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SSC > Trigonometry

Explore popular questions from Trigonometry for SSC. This collection covers Trigonometry previous year SSC questions hand picked by experienced teachers.

Q 1.

Correct4

Incorrect-1

In circular measure, the value of the angle {tex} 11 ^ { \circ } 15 ^ { \prime } {/tex} is

{tex} \frac { \pi ^ { c } } { 16 } {/tex}

B

{tex} \frac { \pi ^ { c } } { 8 } {/tex}

C

{tex} \frac { \pi ^ { c } } { 4 } {/tex}

D

{tex} \frac { \pi ^ { c } } { 12 } {/tex}

Explanation

Q 2.

Correct4

Incorrect-1

In a triangle {tex} \mathrm { ABC } , \angle \mathrm { ABC } = 75 ^ { \circ } {/tex} and {tex} \angle \mathrm { ACB } = \frac { \pi ^ { \mathrm { c } } } { 4 } \cdot {/tex} The circular measure of {tex} \angle \mathrm { BAC } {/tex} is

A

{tex} \frac { 5 \pi } { 12 } {/tex} radian

{tex} \frac { \pi } { 3 } {/tex} radian

C

{tex} \frac { \pi } { 6 } {/tex} radian

D

{tex} \frac { \pi } { 2 } {/tex} radian

Explanation


Q 3.

Correct4

Incorrect-1

The circular measure of an angle of an isosceles triangle is {tex} \frac { 5 \pi } { 9 } {/tex} Circular measure of one of the other angles must be

A

{tex} \frac { 5 \pi } { 18 } {/tex}

B

{tex} \frac { 5 \pi } { 9 } {/tex}

{tex} \frac { 2 \pi } { 9 } {/tex}

D

{tex} \frac { 4 \pi } { 9 } {/tex}

Explanation

Q 4.

Correct4

Incorrect-1

The degree measure of 1 radian (taking {tex} \pi = \frac { 22 } { 7 } {/tex} ) is

A

{tex} 57 ^ { \circ } 61 ^ { ' } 22 ^ { " } {/tex}(approx )

{tex} 57 ^ { \circ } 16 ^ { ' } 22 ^ { "} {/tex} (approx.)

C

{tex} 57 ^ { \circ } 22 ^ { \prime } 16 ^ { "} {/tex} (approx.)

D

{tex} 57 ^ { \circ } 32 ^ { \prime } 16 ^ { " } {/tex} (approx.)

Explanation


Q 5.

Correct4

Incorrect-1

{tex} \left( \frac { 3 \pi } { 5 } \right) {/tex} radians is equal to

A

{tex} 100 ^ { \circ } {/tex}

B

{tex} 120 ^ { \circ } {/tex}

{tex} 108 ^ { \circ } {/tex}

D

{tex} 180 ^ { \circ } {/tex}

Explanation

Q 6.

Correct4

Incorrect-1

If the sum of two angles is {tex} 135 ^ { \circ } {/tex} and their difference is {tex} \frac { \pi } { 12 } , {/tex} then the circular measure of the greater angle is

A

{tex} \frac { 2 \pi } { 3 } {/tex}

B

{tex} \frac { 3 \pi } { 5 } {/tex}

{tex} \frac { 5 \pi } { 12 } {/tex}

D

{tex} \frac { \pi } { 3 } {/tex}

Explanation



Q 7.

Correct4

Incorrect-1

If {tex} 0 \leq \theta \leq \frac { \pi } { 2 } {/tex} and {tex} \sec ^ { 2 } \theta + \tan ^ { 2 } \theta {/tex} {tex} = 7 , {/tex} then {tex} \theta {/tex} is

A

{tex} \frac { 5 \pi } { 12 } {/tex} radian

{tex} \frac { \pi } { 3 } {/tex} radian

C

{tex} \frac { \pi } { 5 } {/tex} radian

D

{tex} \frac { \pi } { 6 } {/tex} radian

Explanation

Q 8.

Correct4

Incorrect-1

If the sum and difference of two angles are {tex} \frac { 22 } { 9 } {/tex} radian and {tex} 36 ^ { \circ } {/tex} respectively, then the value of smaller angle in degree taking the value of {tex} \pi {/tex} as {tex} \frac { 22 } { 7 } {/tex} is:

{tex} 52 ^ { \circ } {/tex}

B

{tex} 60 ^ { \circ } {/tex}

C

{tex} 56 ^ { \circ } {/tex}

D

{tex} 48 ^ { \circ } {/tex}

Explanation



Q 9.

Correct4

Incorrect-1

The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 p.m. will be

A

{tex} \frac { \pi } { 4 } {/tex}

B

{tex} \frac { \pi } { 3 } {/tex}

C

{tex} \frac { 5 \pi } { 12 } {/tex}

{tex} \frac { \pi } { 2 } {/tex}

Explanation

Q 10.

Correct4

Incorrect-1

Which of the following relations is correct for {tex} 0 < \theta < 90 ^ { \circ } ? {/tex}

A

{tex} \sin \theta = \sin ^ { 2 } \theta {/tex}

B

{tex} \sin \theta < \sin ^ { 2 } \theta {/tex}

{tex} \sin \theta > \sin ^ { 2 } \theta {/tex}

D

{tex} \sin \theta = cosec \theta {/tex}

Explanation

Q 11.

Correct4

Incorrect-1

If {tex} \theta {/tex} is an acute angle and {tex} \sin ( \theta + {/tex} {tex} \left. 18 ^ { \circ } \right) = \frac { 1 } { 2 } , {/tex} then the value of {tex} \theta {/tex} in circular measure is :

A

{tex} \frac { \pi } { 12 } {/tex} radians

{tex} \frac { \pi } { 15 } {/tex} radians

C

{tex} \frac { 2 \pi } { 5 } {/tex} radians

D

{tex} \frac { 3 \pi } { 13 } {/tex} radians

Explanation

Q 12.

Correct4

Incorrect-1

What is the measure of central angle of the are whose length is {tex} 11 \mathrm { cm } {/tex} and radius of the circle is {tex} 14 \mathrm { cm } ? {/tex}

{tex} 45 ^ { \circ } {/tex}

B

{tex} 60 ^ { \circ } {/tex}

C

{tex} 75 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

Explanation

Q 13.

Correct4

Incorrect-1

The minimum value of {tex} 2 \sin ^ { 2 } \theta {/tex} {tex} + 3 \cos ^ { 2 } \theta {/tex} is

A

0

B

3

2

D

1

Explanation

Q 14.

Correct4

Incorrect-1

If cosec {tex} 39 ^ { \circ } = x {/tex}, the value of {tex} \frac { 1 } { cosec ^ { 2 } 51 ^ { \circ } } + \sin ^ { 2 } 39 ^ { \circ } + \tan ^ { 2 } 51 ^ { \circ } {/tex}
{tex} - \frac { 1 } { \sin ^ { 2 } 51 ^ { \circ } \sec ^ { 2 } 39 ^ { \circ } } {/tex} is

A

{tex} \sqrt { x ^ { 2 } - 1 } {/tex}

B

{tex} \sqrt { 1 - x ^ { 2 } } {/tex}

{tex} x ^ { 2 } - 1 {/tex}

D

{tex} 1 - x ^ { 2 } {/tex}

Explanation


Q 15.

Correct4

Incorrect-1

The value of {tex} \tan 4 ^ { \circ } . \tan 43 ^ { \circ } . \tan 47 ^ { \circ } . \tan 86 ^ { \circ } \mathrm { is } {/tex}

A

2

B

3

1

D

4

Explanation

Q 16.

Correct4

Incorrect-1

If {tex} \frac { \tan \theta + \cot \theta } { \tan \theta - \cot \theta } = 2 , \quad ( 0 \leq \theta \leq {/tex} {tex} \left. 90 ^ { \circ } \right) , {/tex} then the value of {tex} \sin \theta {/tex} is

A

{tex} \frac { 2 } { \sqrt { 3 } } {/tex}

{tex} \frac { \sqrt { 3 } } { 2 } {/tex}

C

{tex} \frac { 1 } { 2 } {/tex}

D

1

Explanation


Q 17.

Correct4

Incorrect-1

If {tex} \cos x + \cos y = 2 , {/tex} the value of {tex} \sin x + \sin y {/tex} is

0

B

1

C

2

D

- 1

Explanation

Q 18.

Correct4

Incorrect-1

The value of {tex} \tan 1 ^ { \circ } \tan 2 ^ { \circ } \tan 3 ^ { \circ } \ldots \ldots . {/tex} {tex} \tan 89 ^ { \circ } {/tex} is :

1

B

0

C

{tex} \sqrt { 3 } {/tex}

D

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

Explanation

Q 19.

Correct4

Incorrect-1

The measure of the angles of a triangle are in the ratio {tex}2: 7:11 . {/tex} Measures of angles are

A

{tex} 16 ^ { \circ } , 56 ^ { \circ } , 88 ^ { \circ } {/tex}

{tex} 18 ^ { \circ } , 63 ^ { \circ } , 99 ^ { \circ } {/tex}

C

{tex} 20 ^ { \circ } , 70 ^ { \circ } , 90 ^ { \circ } {/tex}

D

{tex} 25 ^ { \circ } , 175 ^ { \circ } , 105 ^ { \circ } {/tex}

Explanation


Q 20.

Correct4

Incorrect-1

The angles of a triangle are {tex} ( x + 5 ) ^ { \circ } , ( 2 x - 3 ) ^ { \circ } {/tex} and {tex} ( 3 x + 4 ) ^ { \circ } . {/tex} The value of {tex} x {/tex} is

A

30

B

31

29

D

28

Explanation

Q 21.

Correct4

Incorrect-1

The value of {tex} \cot 10 ^ { \circ } . {/tex} cot {tex} 20 ^ { \circ }. {/tex} cot {tex} 60 ^ { \circ } . \cot 70 ^ { \circ } . \cot 80 ^ { \circ } {/tex} is

A

{tex}1{/tex}

B

{tex}-1{/tex}

C

{tex} \sqrt { 3 } {/tex}

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

Explanation

Q 22.

Correct4

Incorrect-1

If {tex} \theta {/tex} be an acute angle and {tex} 7 \sin ^ { 2 } \theta + 3 \cos ^ { 2 } \theta = 4 , {/tex} then the value of {tex} \tan \theta {/tex} is

A

{tex} \sqrt { 3 } {/tex}

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

C

1

D

{tex} 0 {/tex}

Explanation

Q 23.

Correct4

Incorrect-1

The value of {tex} \sin ^ { 2 } 1 ^ { \circ } + \sin ^ { 2 } 5 ^ { \circ } + {/tex} {tex} \sin ^ { 2 } 9 ^ { \circ } + \ldots + \sin ^ { 2 } 89 ^ { \circ } {/tex} is

{tex} 11 \frac { 1 } { 2 } {/tex}

B

{tex} 11 \sqrt { 2 } {/tex}

C

11

D

{tex} \frac { 11 } { \sqrt { 2 } } {/tex}

Explanation



Q 24.

Correct4

Incorrect-1

The numerical value of {tex} \cot 18 ^ { \circ } {/tex} {tex} \left( \cot 72 ^ { \circ } \cos ^ { 2 } 22 ^ { \circ } + \frac { 1 } { \tan 72 ^ { \circ } \sec ^ { 2 } 68 ^ { \circ } } \right) {/tex} is

{tex}1{/tex}

B

{tex} \sqrt { 2 } {/tex}

C

{tex}3{/tex}

D

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

Explanation



Q 25.

Correct4

Incorrect-1

If {tex} \tan 15 ^ { \circ } = 2 - \sqrt { 3 } , {/tex} the value of {tex} \tan 15 ^ { \circ } \cot 75 ^ { \circ } + \tan 75 ^ { \circ } \cot 15 ^ { \circ } \mathrm { is } {/tex}

14

B

12

C

10

D

8

Explanation