SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 10

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

In a quadrilateral $A B C D$ , the two diagonals intersect perpendicularly. Prove that $A B^{2} + C D^{2} = B C^{2} + A D^{2}$

Important Questions on Third Summative Test

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 10

In a cyclic quadrilateral

A B C D

, the sides

A B

and

D C

are produced to meet at

P

.Prove that

P A . P B = P C . P D

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 11

Draw a circle with radius

2.8 cm

.Take a point at a distance of

7.5 cm

from the centre of the circle. From this external point draw two tangents to the circle.

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 11

Find the value of

\sqrt{38}

by geometric method. [Only construction to be given]

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 12

If

\cos 43 ° = \frac{x}{\sqrt{x^{2} + y^{2}}}

, find the value of

\tan 47 °

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 12

If

x = \frac{1 + \sin θ}{\cos θ}

, then show that

x^{2} - 2 x \tan θ - 1 = 0

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 12

If

x \tan 30 ° + y c o t 60 ° = 0

and

2 x - y \tan 45 ° = 1

, find the value of

x

and

y

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 13

When the angle of elevation of the sun is

30 °

, the length of shadow of a vertical tower situated on the horizontal plane is

60

metres more than when the angle of elevation of sun is

45 °

. Find the height of the tower.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 35 - Third Summative Test>THIRD SUMMATIVE TEST>Q 13

Standing on a railway overbridge

5 \sqrt{3}

metre high, kausikbabu saw an engine of a train at an angle of depression

30 °

on one side of the bridge.But after

2

seconds he saw the engine on the other side of the bridge at an angle of depression

45 °

.Find the velocity of the train in kilometre per hour. (Use

\sqrt{3} = 1.732

)