M.C.Q (1 Marks)

MCQ 11 Mark

Choose the correct answer from the given four options.
To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that $\angle\text{BAX}$ is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:

A
8
B
10
C
11
✓
12

Answer

Correct option: D.

We know that, to divide a line segment AB in the ratio m : n, first draw a ray AX which makes an acute angle $\angle\text{BAX}$, then marked m + n points at equal distance.Here,
m = 5, n = 7
So, minimum number of these points = m + n = 5 + 7 = 12.

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MCQ 21 Mark

Choose the correct answer from the given four options.
To construct a triangle similar to a given $\triangle\text{ABC}$ with its sides $\frac{8}{5}$ of the corresponding sides of $\triangle\text{ABC}$ draw a ray BX such that $\angle\text{CBX}$ is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is:

A
5
✓
8
C
13
D
3

Answer

Correct option: B.

To construct a triangle similar to a given triangle, with its sides $\frac{\text{m}}{\text{n}}$ of the corresponding sides of given triangle the minimum number of points to be located at equal distance is equal to the greater of m and n is $\frac{8}{5}$
Hence,
$\frac{\text{m}}{\text{n}}=\frac{8}{5}$
So, the minimum number of point to be located at equal distance on ray BX is 8.

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MCQ 31 Mark

Choose the correct answer from the given four options.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$. first draw a ray BX such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $B C$. Then locate points $B_1, B_2, B_3, \ldots$ on $B X$ at equal distances and next step is to join:

A
$B _{10}$ to $C$
B
$B _3$ to $C$
✓
$B _7$ to $C$
D
$B _4$ to $C$

Answer

Correct option: C.

$B _7$ to $C$

Here, we locate points $B_1, B_2, B_3, B_4, B_5, B_6$ and $B_7$ on $B X$ at equal distance and in next step join the last points is $B_7$ to $C.$

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MCQ 41 Mark

Choose the correct answer from the given four options.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be:

A
135°
B
90°
C
60°
✓
120°

Answer

Correct option: D.

120°

The angle between them should be 120° because in that case the figure formed by the intersection point of pair of tangent, the two end points of those-two radii tangents are drawn and the centre of the circle is a quadrilateral.
From figure it is quadrilateral,
$\angle\text{POQ}+\angle\text{PRQ}=180^\circ$ $[\therefore$ sum of opposite angles are 180°$]$
$60^\circ+\theta=180^\circ$
$\theta=120$
Hence, the required angle between them is 120°.

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MCQ 51 Mark

Choose the correct answer from the given four options.
To divide a line segment $A B$ in the ratio $5: 6$, draw a ray $A X$ such that $\angle B A X$ is an acute angle, then draw a ray $B Y$ parallel to $A X$ and the points $A_1, A_2, A_3, \ldots$ and $B_1, B_2, B_3, \ldots$ are located at equal distances on ray $A X$ and $B Y$, respectively. Then the points joined are:

✓
$A _5$ and $B _6$
B
$A _6$ and $B _5$
C
$A _4$ and $B _5$
D
$A _5$ and $B _4$

Answer

Correct option: A.

$A _5$ and $B _6$

Given a line segment $AB$ and we have to divide it in the ratio $5 : 6.$

Steps of construction:
$1.$ Draw a ray $AX$ making an acute $\angle BAX$.
$2.$ Draw a ray $BY$ parallel to $AX$ by making $\angle ABY$ equal to $\angle BAX$.
$3.$ Now, locate the points $A_1, A_2, A_3, A_4$ and $A_5(m=5)$ on $A X$ and $B_1, B_2, B_3, B_4, B_5$ and $B_6(n=6)$
such that all the points are at equal distance from each other.
$4.$ Join $B_6 A_5$. Let it intersect $A B$ at a point $C$.
Then, $A C: B C=5: 6$

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MCQ 61 Mark

Choose the correct answer from the given four options.
To divide a line segment $A B$ in the ratio $4: 7$, a ray $A X$ is drawn first such that $\angle B A X$ is an acute angle and then points $A_1, A_2, A_3, \ldots$. are located at equal distances on the ray $A X$ and the point $B$ is joined to:

A
$A _{12}$
✓
$A _{11}$
C
$A _{10}$
D
$Ag _9$

Answer

Correct option: B.

$A _{11}$

Here, minimum $4 + 7 = 11$ points are located at equal distances on the ray $AX$, and then $B$ is joined to last point is $A_{11}$.

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Maths M.C.Q (1 Marks)

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