Limits and Derivatives

JEE Main 2025 (Online) 7th April Morning ShiftMCQEasy📈 Topic in 14% papers+4−1

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

x 0+ (5(x) 13 ) e (1 + 3x2 ) ( -13 x )2 (e5(x) 43 - 1 ) is equal to

Answer

(3) 13

Solution

As x 0+, use tt 1, e(1 + t)t 1, -1tt 1, et - 1t 1:

(5x 13 ) 5x 13, e(1 + 3x2) 3x2

( -13 x )2 9x, e5x 43 - 1 5x 43

limit = 5x 13 3x29x 5x 43 = 15x 7345x 73

= 13

Answer: (3)

Keep practising — Limits and Derivatives

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

If x 1+ (x - 1)(6 + (x - 1)) + (1 - x)(x - 1)3 = -1, where , R, then + is equal to

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

Let f be a differentiable function on R such that f(2)=1, f'(2)=4. Let x 0(f(2+x))3/x=e . Then the number of times the curve y=4x3-4x2-4( -7)x- meets x-axis is :

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

If x 0 ( xx ) 1x2 = p, then 96 e p is equal to

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

For , , R, if x 0 x2 x + ( - 1)ex2 2x - x = 3, then + - is equal to :

-1
4
6
7

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

If x 0 (2x) + a (4x) - bx4 is finite, then (a + b) is equal to:

0
34
-1
12

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

Let [t] be the greatest integer less than or equal to t. Then the least value of p N for which x 0+ (x ( [ 1x ] + [ 2x ] + + [ px ] ) - x2 ( [ 1x2 ] + [ 22x2 ] + + [ 92x2 ] ) ) 1 is equal to .

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

Let f(x) = n r=0n ( (x/2r+1 ) + 3 (x/2r+1 )1 - 2 (x/2r+1 ) ). Then x 0 ex - ef(x)(x - f(x)) is equal to .

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

x 0 cosecx ( 2 2x+3 x- 2x+ x+4 ) is