Atomos Test Generator Free PYQs ExamsMy practice Log in / Sign up free

Limits and Derivatives

JEE Main 2026 (Online) 21st January Morning ShiftMCQMedium📈 Topic in 33% papers+4−1
Ques. 1JEE Main 2026, 21 January (Morning Shift)

Let f : R (0, ) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f''(3) = 4. Then x 1 e ( f(2 + x)f(3) ) 18(x - 1)2 is equal to :

  1. 9
  2. 18
  3. 1
  4. 2

Answer

(4) 2

Solution

e mn = n e m

L = x 1 18(x - 1)2 e f(2 + x)f(3)

Put x - 1 = h, h 0:

L = h 0 18 [ e f(3 + h) - e f(3) ]h2 ( 00 )

By L'Hôpital's rule:

L = h 0 18 f'(3 + h)f(3 + h)2h = h 0 9f'(3 + h)h f(3 + h) ( 00 ), since f'(3) = 0

Again by L'Hôpital's rule:

L = h 0 9f''(3 + h)f(3 + h) + h f'(3 + h)

= 9f''(3)f(3) = 9 418 = 2

Answer: (4)

Keep practising — Limits and Derivatives

Ques. 2JEE Main 2026, 21 January (Evening Shift)

Let f(x) = x3 + x2 f'(1) + 2x f''(2) + f'''(3), x R. Then the value of f'(5) is :

  1. 6575
  2. 1175
  3. 25
  4. 625
Ques. 3JEE Main 2025, 8 April (Evening Shift)

Given below are two statements: In the light of the above statements, choose the correct answer from the options given below:

  1. Statement I is false but Statement II is true
  2. Both Statement I and Statement II are false
  3. Both Statement I and Statement II are true
  4. Statement I is true but Statement II is false
Ques. 4JEE Main 2025, 7 April (Morning Shift)

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

  1. 53
  2. 1
  3. 13
  4. 115
Ques. 5JEE 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

  1. 20
  2. 19
  3. 18
  4. 17
Ques. 6JEE 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 :

  1. 3
  2. 1
  3. 2
  4. 0
Ques. 7JEE Main 2025, 3 April (Evening Shift)

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

Ques. 8JEE Main 2025, 2 April (Morning Shift)

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

  1. -1
  2. 4
  3. 6
  4. 7
Ques. 9JEE Main 2025, 2 April (Evening Shift)

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

  1. 0
  2. 34
  3. -1
  4. 12
Ques. 10JEE 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. 11JEE 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 .

All Limits and Derivatives PYQs →

PDFDownload Limits and Derivatives PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)