Exam (elaborations)
DIFFERENTIATION JEE TYPE QUESTIONS
- Course
- Institution
All types of jee questions covered till date
[Show more]
Seller
Follow
riyashah120527
Content preview
146 DifferentiationDerivative at a Point
Basic Level
1. If f (x ) | x | , then f (0) [MNR 1982]
(a) 0 (b) 1 (c) x (d) None of these
1 ,x 0
2. If f (x ) then f (0) [MP PET 1994]
1 sin x , 0 x
2
(a) 1 (b) 0 (c) (d) Does not exist
ax b; x 0
2
3. If f (x ) possesses derivative at x = 0, then
x 2; x 0
(a) a = 0, b = 0 (b) a > 0, b = 0 (c) a R , b = 0 (d) None of these
4. The derivative of f (x ) 3 | 2 x | at the point x 0 3 is [Orissa JEE 2002]
(a) 3 (b) – 3 (c) 0 (d) Does not exist
5. The derivative of y = 1 – |x | at x = 0 is [SCRA 1996]
(a) 0 (b) 1 (c) – 1 (d) Does not exist
6. The derivative of f (x ) | x x | at x = 2 is
2
[AMU 1999]
(a) – 3 (b) 0 (c) 3 (d) Not defined
d
7. The value of [| x 1 | | x 5 |] at x = 3 is [MP PET 2000]
dx
(a) – 2 (b) 0 (c) 2 (d) 4
xf (a) af (x )
8. If f(x) has a derivative at x = a, then lim is equal to
x a x a
(a) f (a) af (a) (b) af (a) f (a) (c) f (a) f (a) (d) af (a) f (a)
9. If f (x ) x 2 , then f ( f ( x )) at x = 4 is [DCE 2001]
(a) 8 (b) 1 (c) 4 (d) 5
10. Let 3f(x) – 2f(1/x) = x, then f (2) is equal to [MP PET 2000]
(a) 2/7 (b) 1/2 (c) 2 (d) 7/2
af (x ) xf (a)
11. If f(x) is a differentiable function, then lim is [UPSEA
x a x a
(a) af (a) f (a) (b) af (a) f (a) (c) af (a) f (a) (d) af (a) f (a)
12. The differential coefficient of the function |x – 1|+ |x – 3| at the point x = 2 is [Rajasthan PET 2002]
(a) – 2 (b) 0 (c) 2 (d) Undefined
13. If f (x ) | x 3 | , then f (3) [Rajast
, Differentiation 147
(a) 0 (b) 1 (c) –1 (d) Does not exist
Advance Level
dy
14. If y cot 1 (cos 2 x ) , then the value of at x will be [IIT 19
dx 6
1/2 1/2
2 1
(a) (b) (c) (3) (d) (6)
3 3
2
1 3
15. The values of x, at which the first derivative of the function x w.r.t. x is , are
x 4
1 3 2
(a) 2 (b) (c) (d)
2 2 3
16. The number of points at which the function f (x ) | x 0.5 | | x 1| tan x does not have a derivative in the
interval (0, 2), is
[MNR 1995]
(a) 1 (b) 2 (c) 3 (d) 4
x
17. The set of all those points, where the function f (x ) is differentiable, is
1 | x |
(a) (–, ) (b) [0, ) (c) (–, 0) (0, ) (d) (0, )
18. Let f (x y ) f (x ) f (y ) and f (x ) 1 xg (x )G(x ) where lim g(x ) a and lim G(x ) b then f (x ) is equal to
x 0 x 0
(a) 1+ ab (b) ab (c) a/b (d) None of these
19. f(x) is a function such that f (x ) f (x ) and f (x ) g(x ) and h(x) is a function such that h(x ) [ f (x )]2 [g(x )]2 and
h(5) = 11, then the value of h(10) is
(a) 0 (b) 1 (c) 10 (d) None of these
20. Let f (x y ) f (x ) f (y ) for all x and y. Suppose that f (3) 3 and f (0) 11, then f (3 ) is given by
(a) 22 (b) 33 (c) 28 (d) None of these
Some Standard Differentiation
Basic Level
(1 x )2 dy
21. If y 2
, then is [MP PET 1999]
x dx
2 2 2 2 2 2 2 2
(a) 2 3 (b) 2 3 (c) (d)
x x x x x2 x3 x3 x2
dv
22. If 2 t v 2 , then is equal to [MP PET 1992]
dt
(a) 0 (b) 1/4 (c) 1/2 (d) 1/v
dy
23. If x y 1 y , then
2
[MP PET 2001]
dx
1 y2 1 y2
(a) 0 (b) x (c) (d)
1 2y 2
1 2y 2
dp
24. If pv = 81, then is at v = 9 equal to [MP PET 1999]
dv
(a) 1 (b) –1 (c) 2 (d) None of these
,148 Differentiation
1 x dy
25. If y , then [AISSE 1981; Rajasthan PET
1x dx
1995]
2 1 1 2
(a) (b) (c) (d)
(1 x ) (1 x ) (1 x ) (1 x ) 2(1 x ) (1 x ) (1 x ) (1 x )
26. The derivative of f (x ) x | x | is [SCRA
(a) 2x (b) –2x (c) 2 x 2 (d) 2|x |
27. The derivative of F[ f { (x )}] is [AMU 2001]
(a) F[ f { (x )}] (b) F[ f { (x )}] f { (x )} (c) F[ f { (x )}] f { (x )} (d) F[ f { (x )}] f { (x )} (x )
d
28. (sin 2 x 2 ) equals [Rajasthan PET 1996]
dx
(a) 4x cos (2 x 2 ) (b) 2 sin x 2 . cos x 2 (c) 4x sin (x 2 ) (d) 4x sin (x 2 ). cos( x 2 )
dy
29. If y sec x 0 , then [MP PET 1997]
dx
180
(a) secx tanx (b) sec x 0 tan x 0 (c) sec x 0 tan x 0 (d) sec x 0 tan x 0
180
dy
30. If sin y e x cos y e , then at (1, ) is [Kerala (Engg.) 2002]
dx
(a) sin y (b) –x cos y (c) e (d) sin y – x cos y
2
dy
31. If y a sin x b cos x , then y 2 is a
dx
(a) Function of x (b) Function of y (c) Function of x and y (d) Constant
d
32. [cos(1 x 2 )2 ] [AISSE 1981; AI CBSE 1979]
dx
(a) 2 x (1 x 2 ) sin(1 x 2 )2 (b) 4 x (1 x 2 ) sin(1 x 2 )2 (c) 4 x (1 x 2 ) sin(1 x 2 )2 (d) 2(1 x 2 ) sin(1 x 2 )2
dy
33. If y cos(sin x 2 ) , then at x ,
2 dx
(a) – 2 (b) 2 (c) 2 (d) 0
2
d
34. [sin n x cos nx ] []
dx
(a) n sin n 1 x cos(n 1)x (b) n sin n 1 x cos nx (c) n sinn 1 x cos(n 1)x (d) n sinn 1 x sin(n 1)x
d
35. cos(sin x 2 ) [DSSE 1979]
dx
(a) sin(sin x 2 ). cos x 2 .2 x (b) sin(sin x 2 ). cos x 2 .2 x (c) sin(sin x 2 ). cos 2 x . 2 x (d) None of these
dy
36. If y sin( sin x cos x ) , then [DSSE 1987]
dx
1 cos sin x cos x cos sin x cos x
(a) (b)
2 sin x cos x sin x cos x
1 cos sin x cos x
(c) (cos x sin x ) (d) None of these
2 sin x cos x
1 x2
37. If y sin , then dy [AISSE 1987]
1 x
2
dx
, Differentiation 149
4x 1 x2 x 1 x2 x 1 x2 4x 1 x2
(a) . cos
(b) . cos
(c) . cos
(d) . cos
1x 2
1 x
2
(1 x )
2 2
1 x
2
(1 x )
2
1 x
2
(1 x )
2 2
1 x
2
d 2
38. (x cos x )4 [DSSE 1987]
dx
(a) 4(x 2 cos x )(2 x sin x ) (b) 4(x 2 cos x )(2 x sin x ) (c) 4(x 2 cos x )3 (2 x sin x ) (d) 4(x 2 cos x )3 (2 x sin x )
d cot 2 x 1
39.
dx cot 2 x 1
(a) – sin 2x (b) 2 sin 2x (c) 2 cos 2x (d) – 2 sin 2x
d 1 sin 2 x
40. [AISSE 1985; DSSE 1986]
dx 1 sin 2 x
(a) sec 2 x (b) sec 2 x (c) sec 2 x (d) sec 2 x
4 4 4
tan x cot x dy
41. If y , then
tan x cot x dx
(a) 2 tan 2x sec 2x (b) tan 2x sec 2x (c) – tan 2x sec 2x (d) – 2 tan 2x sec 2x
d
42. sec 2 x cos ec 2 x [DSSE 1981]
dx
(a) 4 cosec 2x . cot 2x (b) – 4 cosec 2x . cot 2x (c) – 4 cosec x . cot 2x (d) None of these
5x dy
43. If y cos 2 (2 x 1) , then [IIT 1980]
3
(1 x ) 2 dx
5(3 x ) 5(3 x ) 5(3 x )
(a) 2 sin(4 x 2) (b) 2 sin(4 x 4 ) (c) 2 sin(2 x 1) (d) None of these
3(1 x ) 3(1 x ) 3(1 x )
dy
44. If y sin x y , then equals to [Rajasthan PET 2001]
dx
sin x cos x sin x cos x
(a) (b) (c) (d)
2y 1 2y 1 2y 1 2y 1
d
45. log | x | .....( x 0)
dx
1 1
(a) (b) (c) x (d) – x
x x
d
46. log x
(1 / x ) is equal to [AMU 1999]
dx
1 1
(a) (b) – 2 (c) (d) 0
2 x x2 x
d
47. log(log x ) [IIT 1985]
dx
x log x
(a) (b) (c) (x log x )1 (d) None of these
log x x
d
48. (log tan x ) [MNR 1986]
dx
(a) 2 sec 2x (b) 2 cosec 2x (c) sec 2x (d) cosec 2x
dy
49. If y log x x , then [MNR 1978]
dx
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller riyashah120527. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75759 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now