Chapter 10 · Constructions

NCERT Exemplar Class 10 Maths Exercise 10.1

All 6 questions of NCERT Exemplar Class 10 Maths Exercise 10.1 (Constructions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   To ​divide a line ​segment $AB$ in the ​ratio $5:7$, ​first a ray $AX$ is drawn so that $\angle BAX$ 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

   1. (a)8
   2. (b)10
   3. (c)11
   4. (d)12
   Show answer

   (d) 12

   Step-by-step solution →
2. Q2
   To divide a line segment $AB$ in the ​ratio $4:7$, a ray $AX$ is ​drawn first such that $\angle BAX$ ​is an acute ​angle and ​then points $A_1,A_2,A_3,\dots$ are located at ​equal distances ​on the ray $AX$ and ​the point $B$ is joined to

   1. (a)$A_{12}$
   2. (b)$A_{11}$
   3. (c)$A_{10}$
   4. (d)$A_9$
   Show answer

   (b) $A_{11}$

   Step-by-step solution →
3. Q3
   To divide a line ​segment ​AB in the ratio 5:6, draw ​a ray AX such ​that $\angle BAX$ ​is an ​acute angle, then draw a ray BY parallel ​to AX and the points $A_1,A_2,A_3,\dots$ and $B_1,B_2,B_3,\dots$ are located at equal distances on ray AX and BY, respectively. Then the points joined are

   1. (a)$A_5$ and $B_6$
   2. (b)$A_6$ and $B_5$
   3. (c)$A_4$ and $B_5$
   4. (d)$A_5$ and $B_4$
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   (a) $A_5$ and $B_6$

   Step-by-step solution →
4. Q4
   To ​construct a triangle similar to a ​given $△ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $△ABC$, 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 BC. ​Then locate points $B_1,B_2,B_3,\dots$ on BX at equal distances and next step ​is ​to join

   1. (a)$B_{10}$ to C
   2. (b)$B_3$ to C
   3. (c)$B_7$ to C
   4. (d)$B_4$ to C
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   (c) $B_7$ to C

   Step-by-step solution →
5. Q5
   To construct a triangle similar to a given $△ABC$ with its sides $\frac{8}{5}$ of the corresponding sides of $△ABC$, draw ​a ray BX such that $\angle CBX$ ​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

   1. (a)$5$
   2. (b)$8$
   3. (c)$13$
   4. (d)$3$
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   (b) $8$

   Step-by-step solution →
6. Q6
   To ​draw ​a ​pair of tangents to a circle which are inclined to each other at an angle ​of $60^{\circ }$, it ​is required to ​draw tangents at end points of those two radii ​of the circle, the angle between ​them should be

   1. (a)$135^{\circ }$
   2. (b)$90^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$120^{\circ }$
   Show answer

   (d) $120^{\circ }$

   Step-by-step solution →