# JEE Main > Trigonometric Ratios & Identities

Explore popular questions from Trigonometric Ratios & Identities for JEE Main. This collection covers Trigonometric Ratios & Identities previous year JEE Main questions hand picked by popular teachers.

Physics
Chemistry
Maths

Q 1.

Correct4

Incorrect-1

A body weighing 13{tex} \mathrm { kg } {/tex} is suspended by two strings {tex} 5 \mathrm { m } {/tex} and {tex} 12 \mathrm { m } {/tex} long, their other ends being fastened to the extremities of a rod {tex} 13 \mathrm { m } {/tex} long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are:

A

12{tex} \mathrm { kg } {/tex} and 13{tex} \mathrm { kg } {/tex}

B

5{tex} \mathrm { kg } {/tex} and 5{tex} \mathrm { kg } {/tex}

5{tex} \mathrm { kg } {/tex} and 12{tex} \mathrm { kg } {/tex}

D

5{tex} \mathrm { kg } {/tex} and 13{tex} \mathrm { kg } {/tex}

##### Explanation

Q 2.

Correct4

Incorrect-1

A tower stands at the centre of a circular park. {tex} A {/tex} and {tex} B {/tex} are two points on the boundary of the park such that {tex} A B ( = a ) {/tex} subtends an angle of {tex} 60 ^ { \circ } {/tex} at the foot of the tower, and the angle of elevation of the top of the tower from {tex} A {/tex} or {tex} B {/tex} is {tex} 30 ^ { \circ } {/tex}. The height of the tower is

A

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

B

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

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

D

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

##### Explanation

Q 3.

Correct4

Incorrect-1

Let {tex} P = ( - 1,0 ) , Q = ( 0,0 ) {/tex} and {tex} R = ( 3,3 \sqrt { 3 } ) {/tex} be three points. The equation of the bisector of the angle {tex} P Q R {/tex} is

{tex} \sqrt { 3 } x + y = 0 {/tex}

B

{tex} x + \frac { \sqrt { 3 } } { 2 } y = 0 {/tex}

C

{tex} \frac { \sqrt { 3 } } { 2 } x + y = 0 {/tex}

D

{tex} x + \sqrt { 3 } y = 0 {/tex}

##### Explanation

Q 4.

Correct4

Incorrect-1

A bird is sitting on the top of a vertical pole {tex} 20 \mathrm { m } {/tex} high and its elevation from a point 0 on the ground is {tex} 45 ^ { \circ } . {/tex} It flies off horizontally straight away from the point {tex} O {/tex} . After one second, the elevation of the bird from {tex} O {/tex} is reduced to {tex} 30 ^ { \circ } . {/tex} Then the speed {tex} ( \text { in } m / s ) {/tex} of the bird is

A

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

20{tex} ( \sqrt { 3 } - 1 ) {/tex}

C

40{tex} ( \sqrt { 2 } - 1 ) {/tex}

D

40{tex} ( \sqrt { 3 } - \sqrt { 2 } ) {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

If the angles of elevation of the top of a tower from three collinear points {tex} A , B {/tex} and {tex} C , {/tex} on a line leading to the foot of the tower are {tex} 30 ^ { \circ } , 45 ^ { \circ } {/tex} and {tex} 60 ^ { \circ } , {/tex} respectively, then the ratio, {tex} A B : B C , {/tex} is

A

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

B

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

C

{tex} 2 : 3 {/tex}

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

##### Explanation

Q 6.

Correct4

Incorrect-1

Let the tangents drawn to the circle {tex} x ^ { 2 } + y ^ { 2 } = 16 {/tex} from the point {tex} P ( 0 , h ) {/tex} meet the {tex} x {/tex} -axis at points {tex} A {/tex} and {tex} B {/tex} . If the area of {tex} \Delta A P B {/tex} is minimum, then {tex} h {/tex} is equal to

A

{tex}4 \sqrt { 3 } {/tex}

B

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

C

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

{tex}4 \sqrt { 2 } {/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

In a {tex} \triangle A B C , \frac { a } { b } = 2 + \sqrt { 3 } {/tex} and {tex} \angle C = 60 ^ { \circ } . {/tex} The ordered pair {tex} ( \angle A , \angle B ) {/tex} is equal to

{tex} \left( 15 ^ { \circ } , 105 ^ { \circ } \right) {/tex}

B

{tex} \left( 105 ^ { \circ } , 15 ^ { \circ } \right) {/tex}

C

{tex} \left( 45 ^ { \circ } , 75 ^ { \circ } \right) {/tex}

D

{tex} \left( 75 ^ { \circ } , 45 ^ { \circ } \right) {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point {tex} A {/tex} on the path, he observes that the angle of elevation of the top of the pillar is {tex} 30 ^ { \circ }{/tex}. After
walking for 10{tex} \mathrm { min } {/tex} from {tex} A {/tex} in the same direction, at a point {tex} B , {/tex} he observes that the angle of elevation of the top of the pillar is now {tex} 60 ^ { \circ } . {/tex} Then, the time taken (in minutes) by him from {tex} B {/tex} to reach the pillar is

5

B

6

C

10

D

20

##### Explanation

Q 9.

Correct4

Incorrect-1

The angle of elevation of the top of a vertical tower from a point {tex} A {/tex} due east of it is {tex} 45 ^ { \circ } . {/tex} The angle of elevation of the top of the same tower from a point {tex} B {/tex} due south of {tex} A {/tex} is {tex} 30 ^ { \circ } {/tex} . If the distance between {tex} A {/tex} and {tex} B {/tex} is 54{tex} \sqrt { 2 } \mathrm { m } {/tex} , then the height of the tower (in metres), is

A

108

B

{tex}36 \sqrt { 3 } {/tex}

C

{tex}54 \sqrt { 3 } {/tex}

54

##### Explanation

Q 10.

Correct4

Incorrect-1

If {tex} \tan x = n \cdot \tan y , n \in R ^ { + } , {/tex} then maximum value of {tex} \sec ^ { 2 } ( x - y ) {/tex} is equal to

A

{tex} \frac { ( n + 1 ) ^ { 2 } } { 2 n } {/tex}

B

{tex} \frac { ( n + 1 ) ^ { 2 } } { n } {/tex}

C

{tex} \frac { ( n + 1 ) ^ { 2 } } { 2 } {/tex}

{tex} \frac { ( n + 1 ) ^ { 2 } } { 4 n } {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

If {tex} \tan x = n \cdot \tan y , n \in R ^ { + } , {/tex} then maximum value of {tex} \sec ^ { 2 } ( x - y ) {/tex} is equal to

A

{tex} \frac { ( n + 1 ) ^ { 2 } } { 2 n } {/tex}

B

{tex} \frac { ( n + 1 ) ^ { 2 } } { n } {/tex}

C

{tex} \frac { ( n + 1 ) ^ { 2 } } { 2 } {/tex}

{tex} \frac { ( n + 1 ) ^ { 2 } } { 4 n } {/tex}