of 19
Magnet and Its Properties
994 Differentiation and Applications of Derivatives
Differentiation and Applications of Derivatives 993
Derivative at a point, Standard differentiation
1.
[MNR 1986](a)
(b)
(c)
(d)
2. =
[IIT 1985](a)
(b)
(c)
(d)None of these
3.
[AI CBSE 1980](a)
(b)
(c)
(d)None of these
4. If , then (a)
(b)
(c)
(d)None of these
5.
(a)
(b)
(c)
(d)None of these
6. If , then
(a)y(b)
(c)
(d)
7. If then
[Karnataka CET 1999](a)y(b)
(c)
(d)None of these
8. If then
(a)
(b)
(c)
(d)
9. If then
(a)
(b)
(c)
(d)None of these
10.
(a)
(b)
(c)
(d)None of these
11.
[AISSE 1984, 85; MNR 1983; RPET 1997](a)
(b)
(c)
(d)1
12. = [AISSE 1981; AI CBSE 1979](a)
(b)
(c)
(d)
13.
(a)
(b)
(c)
(d)None of these
14. If then at =(a) 2(b)2
(c)
(d)0
15. If then
[Roorkee 1981; MP PET 2004](a)
(b)
(c)
(d)None of these
16.
(a)
(b)
(c)x(d)
17. If then is a (a)Function of x(b)Function of y(c)Function of x and y(d)Constant
18. , then the points at which are(a)1, 3(b)1, 3
(c) 1, 3(d)None of these
19. If then
(a)1(b)2
(c)3(d) 3
20. If , then(a)
(b)
(c)
(d)None of these
21. If , then
(a)
(b)
(c)
(d)None of these
22. The differential coefficient of is (a)
(b)
(c)
(d)None of these23.
(a)
(b)
(c)
(d)None of these24. is equal to [MP PET 2004](a)
(b)
(c)
(d)
25.
[AISSE 1985; DSSE 1986](a)
(b)
(c)
(d)
26. If , then (a)
(b)
(c)
(d)
27.
(a)
(b)
(c)
(d)
28. If , then =
[IIT 1979](a)
(b)
(c)
(d)229. If then
(a)
(b)
(c)
(d)None of these
30. If , then
(a)
(b)
(c)
(d)None of these
31.
(a)
(b)
(c)
(d)
32. If then at is [IIT 1985; RPET 2000; MP PET 2000;
Karnataka CET 2002; Pb. CET 2002](a)e(b)
(c)1(d)None of these33. If then
(a)
(b)
(c)
(d)None of these34. If , then
(a)
(b)
(c)
(d)
35. =(a)
(b)
(c)
(d)
36. If , then is [Orissa JEE 2004](a)
(b)
(c)
(d)
37. If , then
(a)
(b)
(c)
(d)
38.
(a)
(b)
(c)
(d)
39. If then
(a)
(b)
(c)
(d)
40.
(a)
(b)
(c)
(d)None of these41.
(a)
(b)
(c)
(d)
42.
(a)
(b)
(c)
(d)
43.
(a)
(b)
(c)
(d)None of these44. [AISSE 1985, 87; DSSE 1982, 84](a)1(b)1/2
(c)
(d)
45.
(a)
(b)
(c)
(d)
46.
[AI CBSE 1985](a)
(b)
(c)
(d)None of these47.
(a)
(b)
(c)
(d)None of these48. If then
(a)
(b)
(c)
(d)
49. If , then
[UPSEAT 1999; AMU 2002; Kerala (Engg.) 2005](a)0(b)
(c)1(d)None of these50.
[RPET 2003](a)
(b)
(c)
(d)
51. If , then =(a)
(b)
(c)
(d)
52. If then
(a)
(b)
(c)
(d)None of these53.
(a)
(b)
(c)
(d)
54. If then
(a)
(b)
(c)
(d)
55. If then
(a)
(b)
(c)
(d)None of these56.
(a)
(b)
(c)
(d)
57. If , then
(a)
(b)
(c)
(d)None of these58. If , then
[AISSE 1986](a)
(b)
(c)
(d)None of these59. If then
(a)
(b)
(c)
(d)
60.
[DSSE 1979](a)
(b)
(c)
(d)None of these
61. If , then [DSSE 1987](a)
(b)
(c)
(d)None of these
62. If , then
[AISSE 1987](a)
(b)
(c)
(d)
63. If , then [AISSE 1981, 83, 84, 85; DSSE 1985; AI CBSE 1981, 83](a)
(b)
(c)
(d)None of these
64.
[DSSE 1979](a)
(b)
(c)
(d)
65.
[AISSE 1985](a)
(b)
(c)
(d)
66.
[DSSE 1981](a)
(b)
(c)
(d)None of these67. [DSSE 1979, 81; CBSE 1981](a)
(b)
(c)
(d)None of these68. =
[AISSE 1979](a)
(b)
(c)
(d)None of these69. If , then [DSSE 1986](a)
(b)
(c)
(d)
70. If , then
[DSSE 1984](a)
(b)
(c)
(d)
71. The differential coefficient of the given function with respect to x is[MP PET 1993](a)
(b)
(c)
(d)
72.
[BIT Ranchi 1990](a)
(b)
(c)
(d)
73.
[BIT Ranchi 1989; Roorkee 1989; RPET 1996](a)
(b)0
(c)
(d)174. If ,then
[BIT Ranchi 1990](a)
(b)
(c)
(d)None of these
75.
[DSSE 1979](a)
(b)
(c)
(d)None of these76.
[AISSE 1982](a)
(b)
(c)
(d)
77.
[DSSE 1981](a)
(b)
(c)
(d)None of these78.
[AI CBSE 1983](a)
(b)
(c)
(d)None of these79. If , then
[AI CBSE 1982](a)
(b)
(c)
(d)
80. If then
[AI CBSE 1982](a)
(b)
(c)
(d)None of these81.
[AI CBSE 1984](a)
(b)
(c)
(d)None of these82. If then
[AI CBSE 1985](a)
(b)
(c)
(d)
83. If , then
[AI CBSE 1986](a)
(b)
(c)
(d)
84.
[AI CBSE 1987](a)
(b)
(c)
(d)
85. If , then
[AI CBSE 1988](a)
(b)
(c)
(d)
86. If , then
[Roorkee 1971](a)
(b)
(c)
(d)None of these87.
[AI CBSE 1982](a)1(b)
(c)
(d)None of these
88. If , then [AI CBSE 1988](a)
(b)
(c)
(d)None of these89. If , then
[MNR 1984](a)0(b)1
(c)2(d)390.
(a)
(b)
(c)
(d)
91.
(a)
(b)
(c)
(d)None of these92.
(a)
(b)
(c)
(d)
93. =
(a)
(b)
(c)
(d)
94. If then
[MNR 1982](a)0(b)1
(c)x(d)None of these
95. At =(a)1(b)1
(c)0(d)None of these96.
(a)0(b)1
(c) 1(d) 297. =
[AISSE 1989](a)
(b)
(c)
(d)None of these98. If , then
[MP PET 1994, 95]
(a)
(b)
(c)
(d)
99. If , then
(a)0(b)1
(c) 1(d)None of these
100. If , then =
[MP PET 1994]
(a)1(b) 1
(c)x(d)
101. If and , then =
[MP PET 1994]
(a)
(b)
(c)
(d)None of these
102. If , where is continuous at , then is equal to
(a)0(b)
(c)
(d)None of these
103. If then
(a)
(b)
(c)
(d)None of these
104. If , then is equal to
(a)
(b)
(c)
(d)None of these
105. is equal to [RPET 1995]
(a)
(b)
(c)
(d)
106. is equal to
[RPET 1995]
(a)
(b)
(c)
(d)
107. If , then is equal to
[Roorkee 1995]
(a)0(b)
(c)1/2(d)1
108. If , then is equal to
[RPET 1995](a)
(b)
(c)1 xy(d)
109. Differential coefficient of is [RPET 1995]
(a)
(b)
(c)
(d)
110. If , then
[RPET 1995, 2000]
(a)1(b)2
(c)3(d) 2
111.
[MP PET 1995]
(a)
(b)
(c)
(d)
112. If , then
[MP PET 1995]
(a)
(b)
(c)
(d)
113. If , then
(a)
(b)
(c)
(d)None of these
114. If , then
(a)
(b)
(c)
115. (d)None of these
116. If , then
[Roorkee 1978; Kurukshetra CEE 1998]
(a)0(b)1
117. (c)2(d)None of these
118. The derivative of tanx x with respect to x is [SCRA 1996]
(a)
(b)tan x119. (c)
(d)
120. If then
(a)2(b)0
121. (c)
(d) 2
122. If ,then
(a)0(b)1
(c)
(d)None of these
123. If , then is equal to
(a)
(b)
(c)
124. (d)None of these
125. equals
(a)
(b)1
(c)
(d)
126. For the curve at is
[Karnataka CET 1993]
(a)1/2(b)1
127. (c)1(d)2
128. Differential coefficient of is[MP PET 1996]
(a) (b)
(c) (d)
129. If , then the value of
[MP PET 1996; Pb. CET 2001]
(a)e(b)1
(c)0(d)
130. For the function , the value of x for which vanishes, is
[MP PET 1996]
(a)
(b)
(c)3(d)
131. If , then is
(a)1(b)3
(c)2(d)0
132. If , then is
[SCRA 1996]
(a)
(b)
133. (c)
(d)
134. If , then
(a)
(b)
(c)3(d)1
135. If , then
[MP PET 1997]
(a)
(b)
(c)
(d)
136. If , then
[MP PET 1997]
(a)
(b)
(c)
(d)
137. If, then is equal to
(a)
(b)
(c)
(d)
138. If , then is equal to
(a)
(b)
139. (c)
(d)
140. The first derivative of the function with respect to x at is
[MP PET 1998]
(a)2(b)1
(c)
(d)
141. The values of x, at which the first derivative of the function w.r.t. x is , are
[MP PET 1998]
(a)
(b)
(c)
(d)
142. If , then is
[MP PET 1999]
(a)
(b)
143. (c)
(d)
144. If , then is at v = 9 equal to [MP PET 1999]
(a)1(b)1
145. (c)2(d)None of these
146. equals
[RPET 1996]
(a)
(b)
(c)
(d)
147.
[RPET 1997]
(a)sec x(b)sin x
(c)tan x(d)cosec x148. If , then is equal to
[Kurukshetra CEE 1998]
(a)
(b)
(c)
(d)
149. The derivative of is
[SCRA 1996]
(a)
(b) 2x150. (c)
(d)
151. The derivative of at is [SCRA 1996]
(a)0(b)1
(c)1(d)Does not exist
152. The derivative of is
[SCRA 1996]
(a)
(b)
(c)
(d)
153. If , then equals
[SCRA 1996]
(a)
(b)
(c)
(d)
154. If then the value of
[Karnataka CET 1999; Pb. CET 2000]
(a)1(b)1/e
155. (c)2/e(d)
156. The derivative of at x = 2 is [AMU 1999](a) 3(b)0
157. (c)3(d)Not defined
158. If then at is
[AMU 1999]
(a)2 / 3(b)3 / 2
(c)2(d)0
159. is equal to
[AMU 1999]
(a)
(b) 2
(c)
(d)0
160. The value of at is[MP PET 2000](a) 2(b)0
(c)2(d)4161.
[AMU 2000]
(a)
(b)
(c)
(d)
162. If then is[AMU 2000](a)0(b)
(c) 1(d)
163. is equal to
[AMU 2000]
(a)
(b)
(c)
(d)
164. If has a derivative at then is equal to
[AMU 2000]
(a)
(b)
(c)
(d)
165. Given that . The relationship is valid if is equal to[AMU 2000](a)
(b)
(c)
(d)
166. The derivative of at is[RPET 2001; Kurukshetra CEE 2002](a)0(b)1
(c)1(d)Not defined
167. If then equals to[RPET 2001](a)
(b)
(c)
(d)
168. If then
[Karnataka CET 2001](a)
(b)
(c)
(d)
169. If then
[MP PET 2001]
(a)0(b)x170. (c)
(d)
171. If then is [UPSEAT 2001](a)
(b)
(c)0(d)1
172. If and at , then the ratio is equal to
[AMU 2001]
(a)
(b)5 : 2
173. (c)3 : 5(d)1 : 2
174.
[Karnataka CET 2001; Pb. CET 2001]
(a)
(b)
(c)
(d)
175. equals to[RPET 2001](a)1(b)
(c)
(d)
176. If then is [DCE 2002; Kurukshetra CEE 2001](a)
(b)
177. (c)
(d)None of these
178. The differential coefficient of the function at the point is [RPET 2002; Pb. CET 2000, 04](a) 2(b)0
179. (c)2(d)Undefined
180. If is a differentiable function, then is
[UPSEAT 2002]
(a)
(b)
(c)
(d)
181. If , then equals[MP PET 2002](a)
(b)
(c)
(d)
182. If then
[EAMCET 2002](a) 1(b)1
(c)0(d)a
183. Derivative of with respect to x is [Kerala (Engg.) 2002]
(a)
(b)
(c)
(d)
184. If then at is [Kerala (Engg.) 2002](a)
(b)
(c)
(d)
185. The derivative of at the point is
[Orissa JEE 2002]
(a)3(b) 3
186. (c)0(d)Does not exist
187. Derivative of the function , is[Orissa JEE 2002]
(a)
(b)
188. (c)
(d)None of these
189. If , then is equal to [Pb. CET 2002](a)
(b)
190. (c)
(d)
191. If then the value of is [Pb. CET 2000] (a)
(b)
192. (c)
(d)
193. If then is equal to [Pb. CET 2004](a)
(b)
194. (c)
(d)
195. If then [Karnataka CET 2004](a)2(b)2
196. (c)1/2(d)1/2197. If where
, then is [J & K 2005]
(a) 1(b)1
198. (c)0(d)Indeterminate
199. If then is equal to
[J & K 2005]
(a)1/2(b)2
200. (c)2m/n(d)m/ 2n201. If then is equal to[Karnataka CET 2005]
(a)
(b)
(c)
(d)
202. The derivative of function is . If then is equal to
[J & K 2005]
(a)1(b)0
(c)1(d)None of these
203. Let be a polynomial function of the second degree. If and are in A.P. then , , are in
[AMU 2005]
(a)A.P.(b)G.P.
204. (c)H.P.(d)None of these
205. =
[Kerala (Engg.) 2005]
(a)
(b)
(c)
(d)
206. (e)
207. If then what is the value of the derivative of at
[Orissa JEE 2005]
(a)
(b)
208. (c)
(d)
209. If , then is
[AMU 2005]
(a)
(b)
210. (c)1(d)
211. The derivative of at is equal to
[Kerala (Engg.) 2005]
(a)0(b)
(c)
(d)
(e)
212. If then
[Kerala (Engg.) 2005]
(a)2(b) 1
(c)
(d)0
(e)
Differentiation of implict function, Parametric and Composite functions, Logarithmic differentiation, Differentiation of infinite series1. If and then
[AISSE 1984; Roorkee 1974; SCRA 1996;
Karnataka CET 2003](a)
(b)
(c)
(d)
2. If and , then
(a)
(b)
(c)
(d)
3. If then
[RPET 1997; MP PET 2001](a)
(b)
(c)
(d)
4. If and then
(a)
(b)
5. (c)1(d)2
6. If and , then
[Karnataka CET 2000; Pb. CET 2002](a)
(b)
(c)
(d)
7. If , then
[Karnataka CET 1993]
(a)
(b)
(c)
(d)
8. If then
[AI CBSE 1979](a)
(b)
(c)
(d)None of these
9. If , then [DSSE 1979](a)
(b)
10. (c)
(d)None of these
11. , then [RPET 1989, 96](a)
(b)
12. (c)
(d)
13. If ,, then at
(a)
(b)
(c)
(d)None of these
14. If then
[Karnataka CET 2000; UPSEAT 2001;
Pb. CET 2001; Kerala (Engg.) 2005](a)
(b)
15. (c)
(d)
16. If then [DSSE 1979](a)
(b)
17. (c)
(d)None of these
18. If , then =[DSSE 1981; CBSE 1981](a)
(b)
(c)
(d)None of these19. If then
[DSSE 1980; CBSE 1980](a)
(b)
20. (c)
(d)None of these21. If , then [AI CBSE 1980](a)
(b)
22. (c)
(d)None of these23. If ,then [AI CBSE 1979](a)
(b)
24. (c)
(d)None of these
25. If , then
(a)
(b)
26. (c)
(d)None of these27. If and , then
[MP PET 1987](a)
(b)
(c)
28. (d)None of these29. If, then the derivative of the composite function is equal to
[Orissa JEE 2003]
(a)0(b)
30. (c)1(d)2
31. Let g (x) be the inverse of an invertible function which is differentiable at x = c, then equals
(a)
(b)
(c)
(d)None of these
32. Let be the inverse of the function and . Then is equal to
[Kurukshetra CEE 1996]
(a)
(b)
33. (c)
(d)
34. Let f and g be differentiable functions satisfying and (identity function). Then is equal to
(a)
(b)2
(c)
(d)None of these
35. The differential coefficient of when is
[Kurukshetra CEE 1998; DCE 2000]
(a)
(b)
36. (c)
(d)
37. The derivative of is
[AMU 2001]
(a)
(b)
(c)
(d)
38. Let , and then
[EAMCET 2002](a)
(b)
(c)
(d)
39. If
EMBED Equation.3 , then
(a)1(b)2
(c)3(d)4
40. If , then
[Kurukshetra CEE 1998]
(a)
(b)
(c)
(d)
41. If then
(a)
(b)
(c)
(d)None of these
42. If then =
(a)
(b)
(c)
(d)
43. If then is equal to
(a)
(b)
(c)
(d)
44. If , , then
=
[EAMCET 1994]
(a)
(b)
45. (c)
(d)
46. If and
EMBED Equation.3 then is [UPSEAT 2002](a)
(b)
47. (c)
(d)
48. Let and then is [UPSEAT 2004](a)
(b)
49. (c)
(d)None of these
50. If , then [EAMCET 1994]
(a)
(b)
51. (c)
(d) None of these
52. If , then dy/dx = [RPET 1987]
(a)
(b)
(c)
(d)None of these
53. If , then
[EAMCET 1992]
(a)
(b)
54. (c)
(d)
55. If , then equals [RPET 1996]
(a)
(b)
56. (c)
(d)
57. If and , then equals [RPET 1996; MP PET 2002]
(a)
(b)
58. (c)
(d)
59. If then equals [RPET 1999](a)
(b)
(c)
(d)None of these
60. If sin(x+y)=log(x+y), then =
[Karnataka CET 1993; RPET 1989, 92; Roorkee 2000]
(a)2(b) 2
61. (c)1(d)1
62. If and , then
[MP PET 1994]
(a)1(b)
63. (c)
(d)1
64. If, then
[DCE 1999](a)
(b)
(c)
(d)cosec(65. If then , at , is[Kerala (Engg.) 2002](a)1(b)1
(c)
(d)
66. If and , then is equal to [Kerala (Engg.) 2002]
(a)1/2(b)2/5
67. (c)3/2(d)1/3
68. If then
[Karnataka CET 2004](a)
(b)
69. (c)
(d)
70. If and , then at the value of is equal to
[Pb. CET 2000](a)2(b)2
71. (c)
(d)
72. If then =
[IIT Screening 2004](a)1(b)1
(c)2(d)0
73. If , then
[AISSE 1984; DSSE 1982; MNR 1979; SCRA 1996;
RPET 1996; Kerala (Engg.) 2002](a)
(b)
74. (c)
(d)
75. The first derivative of the function with respect to x at x = 1 is
[MP PET 1998]
(a)
(b)0
76. (c)
(d)
77. If then [AISSE 1981; RPET 1995](a)
(b)
(c)
(d)
78. If , then
[AISSE 1990; UPSEAT 2002; DCE 2002](a)
(b)
(c)
(d)
79. If , then
[MP PET 1987, 2004; MNR 1984; Roorkee 1954;
BIT Ranchi 1991; RPET 2000](a)
(b)
(c)
(d)None of these
80. then(a)
(b)
81. (c)
(d)None of these
82. If , then [MP PET 1995; AMU 2000](a)
(b)
83. (c)
(d)None of these
84. If then
[MNR 1978](a)
(b)
85. (c)
(d)None of these86. If ,then
(a)
(b)
(c)
(d)
87. If , then
(a)
(b)
(c)
(d)None of these
88. If then
(a)
(b)
(c)
(d)None of these
59. If , then
(a)
(b)
(c)
(d)
60. If then =(a)
(b)
(c)
(d)None of these61. If then
[RPET 1999; UPSEAT 2001](a)
(b)
(c)
(d)
62. If , then
(a)
(b)
63. (c)
(d)
64. If , then =(a)
(b)
65. (c)
(d)
66. The differential equation satisfied by the function , is
[MP PET 1998; Pb. CET 2001](a)
(b)
(c)
(d)
67. If , then
[BIT Ranchi 1992](a)
(b)
(c)
(d)
68.
[MP PET 1993](a)
(b)
69. (c)
(d)
70. If then
[DSSE 1996; MP PET 1997](a)
(b)
(c)
(d)
71. If , then
[AISSE 1989](a)
(b)
(c)
(d)
72. If then
[DSSE 1983, 84](a)
(b)
(c)
(d)None of these
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