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IIT JEE Exam 2025 : Main

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Sayan Chandra
St. Stephen's School, Dum Dum, Kolkata (Calcutta)
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MATHS CLASS XI LIMITS AND DERIVATIVES PRACTICE PAPER 05 Time Allowed: 2 hrs Max. Marks: 50 SECTION A (1 mark) lim 1. Evaluate: 8 x3 1 . 1 x 16 x 4 1 2 2. Evaluate: lim 1 x 1/3 . x 1 1 x 2/3 lim 3. Evaluate: 4. Evaluate: 5. If x 2 ecos x 1 . cos x lim log(1 x3 ) . x 0 sin 3 x lim x9 a9 9 , then find the value of a. x a x a 6. Find the derivative of sec x tanx 7. Find the derivative of (x2 3x + 2) (x + 2) 8. Find the derivative of 3 x. 9. Find the derivative of f(x) = x 1 . x 2 x x 10. Find the derivative of f(x) = sin cos . 2 2 SECTION B (2 marks) 11. Evaluate: lim 3x 33 x 12 x 2 33 x 3x /2 12. Evaluate: lim n2 n 1 2 3 ...... n 13. Evaluate: lim x4 4 x 2 x2 3 2 x 8 Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 - 14. Find the derivative of 1 tan x . 1 tan x 15. Find the derivative of x2 x 1 . x2 x 1 16. Find the derivative of f (x) = sin2 x, by first principle. SECTION C (4 marks) 17. Find the derivative of f (x) = e tan x , by first principle. 18. Find the derivative of f (x) = cot x , by first principle. lim cos 3x 3cosx 19. Evaluate: 3 x 2 x 2 lim 2 3 cosx sinx 20. Evaluate: x (6 x )2 6 SECTION D (6 marks) 21. Evaluate: lim 1 cos x.cos 2 x.cos 3 x x 0 sin 2 2 x 22. (i)If y sec x tan x dy , then find . sec x tan x dx (ii)If y 1 cos 2 x dy , then find . 1 cos 2 x dx Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 -

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