Limits and Derivatives

JEE Main 2024 (Online) 31st January Morning ShiftMCQEasy📈 Topic in 12% papers+4−1

Ques. 1JEE Main 2024, 31 January (Morning Shift)

x 0 e2| x|-2| x|-1x2

Answer

(4) is equal to 2

Put | x| = t; as x 0, t 0+ and t2 = 2 x, so

L = t 0 e2t - 2t - 1t2 x 0 2 xx2

The first limit has the form 00, so we apply L'Hôpital's rule:

t 0 2e2t - 22t = t 0 2 e2t - 12t = 2 1 = 2

Since 2 xx2 1, L = 2 1 = 2.

The limit exists and equals 2, so (1), (2) and (3) are wrong.

Answer: (4)

Ques. 2JEE Main 2024, 31 January (Evening Shift)

Let f: R (0, ) be a strictly increasing function such that x f(7x)f(x)=1. Then, the value of x [ f(5x)f(x)-1 ] is equal to

Ques. 3JEE Main 2024, 31 January (Evening Shift)

If x 0 ax2ex-b e(1+x)+cxe-xx2 x=1, then 16 (a2+b2+c2 ) is equal to .

Ques. 4JEE Main 2024, 30 January (Morning Shift)

Let f: [- 2, 2 ] be a differentiable function such that f(0)= 12. If the x 0 x 0x f(t) dtex2-1= , then 8 2 is equal to :

Ques. 5JEE Main 2024, 29 January (Morning Shift)

Suppose f(x)= (2x+2-x ) x -1 (x2-x+1 ) (7x2+3x+1 )3. Then the value of f (0) is equal to

Ques. 6JEE Main 2024, 29 January (Morning Shift)

x 2 ( 1 (x- 2 )2 x3 ( 2 )3 (t 13 )dt ) is equal to

Ques. 7JEE Main 2024, 29 January (Evening Shift)

Let the slope of the line 45x+5y+3=0 be 27r1+ 9r22 for some r1, r2 R. Then x 3 ( 3x 8t2 3r2x2-r2x2-r1x3-3x dt ) is equal to .

Ques. 8JEE Main 2024, 27 January (Morning Shift)

If a= x 0 1+ 1+x4- 2x4 and b= x 0 2x 2- 1+ x, then the value of ab3 is :

Ques. 9JEE Main 2024, 27 January (Evening Shift)

If x 0 3+ x+ x+ e(1-x)3 2x= 13, then 2 - is equal to :

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