Multiple Choice Questions_Successive Differentiation (CALCULUS)
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The document contains a multiple-choice question paper for a mathematics exam focused on calculus, specifically on successive differentiation. It includes questions numbered 1 to 20, each offering multiple answer choices related to mathematical concepts. It is designed for B.A. / B.Sc. first semester students and is attributed to a mathematics department in Punjab, India.
Multiple Choice Questions_Successive Differentiation (CALCULUS)
- 1. CAT – 2 (MCQ) SEPTEMBER 2019 B.A. / B.Sc. 1st Semester ( Mathematics ) Paper_ Calculus - I , Chapter – 6_ Successive Differentiation Time Allowed : 40 minutes M.M. 20 Note – Each Question carry one marks. 1. If = + , = (a) Constant (b) 0 (c) + (d) None of these 2. If √ + = , = (a) √ (b) (c) (d) 3. = , then = (a) − (b) + (c) + (d) + 4. = ( ) , (a) ( + ) + ( + ) + = (b) ( + ) + ( + ) = (c) ( − ) + ( − ) = (d) ( + ) + ( + ) + = Prof. P.G. Dev Punjab, IndiaCity,Ferozepur Women,ForCollegeSamaj Mathematics,ofDepartment Gupta,Sanjay devsamajcollege.blogspot.in
- 2. 5. ( ) = ≤ > 0 , (a) ( ) ∀ = (b) ( ) ∀ (c) ( ) ∀ (d) None of these 6. If ( ) = , ≠ , = , then (a) ( ) = (b) ( ) = (c) ( ) = (d) None of these 7. If = ( + ) , then = (a) -1 (b) 1 (c) ( + ) (d) 0 8. Find the values of , , for which the function ( ) = + + , ≤ + + , > is twice differentiable at = . (a) = , = , = − (b) = − , = , = (c) = , = − , = (d) = , = − , = devsamajcollege.blogspot.in
- 3. 9. = ( + ), (a) = + + (b) = + + (c) = + + (d) = + + 10. = ( + ), (a) = ( + ) ( + ) (b) = ( + ) ( + + ) (c) = ( + ) ( + + + ) (d) = ( + ) ( + + ) 11. = , = (a) − ! (b) ! (c) ! (d) 0 12. If and are two functions of having derivatives of nth order, then ( ) = + + ⋯ + + ⋯ + This theorem is known as (a) Cauchy's Theorem (b) Lagrange's Theorem (c) Leibnitz's Theorem (d) Lipchitz's Theorem 13. + = , (a) ( − ) + ( + ) + ( − ) = (b) ( − ) + ( + ) + ( − ) = (c) ( + ) + ( + ) + ( − ) = (d) ( − ) + ( + ) + ( + ) = devsamajcollege.blogspot.in
- 4. 14. = ( ) + + = , (a) + ( + ) + ( + ) = (b) + ( + ) + ( + ) = (c) + ( + ) + ( − ) = (d) + ( − ) + ( + ) = 15. = ( − ) − ( + ) − ( + ) = , → = (a) − (b) − (c) + (d) + 16. = , = (a) + + + ( ) (b) + + + ( ) (c) + + + ( ) (d) + + + ( ) 17. = , = (a) + ( + )! (b) + ( − )! (c) − ( − )! (d) + ( − )! 18. If ( − ) + ( − ) = , then = (a) (b) (c) + (d) − devsamajcollege.blogspot.in
- 5. 19. If + − = , then = (a) (b) − (c) − (d) − 20. If = , = then at is (a) √ (b) √ (c) √ (d) √ devsamajcollege.blogspot.in