Trigonometric Functions

JEE Main 2025 (Online) 7th April Evening ShiftMCQHard📈 Topic in 36% papers+4−1

Ques. 1JEE Main 2025, 7 April (Evening Shift)

The number of solutions of the equation 2 2 + 5 2 = 2 3 5 2 in [- 2, 2 ] is :

Answer

(2) 7

Using 4 3 A = 3A + 3 A with A = 5 2,

2 3 5 2 = 12 ( 15 2 + 3 5 2 )

so the equation becomes

2 2 2 + 2 5 2 = 15 2 + 3 5 2

2 2 2 = 15 2 + 5 2

2 2 2 = 5 2 + 3 2,

3 2 = 15 2

15 2 = 2n 3 2, n Z

6 = 2n or 9 = 2n

= n 3 or = 2n 9

In [- 2, 2 ], = n 3 gives 0, 3 and = 2n 9 gives 0, 2 9, 4 9.

The distinct solutions are 0, 3, 2 9, 4 9, i.e. 7 solutions.

Answer: (2)

Ques. 2JEE Main 2025, 4 April (Morning Shift)

If 10 4 + 15 4 = 6, then the value of 27 cosec6 + 8 6 16 8 is

Ques. 3JEE Main 2025, 3 April (Morning Shift)

The number of solutions of the equation 2x + 3 x = , x [-2 , 2 ] - \ 2, 3 2 \ is:

Ques. 4JEE Main 2025, 3 April (Evening Shift)

The number of solutions of the equation (4 - 3) x - 2 3 2 x = - 41 + 3, x [-2 , 5 2 ] is

Ques. 5JEE Main 2025, 2 April (Morning Shift)

If [-2 , 2 ], then the number of solutions of 2 2 2 + (2 - 6) - 3 = 0, is equal to:

Ques. 6JEE Main 2025, 2 April (Evening Shift)

If [- 7 6, 4 3 ], then the number of solutions of 3 cosec2 - 2( 3 - 1) cosec - 4 = 0, is equal to :

Ques. 7JEE Main 2025, 29 January (Evening Shift)

If x + 2 x = 1, x (0, 2 ), then ( 12x + 12x) + 3( 10x + 10x + 8 x + 8 x) + ( 6 x + 6 x) is equal to:

Ques. 8JEE Main 2025, 28 January (Evening Shift)

If r=113 \ 1 ( 4 + (r - 1) 6 ) ( 4 + r 6 ) \ = a 3 + b, a, b Z, then a2 + b2 is equal to :

Ques. 9JEE Main 2025, 24 January (Evening Shift)

Let A= \x (0, )- \ 2 \: (2/ )| x|+ (2/ )| x|=2 \ and B= \x 0: x( x-4)-3| x-2|+6=0 \. Then n(A ) is equal to :

Ques. 10JEE Main 2025, 23 January (Morning Shift)

The value of ( 70 ) ( 10 70 -1 ) is

Ques. 11JEE Main 2025, 23 January (Evening Shift)

Let the range of the function f(x)=6+16 x ( 3-x ) ( 3+x ) 3x 6x, x be [ , ]. Then the distance of the point ( , ) from the line 3x+4y+12=0 is :

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