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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.
| 201. |
निम्नलिखित प्रश्न में `(dy)/(dx) ` ज्ञात कीजिये| ` y= sin ^(-1) ((1-x^(2))/(1+x^(2))), 0lt xlt 1 ` |
| Answer» Correct Answer - ` (-2) /(1+x^(2))` | |
| 202. |
यदि ` xsqrt( (1+y) )+ ysqrt((1+ x))=0` तब सिद्ध कीजिए की `(dy)/(dx) =- (1+x)^(-2)` |
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Answer» ` " "xsqrt ( (1+y))+ysqrt((1+x))=0 ` ` rArr" "xsqrt (( 1+y) )=-ysqrt((1+x))` ` rArr " "x^(2) (1+y)=y^(2) (1=x) ` ` " " `(दोनों और का वर्ग करने पर ) ` rArr" "(x^(2) -y^(2))+xy(x-y) =0 ` ` rArr " "(x-y) [x+ y+ xy] =0` `rArr x-y=0 ` या ` " " x+y (1+x) =0 ` यदि ` x- y=0 " "rArr " "y=x " "rArr " "(dy)/(dx) =1 ` yeh अभीष्ट परिणाम है अतः ` " "x+y (1+x) =0 " "rArr y= (-x) (1+x)` `therefore (dy)/(dx) =- [((1+x) (d)/(dx) (x) -x(d)/(dx) (1+x))/((1+x)^(2))]` ` " "=-[ ((1+ x)-x) /((1+x )^(2))=- [(1)/((1+x)^(2))]` ` therefore " "(dy)/(dx) =-(1+x)^(2) ` |
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| 203. |
यदि `x=2 log cot t ` व `y= tan t+ cot t ,` तब `(dy)/(dx) sin 2t +1=`A. ` cos ^(2)t `B. ` sin ^(2 ) t `C. ` cos2t`D. ` 2cos ^(2) t ` |
| Answer» Correct Answer - D | |
| 204. |
` cos ^(-1) sqrt(1-x^(2))` के सापेक्ष `sin ^(-1) x ` का अवकलन गुणांक है-A. ` (1)/(1-x^(2))`B. ` cos ^(-1) x `C. ` 1`D. इनमें से कोई नहीं |
| Answer» Correct Answer - C | |
| 205. |
यदि `x= 3cos theta - 2cos ^(3) theta ,y =3sin theta - 2sin ^3theta ,` तब `dy//dx=`A. `sin theta `B. ` cos theta `C. ` tan theta `D. ` cot theta ` |
| Answer» Correct Answer - D | |
| 206. |
निम्नलिखित प्रश्न में x के सापेक्ष अवकलन कीजिये- ` x^(x) -2sin x ` |
| Answer» Correct Answer - ` x^(x) (1+ log x) - 2 ^(sin x ) cosx log 2 ` | |
| 207. |
यदि ` y= sin (2sin ^(-1) x ) ` तब `(dy)/(dx) ` =A. ` sqrt(((1-y^(2))/(1-x^(2)))) `B. ` 2sqrt((1-y^(2) )/(1-x^(2)))`C. ` sqrt((1-x^(2))/(1-y^(2)))`D. इनमें से कोई नहीं |
| Answer» Correct Answer - B | |
| 208. |
यदि ` y=sin ^(-1) x+ sin ^(-1) sqrt( (1-x^(2)))` तब ` (dy)/(dx) = `A. ` (1)/(sqrt(1-x^(2)))`B. ` (x)/(sqrt(1-x^(2)))`C. ` 0 `D. इनमें से कोई नहीं |
| Answer» Correct Answer - C | |
| 209. |
यदि ` sqrt( x+y )+ sqrt(y-x)=lambda ,` तब `(d^(2)y)/(dx^(2))=`A. `(-2)/(lambda ^(2))`B. ` (2)/(lambda ^(2))`C. ` (2)/(lambda)`D. इनमें से कोई नहीं |
| Answer» Correct Answer - B | |
| 210. |
यदि ` sqrt((1-x^(2)))+ sqrt((1-y^(2)))= a(x-y) ,` तब `(dy)/(dx) =`A. ` sqrt(((1-y^(2))/(1-x^(2))))`B. ` sqrt(((1-x^(2))/(1-y^(2))))`C. ` sqrt((1-x^(2))(1-y^(2)))`D. इनमें से कोई नहीं |
| Answer» Correct Answer - A | |
| 211. |
` 10^(10x )` |
| Answer» Correct Answer - ` 10^(x) 10^(10x) (log _e x 10)^(2)` | |
| 212. |
` ((x-a)(x-b))/(sqrt((x-c)))` |
| Answer» Correct Answer - ` ((x-a)(x-b))/(sqrt(x-c))[(1)/(x-a)+(1)/(x-b)-(1)/((x-c))]` | |
| 213. |
निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिये-` sqrt((x^(2)+x+1)/(x^(2)-x +1))` |
| Answer» Correct Answer - ` sqrt((x^(2)+x+1)/(x^(2)-x+1))[(1-x^(2))/(x^(4)+x^(2)+1)]` | |
| 214. |
निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए -` tan ^(-1) [(acos x-bsin x )/(b cos x +asin a )] ` |
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Answer» Correct Answer - `-1` ` a = tsin theta ` व ` b= rcostheta ` रखने पर |
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| 215. |
निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिये-` (x+(1)/(x))^(x) +x^ (1+(1)/(x))` |
| Answer» Correct Answer - `(x+ (1)/(x) )^(x) [(x^(2)-1)/(x^(2)+1)+log (x+(1)/(x))]+x ^(1+(1)/(x))[(1)/(x)+(1)/(x^(2))-(log x )/(x ^(2))]` | |
| 216. |
यदि ` y= tan ^(-1) {(acos x -bsin x )/(bcos x + asin x )} ,(dy)/(dx)= `A. ` (1)/(1+x^(2))`B. ` (1)/(sqrt(1-x^(2)))`C. `-1`D. इनमें से कोई नहीं |
| Answer» Correct Answer - C | |
| 217. |
निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए -` sin ^(-1) [(a+ bcos x )/(b+acos x )] ` |
| Answer» Correct Answer - ` (-sqrt((b^(2)-a^(2))))/(b+acos x )` | |