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Limits and Derivatives · Question 15

JEE Main 2025 (Online) 3rd April Evening ShiftNumericalEasy📈 Topic in 32% papers+4
1

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

Answer

32

Solution

The limit is of the form 1 :

p = eL, where L = x 0 1x2 ( xx - 1 ) = x 0 x - xx3

∵ x = x + x33 + 2x515 +

⇒ L = x 0 ( 13 + 2x215 + ) = 13

⇒ p = e1/3

∴ 96 e p = 96 13 = 32

Answer: 32

JEE Main 2025 (Online) 3rd April Evening Shift

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2

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

  1. -1
  2. 4
  3. 6
  4. 7
JEE Main 2025 (Online) 2nd April Morning Shift
3

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

  1. 0
  2. 34
  3. -1
  4. 12
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4

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 .

JEE Main 2025 (Online) 29th January Morning Shift
5

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 .

JEE Main 2025 (Online) 28th January Evening Shift

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