The boundaries of the solids are:
- ACurves.
- BPoints.
- ✓Surfaces.
- DLines.
Answer: C.
View full solution →Question types
Introduction to Euclid Geometry question types
242 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
242
Questions
6
Question groups
5
Question types
01
M.C.Q
188 Q→02Assertion (A) & Reason (B) MCQ
26 Q→03True False[1 Marks ]
5 Q→04Fill In The Blanks[1 Marks ]
4 Q→051 Marks Question
15 Q→06Case study (4 Marks)
4 Q→Sample Questions
Introduction to Euclid Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The basic facts which are taken for granted, without proof, are called:
- ATheorems.
- BPropositions.
- CLemmas.
- ✓Axioms.
Answer: D.
View full solution →A point has:
- AOne part
- BTwo parts
- CMore than two parts
- ✓No parts
Answer: D.
View full solution →The number of end points a ray has:
- A$0$
- B$2$
- ✓$1$
- DNone of these
Answer: C.
View full solution →Write the correct answer in the following:
It is known that if $x + y = 10$ then $x + y + z = 10 + z$. The Euclid’s axiom that illustrates this statement is:
It is known that if $x + y = 10$ then $x + y + z = 10 + z$. The Euclid’s axiom that illustrates this statement is:
- AFirst Axiom.
- ✓Second Axiom.
- CThird Axiom.
- DFourth Axiom.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: According to Euclid’s $1$st axiom- “Things which are equal to the same thing are also equal to one another”.
Reason: If $AB = PQ$ and $PQ = XY$, then $AB = XY$.
Assertion: According to Euclid’s $1$st axiom- “Things which are equal to the same thing are also equal to one another”.
Reason: If $AB = PQ$ and $PQ = XY$, then $AB = XY$.
- ✓Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A Greek mathematician, thales is credited with giving the first known proof.
Reason: The first known proof that ‘the rectangle is bisected by its diameter was given by Pythagoras.
Assertion: A Greek mathematician, thales is credited with giving the first known proof.
Reason: The first known proof that ‘the rectangle is bisected by its diameter was given by Pythagoras.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If a point $C$ be the mid$-$point of a line line segment $AB$, then the relation among $AC, BC$ and $AB$
is $\text{AC}=\text{CB}=\big(\frac{1}{2}\big)\text{AB}.$
Reason: If a point $P$ be the mid$-$point of $MN$ and $C$ is the mid$-$point of $MP$, then the relation between $MC$ and $MN$
is $\text{MC}=\big(\frac{1}{4}\big)\text{MN}.$
Assertion: If a point $C$ be the mid$-$point of a line line segment $AB$, then the relation among $AC, BC$ and $AB$
is $\text{AC}=\text{CB}=\big(\frac{1}{2}\big)\text{AB}.$Reason: If a point $P$ be the mid$-$point of $MN$ and $C$ is the mid$-$point of $MP$, then the relation between $MC$ and $MN$
is $\text{MC}=\big(\frac{1}{4}\big)\text{MN}.$
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: There can be infinite number of lines that can be drawn through a single point.
Reason: From this point we can draw only two lines.
Assertion: There can be infinite number of lines that can be drawn through a single point.
Reason: From this point we can draw only two lines.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Euclid’s fifth postulate does imply the existence of the parallel lines.
Reason: If the sum of the interior angles is equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.
Assertion: Euclid’s fifth postulate does imply the existence of the parallel lines.
Reason: If the sum of the interior angles is equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →In Fig., if $AB = PQ$ and $PQ = XY,$ then $AB = XY.$
View full solution →If two circles are equal, then their radii are equal.
A terminated line can be produced indefinitely on both the sides.
There are infinitely many number of lines which passes through the two distinct points.
Only one line can pass through a single point.
A line separates a plane into ______ parts namely the ______ and the _____ itself.
Given a line and a point, not on the line, there is one and only______ line which passes through the given point and is______ to the given line.
Two distinct _______ in a plane cannot have more than one point in common.
Two distinct points in a plane determine a _______ line.
Why is Axiom $5,$ in the list of Euclid's axioms, considered a 'universal truth'$?$
View full solution →In fig., if $AC = BD,$ then prove that $AB = CD$
View full solution →Point $C$ is called a mid point of line segment $AB,$ prove that every line segment has one and only one mid-point.
View full solution →If a point $'C'$ lies between two points $A$ and $B$ such that $AC = BC,$ then prove that $AC =\frac{1}{2}AB$. Explain by drawing the figure.
View full solution →There exist at least three points that are not on the same line. Does the postulate contain any undefined term? Is this postulate consistent? Does this follow from Euclid’s postulates? Explain.
Raghvan claims that the magnitude of the angle $ABC$ is greater than the magnitude of the area of the right triangle $PQR.$
$7.$ Is his claim correct$?$ Why$?$
$8.$ Two lines intersect at a point $P.$
Which of the following is true for the distance between the two lines as they travel beyond point $P?$
$A.$ The distance becomes constant.
$B.$ The distance increases continuously.
$C.$ The distance decreases continuously.
$D.$ The distance increases and decreases depending upon the intersection point.
$9. $ Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true$?$
$A.$ The measure of an angle depends upon its orientation.
$B.$ The measure of an angle depends upon the instrument used to measure it.
$C.$ The measure of an angle depends on the length of its angle arms.
$D.$ The measure of an angle depends upon the rotation of one arm on another.
$10.$ TAB is a straight line. $C$ is the mid-point of $AB. D$ is the mid-point of $AC.$
Which of the following shows the relation between the line segments?
$A. AD =\frac{1}{2} AB$
$B. AD =\frac{1}{2} CB$
$C. AD =2 AC$
$D. AD =2 DC$
View full solution →$7.$ Is his claim correct$?$ Why$?$
$8.$ Two lines intersect at a point $P.$
Which of the following is true for the distance between the two lines as they travel beyond point $P?$
$A.$ The distance becomes constant.
$B.$ The distance increases continuously.
$C.$ The distance decreases continuously.
$D.$ The distance increases and decreases depending upon the intersection point.
$9. $ Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true$?$
$A.$ The measure of an angle depends upon its orientation.
$B.$ The measure of an angle depends upon the instrument used to measure it.
$C.$ The measure of an angle depends on the length of its angle arms.
$D.$ The measure of an angle depends upon the rotation of one arm on another.
$10.$ TAB is a straight line. $C$ is the mid-point of $AB. D$ is the mid-point of $AC.$
Which of the following shows the relation between the line segments?
$A. AD =\frac{1}{2} AB$
$B. AD =\frac{1}{2} CB$
$C. AD =2 AC$
$D. AD =2 DC$
The map shows three cities Conlen $©,$ Stratford $(S),$ and Texhoma $(T)$ on a straight highway.
$4.$ Which of the following is true for the length of the highway between them$?$
$A.$ The length of the highway between $C$ and $S$ is equal to the length of the highway between $S$ and $T.$
$B.$ The length of the highway between $C$ and $S$ is three-fourth of the length of the highway between $S$ and $T.$
$C.$ The length of the highway between $S$ and $T$ is the sum of the lengths of the highway between $CT$ and $CS.$
$D.$ The length of the highway between $C$ and $T$ is the sum of the lengths of the highway between $CS$ and $ST.$
$5.$ A number $Y$ is greater than a number $X$ and another number $Z < 0.$
Which of the following relations can be true for a unique value of $Z?$
$A. X × Z = Y × Z$
$B. X ÷ Z = Y ÷ Z$
$C. X – Z = Y$
$D. X + Z = Y$
$6.$ The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?
View full solution →$4.$ Which of the following is true for the length of the highway between them$?$
$A.$ The length of the highway between $C$ and $S$ is equal to the length of the highway between $S$ and $T.$
$B.$ The length of the highway between $C$ and $S$ is three-fourth of the length of the highway between $S$ and $T.$
$C.$ The length of the highway between $S$ and $T$ is the sum of the lengths of the highway between $CT$ and $CS.$
$D.$ The length of the highway between $C$ and $T$ is the sum of the lengths of the highway between $CS$ and $ST.$
$5.$ A number $Y$ is greater than a number $X$ and another number $Z < 0.$
Which of the following relations can be true for a unique value of $Z?$
$A. X × Z = Y × Z$
$B. X ÷ Z = Y ÷ Z$
$C. X – Z = Y$
$D. X + Z = Y$
$6.$ The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?
Karan marks his city on the map as point $A.$
$2.$ Savita says, ‘$A$ dot is dimensionless, so your city is also dimensionless.’ Why is Savita wrong? Justify your answer.
$3.$ Which of the following is not true$?$
$A.$ A line has one dimension.
$B. A$ plane has two dimensions.
$C$. A circle can be drawn with any radius and at any point.
$D.$ Two distinct lines can pass through a point in the same direction.
View full solution →$2.$ Savita says, ‘$A$ dot is dimensionless, so your city is also dimensionless.’ Why is Savita wrong? Justify your answer.
$3.$ Which of the following is not true$?$
$A.$ A line has one dimension.
$B. A$ plane has two dimensions.
$C$. A circle can be drawn with any radius and at any point.
$D.$ Two distinct lines can pass through a point in the same direction.
$1.$ Highways $20A$ and $56C$ run parallel to each other for $20 km$ in a state.
Which of the following statements is most likely to be true regarding them$?$
$A.$ Both highways are of the same length.
$B.$ There can be no link road between them.
$C.$ The highways make an angle $90^\circ $ with each other.
$D.$ The distance between the two highways remains almost the same in the state.
View full solution →Which of the following statements is most likely to be true regarding them$?$
$A.$ Both highways are of the same length.
$B.$ There can be no link road between them.
$C.$ The highways make an angle $90^\circ $ with each other.
$D.$ The distance between the two highways remains almost the same in the state.
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