Trigonometric Functions

JEE Main 2025 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 18% papers+4−1

Ques. 1JEE 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 :

Answer

(3) 8

Let Ar = 4 + (r - 1) 6, Br = 4 + r 6 Br - Ar = 6

1 A B = 1 6 (B - A) A B = 2( A - B)

Sum = 2 r=113( Ar - Br) (telescoping, as Br = Ar+1)

= 2 [ 4 - ( 4 + 13 6 ) ]

4 + 13 6 = 2 + 5 12

( 4 + 13 6 ) = 5 12 = 2 - 3

Sum = 2[1 - (2 - 3)] = 2 3 - 2

a = 2, b = -2

a2 + b2 = 4 + 4 = 8

Answer: (3)

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

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

Ques. 4JEE 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. 5JEE Main 2025, 22 January (Evening Shift)

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

All JEE Main Mathematics chapters