Trigonometric Functions

JEE Main 2025 (Online) 2nd April Evening ShiftMCQMedium📈 Topic in 32% papers+4−1

Ques. 1JEE 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 :

Answer

(3) 6

Let cosec = u: 3u2 - 2( 3 - 1)u - 4 = 0

3u2 - 2 3u + 2u - 4 = 0

3u(u - 2) + 2(u - 2) = 0

(u - 2)( 3u + 2) = 0

cosec = 2 or cosec = - 2 3

= 12 or = - 32

In [- 7 6, 4 3 ]:

= 12: = - 7 6, 6, 5 6 (3 values)

= - 32: = - 2 3, - 3, 4 3 (3 values)

number of solutions = 3 + 3 = 6

Answer: (3)

Ques. 2JEE 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. 3JEE 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. 4JEE 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. 5JEE Main 2025, 23 January (Morning Shift)

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

Ques. 6JEE 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 :

Ques. 7JEE Main 2025, 22 January (Evening Shift)

The sum of all values of [0,2 ] satisfying 2 2 = 2 and 2 2 =3 is

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