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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 151. |
`sin^(4)x cos^(3)x` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(1)/(5)sin^(5)x - (1)/(7)sin^(7)x` | |
| 152. |
`((logx)^(4))/(x)` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `2sqrt(tan)x` | |
| 153. |
`(e^(ax)-e^(-ax))/(e^(ax) + e^(-ax))` का समाकलन कीजिये - |
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Answer» Correct Answer - `(1)/(a)log(e^(ax)+e^(-ax))` माना `e^(ax)+e^(-ax) = t rArr (a^(ax) - e^(-ax))dx = (1)/(a)dt` तब `I = (1)/(a)int(1)/(t)dt = (1)/(a)log(e^(ax) + e^(-ax))` |
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| 154. |
`(ax^(n))/(x^(n+1)+b)` का समाकलन कीजिये - |
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Answer» Correct Answer - `(a)/(n+1)log(x^(n+1)+b)` माना `x^(n+1)+b = t rArr x^(n)dx = (1)/(n+1)dt` |
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| 155. |
`a cos (ax +b)` का समाकलन कीजिये - |
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Answer» Correct Answer - `sin(ax+b)` `I = intsin^(2//3) x cos ^(3) x dx` ` =int (cos^(2) x . sin^(2//3)x)cos x dx` `= int{(1-sin^(2)x)sin^(2//3)}(cos x) dx` `=int(sin^(2//3) x - sin^(8//3)x )cos x dx` अब यदि `sin x = t rArr cos x dx = dt` तब `I = int(t^(2//3) - t^(8//3))dt = (t^(5//3))/(5//3) = (t^(11//3))/(11//3)+c` |
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| 156. |
`(x)/(9-4x^(2))` का समाकलन कीजिए - |
| Answer» Correct Answer - `-(1)/(8)log|9-4x^(2)|+c` | |
| 157. |
`sin x sin(cos x)` का समाकलन कीजिए - |
| Answer» Correct Answer - `cos(cos x)+c` | |
| 158. |
`int sec^(2)(3x + 5)dx` समाकलनो का माना ज्ञात कीजिए - |
| Answer» Correct Answer - `(1)/(3)tan(3x + 5)+c` | |
| 159. |
`cot^(3)xcosec x` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `-(1)/(3)cosec^(3)x+ cosecx` | |
| 160. |
`cot^(4) x cosec^(2) x` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `-(1)/(5)cot^(5)x` | |
| 161. |
`(e^(n))/(e^(n) +2)` का समाकलन कीजिये - |
| Answer» Correct Answer - `log (2+e^(x))` | |
| 162. |
`(1+logx)/(x)` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(1)/(2)[1+logx]^(2)` | |
| 163. |
`sqrt(ax + b)` का समाकलन कीजिए - |
| Answer» Correct Answer - `(2)/(3a)(ax +b)^(3//2)+c` | |
| 164. |
`(x)/(sqrt(x+4)),xgt 0` का समाकलन कीजिए - |
| Answer» Correct Answer - `(2)/(3)sqrt(x+4)(x-8)+c` | |
| 165. |
`(1)/(5x -4)` का समाकलन कीजिये - |
| Answer» Correct Answer - `(1)/(5)log(5x - 4)` | |
| 166. |
`intcos 2x dx` समाकलनो का माना ज्ञात कीजिए - |
| Answer» Correct Answer - `(1)/(2)sin 2x + c` | |
| 167. |
`(1)/(e^(x)+e^(-x))` का समाकलन कीजिये - |
| Answer» Correct Answer - `tan^(-1)(e^(x))` | |
| 168. |
`(x)/(a^(4) +x)` का समाकलन कीजिये - |
| Answer» Correct Answer - x-a^4*log(a^4+6)+c | |
| 169. |
`(-4(cot^(-1) x)^(3))/(1+x^(2))` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(cot^(-1)x)^(4)` | |
| 170. |
`e^(2-3x)` का समाकलन कीजिये - |
| Answer» Correct Answer - ` - (1)/(3)e^(2-3x)` | |
| 171. |
`xsqrt(x+2)` का समाकलन कीजिए - |
| Answer» Correct Answer - `(2)/(5)(x+2)^(5//2)-(4)/(3)(x+2)^(3//2)` | |
| 172. |
`(4sin^(-1)x)/(sqrt(1-x^(2)))` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `2(sin^(-1)x)^(2)` | |
| 173. |
`int(3x+5)^(7)dx` समाकलनो का माना ज्ञात कीजिए - |
| Answer» Correct Answer - `((3x + 5)^(8))/(24)+c` | |
| 174. |
`sqrt(((1+x)/(1-x)))` का समाकलन कीजिये - |
| Answer» Correct Answer - `-[cos^(-1) x+ sqrt(1-x^(2))]` | |
| 175. |
`(e^(x))/((1+e^(x))^(3))` का समाकलन कीजिये - |
| Answer» Correct Answer - `(-1)/(2(1+e^(x))^(2))` | |
| 176. |
`(1)/(sqrt((1-x^(2))sin^(-1)x))` का समाकलन कीजिये - |
| Answer» Correct Answer - `logsin^(-1)` | |
| 177. |
`(tanx)/(3+2tan^(2)x)` का समाकलन कीजिये - |
| Answer» Correct Answer - `-(1)/(4)log(2+cos^(2)x)` | |
| 178. |
`(1)/(3x+4)` का समाकलन कीजिये - |
| Answer» Correct Answer - `(1)/(3)log(3x+4)` | |
| 179. |
`(3sec^(-1)x)/(xsqrt(x^(2) -1))` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(3)/(2)(sec^(-1)x)^(2)` | |
| 180. |
`(1)/(xsqrt(x^(4) -1))` का समाकलन कीजिये - |
| Answer» Correct Answer - `(1)/(6)sin^(-1)(3x^(2))` | |
| 181. |
`(x)/(x^(2)+2x+1)` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(1)/(5)(logx)^(5)` | |
| 182. |
`(sin x)/(sqrt(9-cos^(2)x))` का समाकलन कीजिये - |
| Answer» Correct Answer - `-sin^(-1)((cosx)/(3))` | |
| 183. |
`(1)/sqrt((1-x^(2))cos^(-1)x)` का समाकलन कीजिये - |
| Answer» Correct Answer - `- log cos^(-1)` | |
| 184. |
`(sin x + cos x)/(sin x - cosx)` का समाकलन कीजिये - |
| Answer» Correct Answer - `log(sinx - cosx)` | |
| 185. |
`(1)/(sqrt(1-(3x - 7)^(2)))` का समाकलन कीजिये - |
| Answer» Correct Answer - `(1)/(3)sin^(-1)(3x -7)` | |
| 186. |
`(1)/(2+cos x)` का समाकलन कीजिये - |
| Answer» Correct Answer - `(2)/(sqrt(3))tan^(-1)((tanx//2)/(sqrt(3)))` | |
| 187. |
`int(dx)/((25-19x^(2)))` का मान ज्ञात कीजिये | |
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Answer» माना `I = int (dx)/(sqrt(25-16x)) = (1)/(4) int(dx)/(1+((3x)/(2))^(2))` माना `(4x )/(5)=sin theta" " rArr dx = (5)/(4) cos theta d theta` `therefore theta = sin^(-1)((4x)/(5))` `therefore I = (1)/(5) xx(5)/(4) int (cos theta d theta)/(sqrt(1-sin ^(2) theta)) = (1)/(4) int (cos theta d theta)/(cos theta)` ` = (1)/(4) int d theta = (1)/(4) theta = (1)/(4) sin ^(-1)((4x)/(5))` |
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| 188. |
`int(dx)/(xsqrt([(log x)^(2) + 10]))` का मान ज्ञात कीजिये । |
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Answer» माना `I = int (dx)/(xsqrt([(logx)^(2)+10]))` माना `log x = t rArr (1)/(x) dx = dt `तथा `sqrt(10) = a` `therefore " "I int(dt)/(sqrt(t^(2) +a^(2))) = log [ t sqrt(t^(2) +a^(2))]` `= log [log x + sqrt((logx)^(2)+ 10)]` |
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| 189. |
`(1+cosx)/((x+sinx)^(2))` का समाकलन कीजिये - |
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Answer» Correct Answer - `(-1)/(x+sin x)` माना `x+sin x = t " "rArr (1+cosx)dx =dt` तब `I = int(1)/(r^(2))dt` तब `I = int(1)/(r^(2))dt` |
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| 190. |
`(cosx)/(sqrt((1)/(4)+cos^(2)x))` का समाकलन कीजिये - |
| Answer» Correct Answer - `sin^(-1)((2sinx)/(sqrt(5)))` | |
| 191. |
`sqrt(sin) x cos^(3)x` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `log(x+1)+(1)/(x+1)` | |
| 192. |
`(2x-1)/(sqrt(x^(2) -x - 1))` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `tan(log x)` | |
| 193. |
`sqrt(cosx)sin ^(3)x` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `-(2)/(3)cos^(3)(cos x)^(3//2) +(2)/(7)(cosx)^(7//2)` | |
| 194. |
`(cos(sin^(-1)x))/(sqrt(1-x^(2)))` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `-cos(tan^(-1)x)` | |
| 195. |
`(2x+1)sin^(2)(x^(2) +x+1)` फलनो का x के सापेक्ष समाकलन कीजिये । |
| Answer» Correct Answer - `(x^(2)+x + 1)/(2) - (1)/(4)sin 2(x^(2) + x+1)` | |
| 196. |
`int(dx)/(5+4cosx)`का मान ज्ञात कीजिये । |
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Answer» माना ` I = int(dx)/(5+4cosx)` `=int(dx)/(5[sin^(2).(x)/(2) + cos^(2).(x)/(2)] +4[cos^(2).(x)/(2)sin^(2).(x)/(2)])` `= int(dx)/(9cos^(2) x//2 +sin^(2)x//2)` अश व हर को `cos^(2)s//2` से भगा देने पर `I = int (sec^(2)x//2dx)/(9+tan^(2)x//2)=(1)/(9)int(sec^(2)x//2sx)/(1+((tanx//2)/(3)))` माना `(tan x//2)/(3) = t therefore (1)/(6) sec^(2)x//2 dx = dt` `rArr " "sec^(2) x//2 dx = 6dt` `therefore " "I= (6)/(9)int(dt)/(1+t^(2)) = (2)/(3) tan^(-1) t = (2)/(3) tan^(-1)((tanx//2)/(3))` |
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| 197. |
`cosx^(@)` का समाकलन कीजिये - |
| Answer» Correct Answer - `(1)/(3)sin(3x +pi//3)` | |
| 198. |
`cos x^(@)` का समाकलन कीजिये - |
| Answer» Correct Answer - `(180)/(pi)sin x^(@)` | |
| 199. |
`int tan^(4) x sec^(2) x dx `का मान ज्ञात कीजिये | |
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Answer» माना `I= int tan^(4) x sec^(2) x dx` माना `tan x = t" "therefore" "sec^(2) x dx = dt` `therefore" "I = int t^(4) dt = (1)/(5)t^(5) = (1)/(5)tan^(5) x` |
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| 200. |
`(sin^(-1)x)/(sqrt(1-x^(2)))` का समाकलन कीजिए - |
| Answer» Correct Answer - `2sinsqrt(x)+c` | |