(A$ does not lie on $PQ)$
$1.$ Join $R$ − $S$ passing through $A$.
$2.$  $P$lace the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $P$$Q$ with the same radius.
$3.$ From points $D$ and $E$, mark two intersecting arcs on either side of $P$ $Q$ and name them $R$ and $S$.
$4.$ $D$raw a line $P$ $Q$ and take a point $A$ anywhere outside the line.The second step in the process is:
  • A
    $1$
  • ✓
    $2$
  • C
    $3$
  • D
    $4$ 
Answer
Correct option: B.
$2$
Correct sequence is:
$1.$ Draw a line $P$ $Q$ and take a point $A$ anywhere outside the line.
$2.$ $P$lace the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $P$ $Q$ with the same radius.
$3.$ From points $D$ and $E$, mark two intersecting arcs on either side of $P$ $Q$ and name them $R$ and $S$.
$4.$ Join $R$ − $S$ passing through $A.$
$5.\ S$o the second step is $2$.
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MCQ 671 Mark
The last step in the process is:
  • A
    $1$
  • ✓
    $2$
  • C
    $4$
  • D
    $5$
Answer
Correct option: B.
$2$
Correct sequence is
Step $1$. Draw a ray $QR$
Step $2$. Place the pointed end of the compass on $Q$ and draw a semi circular arc with arbitrary radius.
Step $3$. Mark a point $B$ on the same arc with the same radius from point $A$. Similarly, mark a point $C$ from $B$.
Step $4$. Draw two intersecting arcs from $B$ and $C$ and mark the intersection as point $D$.
Step $5$. Join $Q-D$ and extend it to obtain $QP$.
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MCQ 681 Mark
Read the statements carefully.
Statement 1: Two lines are said to be perpendicular if they intersect each other at an angle of $90^\circ $.
Statement 2: A unique circle can be drawn passing through the given centre.
Which of the following options holds?
  • A
    Both Statement - $1$ and Statement - $2$ are true.
  • ✓
    Statement - $1$ is true and Statement - $2$ is false.
  • C
    Statement -$1$ is false and Statement - $2$ is true.
  • D
    Both Statement -$1$ and Statement - $2$ are false.
Answer
Correct option: B.
Statement - $1$ is true and Statement - $2$ is false.
Statement - $1$ is true and Statement - $2$ is false.
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MCQ 691 Mark
At $7\ a.m$. the angle between the Sun's ray and the ground at a point is $43^\circ $ What would be the angle at $10\ a.m.$?
  • A
    $40^\circ $
  • B
    $90^\circ $
  • ✓
    Between $43^\circ $ and $90^\circ $
  • D
    Greater than $90^\circ $
Answer
Correct option: C.
Between $43^\circ $ and $90^\circ $
Let QP be the sun's ray and RP be the ground.

The angle between $QP$ and $PR$ at $P$ is $43^\circ $ at $7\ a.m.$ At $10\ a.m$., the sun's ray is $Q'P$.
We know that at $12$ noon the sun is exactly above our head.
So, the sun's ray will be perpendicular to the ground.
So, clearly at $10\ am$, the required angle will be between $43^\circ $ and $90^\circ $.
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MCQ 701 Mark
A vertex of square is $(3,4)$ and diagonals equation is given by $x + 2y = 1,$
then the second diagonal which passes through given vertex will be
  • A
    $2x - y + 2 = 0$
  • B
    $x + 2y = 11$
  • ✓
    $2x - y = 2$
  • D
    None of these
Answer
Correct option: C.
$2x - y = 2$
$2x - y = 2$
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MCQ 711 Mark
The figure shows $\angle{\text{PQR}}$ which measures 48° $\overrightarrow{\text{QX}}$ is drawn such that $\angle{\text{PQX}}=\angle{\text{XQR}}.$ What is $\overrightarrow{\text{QX}}$ called?
  • A
    Perpendicular bisector
  • B
    Divider ray
  • ✓
    Angle bisector
  • D
    Either $[a]$ or $[b]$
Answer
Correct option: C.
Angle bisector
Angle bisector
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MCQ 731 Mark
A maths teacher asked his students to draw a pair of parallel lines. Which instrument $(s)$ are the students most likely to use?
  • A
    A ruler and a compass
  • B
    Two edges of a ruler
  • C
    A ruler and a setsquare
  • ✓
    Both $[b]$ and $[c]$
Answer
Correct option: D.
Both $[b]$ and $[c]$
The lines drawn using the two edges of a ruler are parallel.
Also a ruler and a setsquare can be used to draw a pair of parallel lines.
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MCQ 741 Mark
The fourth step in the process is:
  • ✓
    $1$
  • B
    $3$
  • C
    $4$
  • D
    $5$
Answer
Correct option: A.
$1$
$0^\circ <$ acute angle $< 90^\circ <$ obtuse angle $< 180^\circ $.
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MCQ 751 Mark
An angle of $15$ is drawn using a pair of compasses and a ruler. How is it done?
  • A
    Bisecting $60^\circ $ angle.
  • B
    Bisecting $60^\circ$ and $120^\circ $ angles.
  • ✓
    Bisecting $60^\circ $ and then bisecting it again.
  • D
    Bisecting a $60^\circ $ and $180^\circ $ angles.
Answer
Correct option: C.
Bisecting $60^\circ $ and then bisecting it again.
Bisecting $60^\circ $ and then bisecting it again.
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MCQ 761 Mark
An angle which can be constructed using a pair of compass and ruler is
  • A
    $20^\circ $
  • B
    $80^\circ $
  • ✓
    $60^\circ $
  • D
    $110^\circ $
Answer
Correct option: C.
$60^\circ $
An angle which can be constructed using a pair of compass and ruler is $60^\circ $ as multiples of
$15^\circ $ can be drawn using a compass.
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MCQ 771 Mark
A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is:
  • A
    $4$
  • ✓
    $5$
  • C
    $7$
  • D
    $10$
Answer
Correct option: B.
$5$
The two least consecutive primes are $2$ and $3$.
$2 + 3 = 5$
So, sides of polygon $(n) = 5$
Number of diagonals $=\frac{\text{n}(\text{n}-3)}{2}=\frac{5(5-3)}{2}=5$
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MCQ 781 Mark
Identify the condition to be checked before constructing a triangle.
  • A
    Sum of the three angles is $180^\circ $
  • B
    The sum of any two of the sides is greater than the third side.
  • C
    The difference of any two sides in lesser than the third side.
  • ✓
    All the above.
Answer
Correct option: D.
All the above.
All the above.
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MCQ 791 Mark
The measurements of $\triangle\text{DEF}$ are $\text{EF}=8.4\text{cm},$ $\angle\text{E}=100^∘$ and $\angle=82^∘$. Which of the following is correct?
  • A
    $ADEF$ can be constructed.
  • B
    $ADEF$ is an obtuse angled triangle.
  • ✓
    A cannot be constructed
  • D
    $ADEF$ is an acute angled triangle.
Answer
Correct option: C.
A cannot be constructed
$\triangle\text{le} $ cannot be constructed as sum of only two $\triangle\text{les}$ $\angle\text{E}$ & $\angle\text{F}>180^∘(\angle\text{E}+\angle\text{F}=182^∘),$ which is not possible in a Ale.
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MCQ 801 Mark
Which of the following statement is true about the given figure?
  • A
    It is an octagon.
  • B
    It is a regular polygon.
  • ✓
    It is a polygon.
  • D
    It is a quadrilateral.
Answer
Correct option: C.
It is a polygon.

Given figure is a polygon.

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MCQ 811 Mark
What do you call two lines intersecting at a point?
  • A
    Perpendicular lines
  • B
    Parallel lines
  • C
    Bisectors lines
  • ✓
    Intersecting lines
Answer
Correct option: D.
Intersecting lines
Intersecting lines
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MCQ 821 Mark
Mark $(\checkmark)$ against the correct answer in the following:
Which of the following has no end points?
  • A
    A line segment.
  • B
    A ray.
  • ✓
    A line.
  • D
    None os these.
Answer
Correct option: C.
A line.
A line has no end points. We can produce it infinitely in both directions.
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MCQ 831 Mark
How many complete turns is equivalent to $90^\circ ?$
  • A
    $2$
  • B
    $1$
  • C
    $\frac{1}{2}$
  • ✓
    $\frac{1}{4}$
Answer
Correct option: D.
$\frac{1}{4}$
$\frac{1}{4}$
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MCQ 841 Mark
The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along $XY$ so the other short side touches Point $P$.
$2.$ Use the edge of the set square to draw a line through Point $P$.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line $XY$.
Which of the following will be the first step:
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $4$
Answer
Correct option: D.
$4$
$1.$ Draw a line $XY$ and mark a point $P$ on it.
$2.$ Place one short side of the set square on the line $XY$.
$3.$ Move the set square along $XY$ so the other short side touches point $P$.
$4.$ Use the edge of the set square to draw a line through point $P$.
$5.$ So is the second step.Option $D$ is correct.
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MCQ 851 Mark
The first step in the process will be:
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $4$
Answer
Correct option: D.
$4$
Correct sequence of steps is :
Step $1$: Draw segment $AB$ and take a point $P$ on it.
Step $2$: From point $P$, mark two equidistant points from $P$ on line $AB$, and name them $C$ and $D$
Step $3$ : From points $C$ and $D$ mark two intersecting arcs on either side of the line $AB$. Name the intersection point as $E$
Step $4$: Join $E$ and $P$. $EP$ is the required perpendicular. So the first step is $4$
So option $D$ is correct.
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MCQ 861 Mark
When two line segments meet at a point forming right angle they are said to be __________ to each other.
  • A
    Parallel
  • ✓
    Perpendicular
  • C
    Equal
  • D
    None of the above
Answer
Correct option: B.
Perpendicular
When two line segments meet at a point forming right angle
they are said to be perpendicular to each other.
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MCQ 871 Mark
When a perpendicular is drawn to a given line, in what ratio is the line divided into?
  • A
    $1 : 1$
  • B
    $1 : 2$
  • C
    $2 : 1$
  • ✓
    Cannot be said
Answer
Correct option: D.
Cannot be said
A line does not have a definite length.Hence, when a perpendicular is drawn to the given line,
nothing can be said about the ratio it gets divided into.
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MCQ 881 Mark
A line segment $\overrightarrow{\text{TP}}$is bisected at I. What is the measure of $\overrightarrow{\text{Tl}}$?
  • A
    $\frac{1}{2}\overrightarrow{\text{ IP}}$
  • ✓
    $\overrightarrow{\text{IP}}$
  • C
    $\overrightarrow{\text{TP}}$
  • D
    $\frac{1}{3}\overrightarrow{\text{ TP}}$
Answer
Correct option: B.
$\overrightarrow{\text{IP}}$
$\overrightarrow{\text{TI}}=\frac{1}{2}\overrightarrow{\text{ TP}}=\text{IP}$
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MCQ 891 Mark
When two lines are perpendicular to each other, the angle is said to be _______ angle.
  • A
    acute
  • ✓
    right
  • C
    obtuse
  • D
    equal
Answer
Correct option: B.
right
Two given lines are perpendicular means the angle between them is $90^\circ$, i.e. a right angle.
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MCQ 901 Mark
Which of the following angles is possible to construct using a compass?
  • ✓
    $60^\circ$
  • B
    $32^\circ$
  • C
    $51.25^\circ$
  • D
    $49^\circ$
Answer
Correct option: A.
$60^\circ$
An angle of $60^\circ$ can be constructed using a compass.
Step $1$ : Make a compelete arc on a straight line.
Step $2$ : Make an arc on the previous arc with the same opening of compass from the start point of previous arc.
Step $3$: Draw a line through the centre of arc and point of intersection.
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MCQ 911 Mark
The line segment connecting $(x, 6)$ and $(9, y)$ is bisected by the point $(7, 3)$ Find the values of $x$ and $y$
  • A
    $15, 6$
  • B
    $33, 12$
  • ✓
    $5, 0$
  • D
    $14, 6$
Answer
Correct option: C.
$5, 0$

Since line segment connecting $(x,6)$ and $(9,y)$ is bisected by the point $(7,3)$
Therefore, $\frac{\text{x}+9}{2}=7\Rightarrow\text{x}=5$ and $\frac{6+\text{y}}{2}=3\Rightarrow\text{y}=0$
$\therefore\text{x}=5,\text{y}=0$

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MCQ 921 Mark
Each angle of equilateral triangle is $60^\circ$. The angles are bisected then each angle will be of:
  • A
    $60^\circ$
  • ✓
    $30^\circ$
  • C
    $90^\circ$
  • D
    $120^\circ$
Answer
Correct option: B.
$30^\circ$
Angle bisector divide the angle in two equal parts.
$\therefore$ bisected angle $=\frac{60{^\circ}}{2}=30{^\circ}$ So option $B$ is correct.
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MCQ 931 Mark
Which of the following can be drawn on a piece of paper?
  • A
    A line
  • ✓
    A line segment
  • C
    A ray
  • D
    A plane
Answer
Correct option: B.
A line segment
A line segment can be drawn on a paper.
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MCQ 941 Mark
In Fig. $AB = BC$ and $AD = BD = DC.$
The number of isoscles triangles in the figure is:
  • A
    $1$
  • B
    $2$
  • ✓
    $3$
  • D
    $4$
Answer
Correct option: C.
$3$
A triangle, in which two sides are equal, is known as an isosceles triangle.
Hence, there are $3$ isosceles triangles in the given figure,
i.e. $A ABC, AABD$ and $ABDC. [AB = BC, AD = DB$ and $BD = DC]$
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MCQ 951 Mark
Which of the following is used to draw a line parallel to a given line?
  • A
    A protractor
  • B
    A set square
  • C
    A ruler
  • ✓
    A ruler and compass
Answer
Correct option: D.
A ruler and compass
A ruler and compass
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MCQ 961 Mark
Which of the following can be used to construct a $30o$ angle?
  • ✓
    Construct $60o$ angle using compasses and bisect it.
  • B
    Contact a perpendicular bisector of a line segment.
  • C
    Construct the bisector of any angle.
  • D
    Construct an angle congruent to any given angle.
Answer
Correct option: A.
Construct $60o$ angle using compasses and bisect it.
Construct $60o$ angle using compasses and bisect it.
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MCQ 971 Mark
Number of line segments in Fig is:
  • A
    $5$
  • ✓
    $10$
  • C
    $15$
  • D
    $20$
Answer
Correct option: B.
$10$
A line segment is a part of a line that has finite length and is bounded by two distinct end points.
In the given figure, the line segments are $AS, SC, CD, DE, AC, AD, BD, BE, CE$ and $AE$.
Hence, there are $10$ line segments in the given figure.
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MCQ 981 Mark
Mark $(\checkmark)$ against the correct answer in the following:
An angle measuring $270^\circ $ is:
  • A
    An obtuse angle.
  • B
    An acute angle.
  • C
    A straight line.
  • ✓
    A reflex angle.
Answer
Correct option: D.
A reflex angle.
This is because it is more than $180^\circ $ and less than $360^\circ $.
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MCQ 991 Mark
Mark $(\checkmark)$ against the correct answer in the following:
Which of the following has two end point?
  • ✓
    A line segment.
  • B
    A ray.
  • C
    A line.
  • D
    None os these.
Answer
Correct option: A.
A line segment.
A line segment has two end points and both of them are fixed. Thus, a line segment has a fixed length.
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MCQ 1001 Mark
Two lines are said to be perpendicular to each other when they meet at ____angle.
  • A
    $180^\circ $
  • ✓
    $90^\circ $
  • C
    $60^\circ $
  • D
    $360^\circ $
Answer
Correct option: B.
$90^\circ $
$90^\circ $
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MCQ 1011 Mark
To draw an angle of $150^\circ $ using a pair of compass and ruler _______.
  • ✓
    Bisect angle between $120^\circ $ and $180^\circ $
  • B
    Bisect angle between $60^\circ $ and $120^\circ $
  • C
    Bisect angle between $0^\circ $ and $160^\circ $
  • D
    None of these
Answer
Correct option: A.
Bisect angle between $120^\circ $ and $180^\circ $
Bisect angle between $120^\circ $ and $180^\circ $
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MCQ 1021 Mark
In Fig. ${\text{PQ}}\perp{\text{RQ}}$, $PQ = 5\ cm$ and $QR = 5\ cm$. Then$ \triangle{\text{PQR}}$ is:
  • A
    a right triangle but not isosceles
  • ✓
    an isosceles right triangle
  • C
    isosceles but not a right triangle
  • D
    neither isosceles nor right triangle
Answer
Correct option: B.
an isosceles right triangle
an isosceles right triangle
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MCQ 1031 Mark
A line segment $\overline{\text{PQ}}=8.2\text{cm}$ is bisected at $O$, then length of $\overline{\text{PO}}$ is _______.
  • A
    $4.2\ cm$
  • B
    $4\ cm$
  • ✓
    $4.1\ cm$
  • D
    $16.4\ cm$
Answer
Correct option: C.
$4.1\ cm$

Length of $PO$ $=\big(\frac{8.2}{2}\big)$ $cm = 4.1 \ cm$

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MCQ 1041 Mark
In Fig. $\angle\text{BAC}-90^\circ$ and $\text{AD}\perp\text{BC}.$
The number of right triangles in the figure is:
  • A
    $1$
  • B
    $2$
  • ✓
    $3$
  • D
    $4$
Answer
Correct option: C.
$3$
A triangle, in which one angle is equal to $90^\circ $, is called a right angled triangle. Since, $\angle\text{BAC}=90^\circ$
$ABAC$ is a right angled triangle.
Also, $\angle\text{ADB}=\angle\text{ADC}=90^\circ$ $[AD$ Perpendicular to $BC]$
$A ADB$ and $A ADC$ are also right angled triangles.
Hence, there are $3$ right angled triangles.
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MCQ 1051 Mark
Which among the following is sufficient to construct a triangle?
  • ✓
    The lengths of the three sides
  • B
    The perimeter of the triangle
  • C
    The measures of three angles
  • D
    The names of three vertices.
Answer
Correct option: A.
The lengths of the three sides
The lengths of the three sides
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MCQ 1061 Mark
The second step in the process is:
  • A
    $1$
  • ✓
    $2$
  • C
    $4$
  • D
    $5$
Answer
Correct option: B.
$2$
Correct sequence is: step
$1.$ Draw a ray $BC.$
$2.$ Place the pointed end of the compass on $B$ and draw a semi $-$ circular arc with arbitrary radius and name its intersection with the ray $BC$ as $D$.
$3.$ From $D$ mark a point $E$ on the arc with the same radius.
$4.$ From point $E$, mark a point $F$ on the same arc with same radius.
$5.$ Join $B − F$ and extend it to obtain ray $BA$ So the second step is $2$
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MCQ 1071 Mark
An angle $\angle{\text{XYZ}}=75^\circ $ is bisected by an angular bisector $\overrightarrow{\text{YU}}.$Then what is the measure of $\angle{\text{UYZ}}$?
  • A
    $37^\circ $
  • ✓
    $37.5^\circ $
  • C
    $47.5^\circ $
  • D
    $47^\circ $
Answer
Correct option: B.
$37.5^\circ $
$37.5^\circ $
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MCQ 1081 Mark
A line segment $ \overline{\text{IP}}$is bisected at $T$. Which of the following equals $\overline{\text{IT}}$?
  • ✓
    $\overline{\text{IP}}$
  • B
    $\overline{\text{TP}}$
  • C
    $\overline{\text{TC}}$
  • D
    $\overline{\text{IQ}}$
Answer
Correct option: A.
$\overline{\text{IP}}$
$\overline{\text{TP}}$
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MCQ 1091 Mark
In Fig. if point $A$ is shifted to point $B$ along the ray $PX$ such that $PB = 2PA$, then the measure of $\angle\text{BPY}$ is:
  • A
    Greater than $45^\circ $
  • ✓
    $45^\circ $
  • C
    Less than $45^\circ $
  • D
    $90^\circ $
Answer
Correct option: B.
$45^\circ $
There will be no change in the measure of $\angle\text{BPY}$
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MCQ 1101 Mark
Identify the instruments used to bisect a given line segment.
  • A
    A scale and a protractor
  • ✓
    Scale and compasses
  • C
    Scale and setsquares
  • D
    A scale
Answer
Correct option: B.
Scale and compasses
Scale and compasses
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MCQ 1121 Mark
Identify the one with no definite length.
  • ✓
    $\overleftrightarrow{\text{AB}}$
  • B
    $\overline{\text{PQ}}$
  • C
    $-\text{XYZ}$
  • D
    $\overline{\text{MN}}$
Answer
Correct option: A.
$\overleftrightarrow{\text{AB}}$
$\overleftrightarrow{\text{AB}}$ has no definite length.
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MCQ 1131 Mark
The point $M$ on $\overleftrightarrow{\text{AB}}$ is such that $\overline{\text{AM}}=\overline{\text{MB}}$ Which of the following is a false statement?
  • A
    $M$ is the mid-point of $\overleftrightarrow{\text{AB}}$.
  • B
    $\overline{\text{AM}}=\frac{1}{2}\overline{\text{AB}}$
  • ✓
    $\overline{\text{MB}}=2\overline{\text{AB}}$
  • D
    The point $M$ bisects $AB$.
Answer
Correct option: C.
$\overline{\text{MB}}=2\overline{\text{AB}}$
$M$ is a point on $\overleftrightarrow{\text{AB}}$ such that $\overline{\text{AM}}=\overline{\text{MB}}$ Then $M$ is the midpoint of $\overleftrightarrow{\text{AB}}$, $\overline{\text{AM}}=\frac{1}{2}\overline{\text{AB}}$ and $\overrightarrow{\text{M}}$ bisects $\overleftrightarrow{\text{AB}}$ are true.
Hence the only false statement is $\overline{\text{MB}}=2\overline{\text{AB}}$
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MCQ 1141 Mark
Identify the false statement.
  • A
    A triangle with three equal sides is called an equilateral triangle.
  • B
    A triangle with a right angle is called a right angled triangle.
  • ✓
    A triangle with two equal sides is called a scalene triangle.
  • D
    A right angled triangle has two acute angles and a right angle.
Answer
Correct option: C.
A triangle with two equal sides is called a scalene triangle.
In $[c],$ such a $\triangle\text{le}$ is called isosceles $\triangle\text{le}$
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MCQ 1151 Mark
Number of perpendicular bisectors for a line segment is
  • A
    Three
  • B
    Five
  • ✓
    One
  • D
    Infinite
Answer
Correct option: C.
One
One
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MCQ 1161 Mark
Number of lines passing through five points such that no three of them are collinear is:
  • ✓
    $10$
  • B
    $5$
  • C
    $20$
  • D
    $8$
Answer
Correct option: A.
$10$
Let $A, B, C, D$ and $E$ be five points such that no three of them are $4$ collinear.
Lines passing through these five points are $AB, BC, CD, DE, EA, BA, BD, CE, AC$ and $AD$.

Hence, the number of lines is $10$.
Note: Three or more points are said to be collinear, if they lie on a single straight line.
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MCQ 1171 Mark
In Fig.$ −DXYZ$ cannot be written as:
  • A
    $\angle{\text{Y}}$
  • ✓
    $\angle{\text{ZXY}}$
  • C
    $\angle{\text{ZYX}}$
  • D
    $\angle{\text{XYP}}$
Answer
Correct option: B.
$\angle{\text{ZXY}}$
$\angle{\text{ZXY}}$
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MCQ 1181 Mark
The steps of construction of an $\angle\text{AOB}=45^\circ$ is given in jumbled order below:
$1.$ Place compass on intersection point.
$2.$ Place ruler on start point and where arc intersects perpendicular line.
$3.$ Adjust compass width to reach start point.
$4.$ Construct a perpendicular line.
$5.$ Draw $45$ degree line.
$6.$ Draw an arc that intersects perpendicular line.
$7.$ The third step in process is:
  • A
    $2$
  • B
    $3$
  • ✓
    $4$
  • D
    $5$
Answer
Correct option: C.
$4$
Correct sequence is:
$1.$ Construct a perpendicular line.
$2.$ Draw an arc that intersect the perpendicular line.
$3.$ Adjust the compass width to reach the start point.
$4.$ Place compass on intersection point.
$5.$ Place ruler on start point and where the arc intersects the perpendicular line.
$6.$ Draw $45$ degree line.
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MCQ 1191 Mark
In which of the following cases can a triangle be constructed?
  • A
    Measures of three sides are given.
  • B
    Measures of two sides and an included angle are given.
  • C
    Measures of two angles and the side between them are given.
  • ✓
    All the above.
Answer
Correct option: D.
All the above.
All the above.
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MCQ 1201 Mark
If a bicycle wheel has $48$ spokes, then the angle between a pair of two consecutive spokes is:
  • A
    $\Big(5\frac{1}{2}\Big)$
  • ✓
    $\Big(7\frac{1}{2}\Big)$
  • C
    $\Big(\frac{2}{11}\Big)$
  • D
    $\Big(\frac{2}{15}\Big)$
Answer
Correct option: B.
$\Big(7\frac{1}{2}\Big)$
Given, number of spokes$ = 48$ A complete angle $= 360^\circ .$
Angle between a pair of two consecutive spokes = Complete angle,
Number of spokes $48.2$
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MCQ 1211 Mark
Which of the following best describes the given triangle.
  • A
    Isosceles acute triangle
  • B
    Isosceles right triangle
  • C
    Equilateral obtuse triangle
  • ✓
    Isosceles obtuse triangle
Answer
Correct option: D.
Isosceles obtuse triangle
Isosceles obtuse triangle.
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MCQ 1221 Mark
Identify the uses of a ruler.
  • A
    To draw a line segment of a given length
  • B
    To draw a copy of a given segment.
  • C
    To draw a diameter of a circle.
  • ✓
    All the above.
Answer
Correct option: D.
All the above.

A ruler is used to draw a line segment of a given length, to draw the copy of a given segment, and to draw a diameter of a circle.
Thus, all the given options are correct.

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MCQ 1231 Mark
In order to duplicate agiven angle, which of the following instruments can be used?
  • ✓
    Compass
  • B
    Set Square
  • C
    Protractor
  • D
    Divider
Answer
Correct option: A.
Compass

A Compass can be used to make the duplicate of any angle. A protractor can also be used
to duplicate angles but only of integral values.So option A is correct.

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MCQ 1241 Mark
$\overrightarrow{\text{XY}}$ bisects $\angle{\text{AXB}}.$ If $\angle{\text{YXB}}=37.5,$ what is the measure of $\angle{\text{AXB}}$?
  • A
    $37.5^\circ $
  • B
    $74^\circ $
  • C
    $64^\circ $
  • ✓
    $75^\circ $
Answer
Correct option: D.
$75^\circ $
$75^\circ $
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MCQ 1251 Mark
If sum of two angles of a triangle is $60^\circ.$ Then, the measure of third angle of a triangle is:
  • A
    $60^\circ$
  • B
    $90^\circ$
  • ✓
    $120^\circ$
  • D
    $180^\circ$
Answer
Correct option: C.
$120^\circ$
Let the angles be $x, y$ and $z$ Sum of two angles $= x + y$
Given $x + y = 60^\circ$
Using angle sum property $x + y + z = 180^\circ 60^\circ + z = 180 z = 120^\circ$
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MCQ 1261 Mark
Angles to be bisected to obtain an angle of $90^\circ $ are:
  • A
    $60^\circ $
  • ✓
    $60^\circ $ and $120^\circ $
  • C
    $120^\circ $ and $180^\circ $
  • D
    $0^\circ $ and $60^\circ $
Answer
Correct option: B.
$60^\circ $ and $120^\circ $
Angles to be bisected to obtain an angle of $90^\circ$ are $60^\circ$ and $120^\circ $ as it exactly lies between
these two angles. $\frac{60^\circ + 120^\circ}{2}$
$= 90^\circ $ Hence, option $B$.
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MCQ 1271 Mark
If two lines have only one point in common, what are they called?
  • A
    Parallel lines
  • ✓
    Intersecting lines
  • C
    Perpendicular lines
  • D
    Transversal
Answer
Correct option: B.
Intersecting lines
Intersecting lines have only one point in common.
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MCQ 1281 Mark
Arrange the given steps in $CORRECT$ order of constructing a perpendicular using ruler and compases. Steps of construction:
$1.$ With $A$ and $B$ as centres and a radius greater than $AP$ construct two arcs, which cut each other at $Q$.
$2.$ Join $PQ$. Then $\overline{\text{PQ}}$ is perpendicular to $l$. We write $0$ $\overline{\text{PQ}}\perp\text{l}$
$3.$ With $P$ as centre and a convenient radius, construct an arc intersecting the line l at two points $A$ and $B$.
$4.$ Given a point $P$ on a line $l$
  • ✓
    $4 - 3 - 1 - 2$
  • B
    $3 - 4 - 2 - 1$
  • C
    $4 - 1 - 3 - 2$
  • D
    $1 - 2 - 3 - 4$
Answer
Correct option: A.
$4 - 3 - 1 - 2$
$4 - 3 - 1 - 2$
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MCQ 1301 Mark
In Fig. $\text{PQ}\perp\text{RQ},\text{PQ}=5\text{cm}$ and $\text{QR}=5\text{cm}.$ Then $\triangle\text{PQR}$ is:
  • A
    A right triangle but not isosceles.
  • ✓
    An isosceles right triangle.
  • C
    Isosceles but not a right triangle.
  • D
    Neither isosceles nor right triangle.
Answer
Correct option: B.
An isosceles right triangle.
Since, $PQ$ Perpendicular to $RQ$,
So, $\triangle\text{PQR}=90^\circ$
$\therefore\triangle\text{PQR}$ is right angled triangle.
Also, in $\triangle\text{PQR},$
$\text{PQ}=\text{QR}$
$\triangle\text{PQR}$ is an isosceles triangle.
Hence, $\triangle\text{PQR}$ is an isosceles right angled triangle.
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MCQ 1311 Mark
In Fig. $AB = BC$ and $AD = BD = DC$. The number of isosceles triangles in the figure is:
  • A
    $1$
  • B
    $2$
  • ✓
    $3$
  • D
    $4$
Answer
Correct option: C.
$3$
$3$
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MCQ 1331 Mark
Anitha's maths book has the figure given. Which instrument $(s)$ did she use to draw the figure?
  • ✓
    The compasses and a ruler
  • B
    Only compasses
  • C
    Only ruler
  • D
    Cannot be said.
Answer
Correct option: A.
The compasses and a ruler
The compasses and a ruler
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MCQ 1341 Mark
$ABC$ is a triangle. The bisectors of theinternal angle $\angle B$ and external angle $\angle C$ intersect at $D$. if $\angle BDC = 60^\circ$ then $\angle A$ is
  • A
    $120^\circ$
  • B
    $180^\circ$
  • ✓
    $60^\circ$
  • D
    $150^\circ$
Answer
Correct option: C.
$60^\circ$
Consider $△ABC$ Let $BC$ be extended to $E$ Since Angular bisectors Meet at $D \angle ABD = \angle DBC ⋯ (1)$
$\angle ACD =\angle DCE ⋯ (2)$
Consider $△DBC$ By External sum property $\angle DCE = \angle BDC + \angle DBC $
$⟹ 2 \angle DCE = 2(60^\circ ) + 2 \angle DBC $
$⟹ \angle ACE = 120^\circ +\angle ABC $
By external sum property of
$△ABC \angle ACE = \angle BAC + \angle ABC$
$⟹ \angle A = 60^\circ$
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MCQ 1351 Mark
Draw perpendicular to the line of length $99\ cm$ so that the perpendicular divides the line in the ratio $1:21:2$. Then length of the line on the left will be:
  • ✓
    $3 \ cm$
  • B
    $4 \ cm$
  • C
    $5 \ cm$
  • D
    $6 \ cm$
Answer
Correct option: A.
$3 \ cm$
Draw a line say $B$ of length $9 \ cm$ using a ruleNow we have to divide the line in $1:2.$
Let the length of left part be $x$ then length of right part is$2\text{x}\Rightarrow{\text{x + 2x =9}}\Rightarrow{\text{3x = 9}}\Rightarrow{\text{x = }}\frac{9}{3}=3$$cm$
So, the lenght of left part is $3 \ cm$ So, option $A$ is correct.
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MCQ 1361 Mark
$\overrightarrow{\text{QZ}}$ is the bisector of $\angle{\text{PQZ}}=\angle{\text{PQR}}$ Which of the following is true?
  • A
    $\angle{\text{PQZ}}=\angle{\text{PQR}}$
  • B
    $\angle{\text{PQZ}}=\angle{\text{ZQR}}$
  • C
    $\angle{\text{PQZ}}=\frac{1}{2}\angle{\text{ZQR}}$
  • ✓
    $\text{Both [b] and [c]}  $
Answer
Correct option: D.
$\text{Both [b] and [c]}  $
$\overrightarrow{\text{QZ}}$ bisects $\angle{\text{PQZ}}$ (Given) )

Thus. $\angle{\text{PQZ}}=\angle{\text{ZQR}}=\frac{1}{2}\angle{\text{PQR}}$
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MCQ 1371 Mark
The number of triangles in Fig. is:
  • A
    $10$
  • B
    $12$
  • ✓
    $13$
  • D
    $14$
Answer
Correct option: C.
$13$

By observing the figure, we can say that, number of triangles is $13$.

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MCQ 1381 Mark
The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along $XY$ so the other short side touches Point $P$.
$2.$ Use the edge of the set square to draw a line through Point $P$.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line $XY$.
Which of the following will be the fourth step:
 
  • A
    $1$
  • ✓
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: B.
$2$
 
$1.$ Draw a line $XY$ and mark a point $P$ on it.
$2.$ Place one short side of the set square on the line $XY$.
$3.$ Move the set square along $XY$ so the other short side touches point $P.$
$4.$ Use the edge of the set square to draw a line through point $P.$
So $2$. is the fourth step.Option $B$ is correct.
 
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MCQ 1391 Mark
Which of the following is an angle that can be constructed using compasses and a ruler?
  • A
    $20^\circ $
  • B
    $80^\circ $
  • ✓
    $60^\circ $
  • D
    $110^\circ $
Answer
Correct option: C.
$60^\circ $
$60^\circ $
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MCQ 1401 Mark
Which of the following can be drawn on a piece of paper?
  • A
    A line
  • ✓
    A line segment
  • C
    A ray
  • D
    A plane
Answer
Correct option: B.
A line segment
A line segment can be drawn on a paper.
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MCQ 1411 Mark
To construct a perpendicular to a line $(L)$ from a point $(P)$ outside the line, steps are given in jumbled form. Identify the second step from the following.
$1.$ Draw line $PQ.$
$2.$ Draw a line $L$ and consider point $P$ outside the line.
$3.$ Take $P$ as a center, draw $2$ arcs on line L and name it as points $A$ and $B$ respectively.
$4.$ Taking $A$ and $B$ as a center one by one and keeping the same distance in compass,
draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.
  • A
    $4$
  • ✓
    $3$
  • C
    $2$
  • D
    $1$
Answer
Correct option: B.
$3$
 
The correct sequence is:
$a.\ $Draw a line $L$ and consider a point $P$ outside the line.
$b.\ $Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
$c.\ $Taking $A$ and $B$ as centres one by one and keeping the same distance in compass, draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$.
$d.\ $Draw line $PQ$ So the second
Option $B$ is correct.
 
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MCQ 1421 Mark
A perpendicular is drawn to a line segment $\overline{\text{NM}}$ at $N$ using a protractor and a point $P$ is marked on it. Which of the following is true?
  • A
    $\overline{\text{MP}}\perp\overline{\text{NP}}$
  • B
    $\overline{\text{MN}}\perp\overline{\text{MP}}$
  • C
    ${\text{M}\perp{P}}$
  • ✓
    $\overline{\text{NM}}\perp\overline{\text{NP}}$
Answer
Correct option: D.
$\overline{\text{NM}}\perp\overline{\text{NP}}$
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MCQ 1441 Mark
Which type of triangle is in the classification based on angles only?
  • A
    An equilateral triangle
  • B
    A scalene triangle
  • ✓
    A right angled triangle
  • D
    An isosceles triangle
Answer
Correct option: C.
A right angled triangle
A right angled triangle
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MCQ 1451 Mark
The number of obtuse angles in Fig. is:
  • A
    $2$
  • B
    $3$
  • ✓
    $4$
  • D
    $5$
Answer
Correct option: C.
$4$
There are $4$ obtuse angles.
$1.\ 30^\circ + 65^\circ = 95^\circ $
$2.\ 30^\circ + 65^\circ + 45^\circ = 140^\circ $
$3.\ 65^\circ + 45^\circ = 110^\circ $
$4.\ 65^\circ + 45^\circ + 40^\circ = 150^\circ [$van obtuse angle is more than $90^\circ $ but less than $180^\circ ]$
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MCQ 1461 Mark
The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along $XY$ so the other short side touches Point $P$
$2.$ Use the edge of the set square to draw a line through Point $P$.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line $XY$.
Which of the following will be the second step:
  • A
    $1$
  • B
    $2$
  • ✓
    $3$
  • D
    $4$
Answer
Correct option: C.
$3$
Draw a line $XY$ and mark a point $P$ on it.
Place one short side of the set square on the line $XY.$
Move the set square along $XY$ so the other short side touches point $P$.
Use the edge of the set square to draw a line through point $P$.
So $3$. is the first step.Option $C$ is correct.
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MCQ 1471 Mark
If a quadrilateral with two pairs of adjacent sides equal but opposite sides are not equal then it is called.
  • A
    parallelogram
  • ✓
    square
  • C
    rectangle
  • D
    kite
Answer
Correct option: B.
square
square
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MCQ 1481 Mark
Identify the instruments used to bisect a given line segment.
  • A
    A scale and a protractor
  • ✓
    Scale and compasses
  • C
    Scale and setsquares
  • D
    A scale
Answer
Correct option: B.
Scale and compasses
Scale and compasses
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MCQ 1491 Mark
An angle of $15^\circ $ is drawn using a pair of compasses and a ruler. How is it done?
  • A
    Bisecting $60^\circ $ angle.
  • B
    Bisecting $60^\circ $ and $120^\circ $ angles.
  • ✓
    Bisecting $60^\circ $ and then bisecting it again.
  • D
    Bisecting a $60^\circ $ and $180^\circ $ angles.
Answer
Correct option: C.
Bisecting $60^\circ $ and then bisecting it again.
Bisecting $60^\circ $ and then bisecting it again.
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MCQ 1501 Mark
How do you draw a $90^\circ $ angle?
  • ✓
    By drawing a perpendicular to a line from a point lying on it.
  • B
    By bisecting a $120^\circ $ angle.
  • C
    By bisecting a $60^\circ $ angle.
  • D
    By drawing multiples of $45^\circ $ angle.
Answer
Correct option: A.
By drawing a perpendicular to a line from a point lying on it.
By drawing a perpendicular to a line from a point lying on it.
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MCQ 1511 Mark
A line segment $IP$¯¯¯¯¯¯ is bisected at $T$. Which of the following equals $IT$¯¯¯¯¯¯?
  • A
    $IP$¯¯¯¯¯¯
  • ✓
     $TP$¯¯¯¯¯¯¯
  • C
     $TC$¯¯¯¯¯¯¯
  • D
     $IQ$¯¯¯¯¯¯¯
Answer
Correct option: B.
 $TP$¯¯¯¯¯¯¯
 $TP$¯¯¯¯¯¯¯
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MCQ 1521 Mark
Two lines are said to be perpendicular to each other when they meet at ____angle.
  • A
    $180^\circ $
  • ✓
    $90^\circ $
  • C
    $60^\circ $
  • D
    $360^\circ $
Answer
Correct option: B.
$90^\circ $
$90^\circ $
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MCQ 1531 Mark
If two lines have only one point in common, what are they called?
  • A
    Parallel lines
  • ✓
    Intersecting lines
  • C
    Perpendicular lines
  • D
    Transversal
Answer
Correct option: B.
Intersecting lines
Intersecting lines
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MCQ 1541 Mark
Identify the one with no definite length.
  • ✓
     $AB\leftarrow\rightarrow $
  • B
    $PQ$¯¯¯¯¯¯¯¯
  • C
    $-XYZ$
  • D
     $MN$¯¯¯¯¯¯¯¯¯¯
Answer
Correct option: A.
 $AB\leftarrow\rightarrow $
$AB\leftarrow\rightarrow $
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MCQ 1551 Mark
Identify the pair of parallel lines.
  • A
    $(i)$ and $(ii)$ only
  • ✓
    $(ii)$ only
  • C
    $(ii)$ and $(iii)$ only
  • D
    $(i), (ii)$ and $(iii)$
Answer
Correct option: B.
$(ii)$ only
$(ii)$ only
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MCQ 1561 Mark
$QZ−\rightarrow −$ is the bisector of $\angle PQZ = \angle PQR$. Which of the following is true?
  • A
    $\angle PQZ = \angle PQR$
  • B
    $\angle PQZ = \angle ZQR$
  • C
    $\angle PQZ = 12 \angle ZQR$
  • ✓
    Both $[b]$ and $[c]$
Answer
Correct option: D.
Both $[b]$ and $[c]$
Both $[b]$ and $[c]$
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MCQ 1571 Mark
Lines $a, b, p, q, m, n$ and $x$ have a point $P$ common to all of them. What is the name of $P$?
  • ✓
    Point of concurrence
  • B
    Point of intersection
  • C
    Common point
  • D
    Distinct point
Answer
Correct option: A.
Point of concurrence
Point of concurrence
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MCQ 1581 Mark
$X$ and $Y$ are two distinct points in a plane. How many lines can be drawn passing through both $X$ and $Y$?
  • A
    $0$
  • ✓
    $1$
  • C
    Only $2$
  • D
    Infinitely many
Answer
Correct option: B.
$1$
$1$
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MCQ 1591 Mark
$XY−\rightarrow −$ bisects $\angle AXB$. If $\angle YXB = 37.5^\circ$, what is the measure of $\angle AXB?$
  • A
    $37.5^\circ$
  • B
    $74^\circ $
  • C
    $64^\circ $
  • ✓
    $75^\circ $
Answer
Correct option: D.
$75^\circ $
$75^\circ $
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MCQ 1601 Mark
$P$ is the midpoint of $AB$¯¯¯¯¯¯¯¯. $M$ and $N$ are midpoints of $AP$¯¯¯¯¯¯¯¯ respectively. What is the measure of $MN$¯¯¯¯¯¯¯¯¯¯?
  • A
     $13$ $AB$¯¯¯¯¯¯¯¯
  • ✓
    $12$ $AB$¯¯¯¯¯¯¯¯
  • C
     $12$ $AP$¯¯¯¯¯¯¯¯
  • D
    $32$ $AB$¯¯¯¯¯¯¯¯
Answer
Correct option: B.
$12$ $AB$¯¯¯¯¯¯¯¯
$12$ $AB$¯¯¯¯¯¯¯¯
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MCQ 1611 Mark
Identify the uses of a ruler.
  • A
    To draw a line segment of a given length
  • B
    To draw a copy of a given segment.
  • C
    To draw a diameter of a circle.
  • ✓
    All the above.
Answer
Correct option: D.
All the above.
All the above.
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MCQ 1621 Mark
$MN−\rightarrow −$ is the perpendicular bisector of $AB\leftarrow\rightarrow $. Which of the given statements is correct?
  • A
    $(i)$ and $(iii)$ only
  • B
    $(ii)$ and $(iv)$ only
  • ✓
    $(i)$ and $(ii)$ only
  • D
    $(ii)$ and $(iii)$ only
Answer
Correct option: C.
$(i)$ and $(ii)$ only
$(i)$ and $(ii)$ only
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MCQ 1631 Mark
$XY−\rightarrow −$ divides $\angle MXN = 72^\circ $ in the ratio $1 : 2$. What is the measure of $\angle YXN$?
  • ✓
    $48^\circ $
  • B
    $24^\circ $
  • C
    $72^\circ $
  • D
    $96^\circ $
Answer
Correct option: A.
$48^\circ $
$48^\circ $
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MCQ 1641 Mark
At $7\ a.m.$ the angle between the Sun’s ray and the ground at a point is $43^\circ $. What would be the angle at $10\ a.m.$?
  • A
    $40^\circ $
  • B
    $90^\circ $
  • ✓
    Between $43^\circ $ and $90^\circ $
  • D
    Greater than $90^\circ $
Answer
Correct option: C.
Between $43^\circ $ and $90^\circ $
Between $43^\circ $ and $90^\circ $
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MCQ 1651 Mark
$l\ ||\ m$. $P$ and $Q$ are points on land m respectively such that $PQ ⊥ lR$ is a point on $a$ line $n$ in the same plane such that $PQ$¯¯¯¯¯¯¯¯ $= QR$¯¯¯¯¯¯¯¯. Which of the following is true?
  • A
    $l\ ||\ n$
  • B
    $m\ ||\ n$
  • ✓
    Both $[a]$ and $[b]$
  • D
    Neither $[a]$ nor $[b]$
Answer
Correct option: C.
Both $[a]$ and $[b]$
Both $[a]$ and $[b]$
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MCQ 1661 Mark
Which of the following can be drawn on a piece of paper?
  • A
    A line
  • ✓
    A line segment
  • C
    A ray
  • D
    A plane
Answer
Correct option: B.
A line segment
A line segment
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MCQ 1671 Mark
A line segment $TP−\rightarrow −$ is bisected at I. What is the measure of $TI−\rightarrow $?
  • A
     $12TP−\rightarrow −$
  • ✓
    $IP−\rightarrow $
  • C
     $TP−\rightarrow −$
  • D
    $ 13 TP−\rightarrow −$
Answer
Correct option: B.
$IP−\rightarrow $
$IP−\rightarrow $
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