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.

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
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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) = , = − , =
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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) ( − ) + ( + ) + ( + ) =
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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) −
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5. 19. If + − = , then =
(a) (b) −
(c) − (d) −
20. If = , = then at is
(a)
√
(b)
√
(c)
√
(d) √
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