MCQOPTIONS
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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 8201. |
If \[y=\frac{1}{1+{{x}^{\beta -\alpha }}+{{x}^{\gamma -\alpha }}}+\frac{1}{1+{{x}^{\alpha -\beta }}+{{x}^{\gamma -\beta }}}+\frac{1}{1+{{x}^{\alpha -\gamma }}+{{x}^{\beta -\gamma }}}\]then \[\frac{dy}{dx}\] is equal to |
| A. | 0 |
| B. | 1 |
| C. | \[(\alpha +\beta +\gamma ){{x}^{\alpha +\beta +\gamma -1}}\] |
| D. | None of these |
| Answer» B. 1 | |
| 8202. |
Let \[f(x)=\sqrt{x-1}+\sqrt{x+24-10\sqrt{x-1}};\] \[1 |
| A. | 0 |
| B. | \[\frac{1}{\sqrt{x-1}}\] |
| C. | \[2\sqrt{x-1}-5\] |
| D. | None of these |
| Answer» B. \[\frac{1}{\sqrt{x-1}}\] | |
| 8203. |
If \[\frac{d}{dx}\left( \frac{1+{{x}^{4}}+{{x}^{8}}}{1+{{x}^{2}}+{{x}^{4}}} \right)=a{{x}^{3}}+bx,\] then |
| A. | \[a=4,b=2\] |
| B. | \[a=4,b=-2\] |
| C. | \[a=-2,b=4\] |
| D. | None of these |
| Answer» C. \[a=-2,b=4\] | |
| 8204. |
Let\[f(x)=\underset{n\,\to \,\infty }{\mathop{\lim }}\,\frac{\log (2+x)-{{x}^{2n}}\sin x}{1+{{x}^{2n}}}\]. Then |
| A. | \[\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,f(x)\ne \underset{x\to {{1}^{-}}}{\mathop{\lim }}\,f(x)\] |
| B. | \[\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,f(x)=sin1\] |
| C. | \[\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,f(x)\] doesn?t exist |
| D. | None of these |
| Answer» B. \[\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,f(x)=sin1\] | |
| 8205. |
Let \[f(x)=\left\{ \begin{matrix} x\sin \left( \frac{1}{x} \right)+\sin \left( \frac{1}{{{x}^{2}}} \right),x\ne 0 \\ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]then \[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\] equals |
| A. | 0 |
| B. | \[-1/2\] |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 8206. |
If \[{{x}_{1}}=3\] and \[{{x}_{n+1}}=\sqrt{2+{{x}_{n}},}n\ge 1,\] then \[\underset{n\,\to \,\infty }{\mathop{\lim }}\,{{x}_{n}}\] is equal to |
| A. | \[-1\] |
| B. | \[2\] |
| C. | \[\sqrt{5}\] |
| D. | \[3\] |
| Answer» C. \[\sqrt{5}\] | |
| 8207. |
Let \[f(x)={{x}^{2}}-1,0 |
| A. | \[{{x}^{2}}-6x+9=0\] |
| B. | \[{{x}^{2}}-10x+21=0\] |
| C. | \[{{x}^{2}}-14x+49=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}-14x+49=0\] | |
| 8208. |
Derivative of \[{{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{2}}\] is |
| A. | \[\frac{1}{{{x}^{2}}}\] |
| B. | \[1-\frac{1}{{{x}^{2}}}\] |
| C. | 1 |
| D. | \[1+\frac{1}{{{x}^{2}}}\] |
| Answer» C. 1 | |
| 8209. |
A triangle has two of its vertices at \[P(a,0),Q(0,b)\] and the third vertex \[R(x,\,\,y)\] is moving along the straight line \[y=x.\] If A be the area of the triangle. Then \[\frac{dA}{dx}\] is equal to |
| A. | \[\frac{a-b}{2}\] |
| B. | \[\frac{a-b}{4}\] |
| C. | \[=-\left( \frac{a+b}{2} \right)\] |
| D. | \[\frac{a+b}{4}\] |
| Answer» D. \[\frac{a+b}{4}\] | |
| 8210. |
If \[y=\left( 1+\frac{1}{x} \right)\left( 1+\frac{2}{x} \right)\left( 1+\frac{3}{x} \right)....\left( 1+\frac{n}{x} \right)\] and \[x\ne 0.\] then \[\frac{dy}{dx}\] when \[x=-1\] is |
| A. | \[n!\] |
| B. | \[(n-1)!\] |
| C. | \[{{(-1)}^{n}}(n-1)!\] |
| D. | \[{{(-1)}^{n}}n!\] |
| Answer» D. \[{{(-1)}^{n}}n!\] | |
| 8211. |
Let \[f(x)=\alpha (x)\beta (x)\gamma (x)\] for all real x, where \[\alpha (x),\beta (x)\] and \[\gamma (x)\] are differentiable functions of\[x.\] If \[f'(2)=18f(2),\alpha '(2)=3\alpha (2),\beta '(2)=-4\beta (2)\] and \[\gamma '(2)-k\gamma (2),\] then the value of k is |
| A. | 14 |
| B. | 16 |
| C. | 19 |
| D. | None of these |
| Answer» D. None of these | |
| 8212. |
If \[\underset{x\to 0}{\mathop{\lim }}\,\,\,kx\cos ec\,x=\underset{x\to 0}{\mathop{\lim }}\,x\cos ec\,\,kx,\] then \[k=\] |
| A. | 1 |
| B. | -1 |
| C. | \[\pm 1\] |
| D. | \[\pm 2\] |
| Answer» D. \[\pm 2\] | |
| 8213. |
If \[F(u)=f(x,\,y,\,z)\] be a homogeneous function of degree \[n\] in \[x,\,y,\,z\] then \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}+z\frac{\partial u}{\partial z}=\] |
| A. | \[nu\] |
| B. | \[n\,F(u)\] |
| C. | \[\frac{n\,F(u)}{{F}'(u)}\] |
| D. | None of these |
| Answer» D. None of these | |
| 8214. |
If \[u={{\tan }^{-1}}\left( \frac{{{x}^{3}}+{{y}^{3}}}{x-y} \right)\], then \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=\] [EAMCET 1999] |
| A. | \[\sin 2u\] |
| B. | \[\cos 2u\] |
| C. | \[\tan 2u\] |
| D. | \[\sec 2u\] |
| Answer» B. \[\cos 2u\] | |
| 8215. |
If \[z={{\tan }^{-1}}\left( \frac{x}{y} \right)\], then \[{{z}_{x}}:{{z}_{y}}=\] |
| A. | \[y:x\] |
| B. | \[x:y\] |
| C. | \[-y:x\] |
| D. | \[-x:y\] |
| Answer» D. \[-x:y\] | |
| 8216. |
If \[z=\sec \,(y-ax)+\tan (y+ax),\] then \[\frac{{{\partial }^{2}}z}{\partial {{x}^{2}}}-{{a}^{2}}\frac{{{\partial }^{2}}z}{\partial {{y}^{2}}}=\] [EAMCET 2002] |
| A. | z |
| B. | 2z |
| C. | 0 |
| D. | ?z |
| Answer» D. ?z | |
| 8217. |
If \[{{z}^{2}}=\frac{{{x}^{1/2}}+{{y}^{1/2}}}{{{x}^{1/3}}+{{y}^{1/3}}}\] then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=\] [EAMCET 1999] |
| A. | \[\frac{z}{6}\] |
| B. | \[\frac{z}{3}\] |
| C. | \[\frac{z}{2}\] |
| D. | \[\frac{z}{12}\] |
| Answer» E. | |
| 8218. |
If \[\underset{x\to \infty }{\mathop{\lim }}\,\left\{ \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right\}=2\], then |
| A. | \[a=1,\text{ }b=1\] |
| B. | \[a=1,\text{ }b=2\] |
| C. | \[a=1,\text{ }v=-2\] |
| D. | None of these |
| Answer» D. None of these | |
| 8219. |
If \[\sqrt{1-{{x}^{2}}}+\sqrt{1-{{y}^{2}}}=a(x-y)\], then \[\frac{dy}{dx}\]= |
| A. | \[\sqrt{\frac{1-{{x}^{2}}}{1-{{y}^{2}}}}\] |
| B. | \[\sqrt{\frac{1-{{y}^{2}}}{1-{{x}^{2}}}}\] |
| C. | \[\sqrt{\frac{{{x}^{2}}-1}{1-{{y}^{2}}}}\] |
| D. | \[\sqrt{\frac{{{y}^{2}}-1}{1-{{x}^{2}}}}\] |
| Answer» C. \[\sqrt{\frac{{{x}^{2}}-1}{1-{{y}^{2}}}}\] | |
| 8220. |
\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+3} \right)}^{1/x}}\]is equal to |
| A. | \[{{e}^{4}}\] |
| B. | \[{{e}^{2}}\] |
| C. | \[{{e}^{3}}\] |
| D. | 1 |
| Answer» E. | |
| 8221. |
\[\frac{d}{dx}{{\cos }^{-1}}\sqrt{\cos x}=\] |
| A. | \[\frac{1}{2}\sqrt{1+\sec x}\] |
| B. | \[\sqrt{1+\sec x}\] |
| C. | \[-\frac{1}{2}\sqrt{1+\sec x}\] |
| D. | \[-\sqrt{1+\sec x}\] |
| Answer» B. \[\sqrt{1+\sec x}\] | |
| 8222. |
If \[y=\sqrt{x+\sqrt{x+\sqrt{x+........\text{to}}}}\infty \,,\,\text{then}\frac{dy}{dx}=\] [RPET 2002] |
| A. | \[\frac{x}{2y-1}\] |
| B. | \[\frac{2}{2y-1}\] |
| C. | \[\frac{-1}{2y-1}\] |
| D. | \[\frac{1}{2y-1}\] |
| Answer» E. | |
| 8223. |
\[\frac{d}{dx}\{{{(\sin x)}^{x}}\}\]= [DSSE 1985, 87; AISSE 1983] |
| A. | \[\left[ \frac{x\cos x+\sin x\log \sin x}{\sin x} \right]\] |
| B. | \[{{(\sin x)}^{x}}\left[ \frac{x\cos x+\sin x\log \sin x}{\sin x} \right]\] |
| C. | \[{{(\sin x)}^{x}}\left[ \frac{x\sin x+\sin x\log \sin x}{\sin x} \right]\] |
| D. | None of these |
| Answer» C. \[{{(\sin x)}^{x}}\left[ \frac{x\sin x+\sin x\log \sin x}{\sin x} \right]\] | |
| 8224. |
If \[y=\frac{\sqrt{a+x}-\sqrt{a-x}}{\sqrt{a+x}+\sqrt{a-x}}\], then \[\frac{dy}{dx}=\] [AISSE 1986] |
| A. | \[\frac{ay}{x\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| B. | \[\frac{ay}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| C. | \[\frac{ay}{x\sqrt{{{x}^{2}}-{{a}^{2}}}}\] |
| D. | None of these |
| Answer» B. \[\frac{ay}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] | |
| 8225. |
\[\frac{d}{dx}\left\{ \log \left( \frac{{{e}^{x}}}{1+{{e}^{x}}} \right) \right\}=\] |
| A. | \[\frac{1}{1-{{e}^{x}}}\] |
| B. | \[-\frac{1}{1+{{e}^{x}}}\] |
| C. | \[-\frac{1}{1-{{e}^{x}}}\] |
| D. | None of these |
| Answer» E. | |
| 8226. |
If \[{{x}^{3}}+{{y}^{3}}-3axy=0\], then \[\frac{dy}{dx}\] equals [RPET 1996] |
| A. | \[\frac{ay-{{x}^{2}}}{{{y}^{2}}-ax}\] |
| B. | \[\frac{ay-{{x}^{2}}}{ay-{{y}^{2}}}\] |
| C. | \[\frac{{{x}^{2}}+ay}{{{y}^{2}}+ax}\] |
| D. | \[\frac{{{x}^{2}}+ay}{ax-{{y}^{2}}}\] |
| Answer» B. \[\frac{ay-{{x}^{2}}}{ay-{{y}^{2}}}\] | |
| 8227. |
The differential coefficient of \[{{x}^{6}}\] with respect to \[{{x}^{3}}\] is [EAMCET 1988; UPSEAT 2000] |
| A. | \[5{{x}^{2}}\] |
| B. | \[3{{x}^{3}}\] |
| C. | \[5{{x}^{5}}\] |
| D. | \[2{{x}^{3}}\] |
| Answer» E. | |
| 8228. |
If \[y={{\tan }^{-1}}\left( \frac{x}{1+\sqrt{1-{{x}^{2}}}} \right)\], then \[\frac{dy}{dx}=\] |
| A. | \[\frac{1}{2\sqrt{1-{{x}^{2}}}}\] |
| B. | \[1-\sqrt{1-{{x}^{2}}}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| Answer» B. \[1-\sqrt{1-{{x}^{2}}}\] | |
| 8229. |
If \[y={{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}},\]where \[0 |
| A. | \[\frac{2}{1+{{x}^{2}}}\] |
| B. | \[\frac{2x}{1+{{x}^{2}}}\] |
| C. | \[\frac{-2}{1+{{x}^{2}}}\] |
| D. | \[\frac{-x}{1+{{x}^{2}}}\] |
| Answer» B. \[\frac{2x}{1+{{x}^{2}}}\] | |
| 8230. |
The general solution of the differential equation \[{{e}^{y}}\frac{dy}{dx}+({{e}^{y}}+1)\cot x=0\] is |
| A. | \[({{e}^{y}}+1)\cos x=K\] |
| B. | \[({{e}^{y}}+1)\text{cosec}\,x=K\] |
| C. | \[({{e}^{y}}+1)\sin x=K\] |
| D. | None of these |
| Answer» D. None of these | |
| 8231. |
The solution of \[(x\sqrt{1+{{y}^{2}}})dx+(y\sqrt{1+{{x}^{2}}})dy=0\] is |
| A. | \[\sqrt{1+{{x}^{2}}}+\sqrt{1+{{y}^{2}}}=c\] |
| B. | \[\sqrt{1+{{x}^{2}}}-\sqrt{1+{{y}^{2}}}=c\] |
| C. | \[{{(1+{{x}^{2}})}^{3/2}}+{{(1+{{y}^{2}})}^{3/2}}=c\] |
| D. | None of these |
| Answer» B. \[\sqrt{1+{{x}^{2}}}-\sqrt{1+{{y}^{2}}}=c\] | |
| 8232. |
The solution of the differential equation \[x({{e}^{2y}}-1)dy+({{x}^{2}}-1){{e}^{y}}dx=0\]is [AISSE 1990] |
| A. | \[{{e}^{y}}+{{e}^{-y}}=\log x-\frac{{{x}^{2}}}{2}+c\] |
| B. | \[{{e}^{y}}-{{e}^{-y}}=\log x-\frac{{{x}^{2}}}{2}+c\]\[\] |
| C. | \[{{e}^{y}}+{{e}^{-y}}=\log x+\frac{{{x}^{2}}}{2}+c\] |
| D. | None of these |
| Answer» B. \[{{e}^{y}}-{{e}^{-y}}=\log x-\frac{{{x}^{2}}}{2}+c\]\[\] | |
| 8233. |
The solution of the equation \[\frac{dy}{dx}=y({{e}^{x}}+1)\]is [AISSE 1986; AI CBSE 1984] |
| A. | \[y+{{e}^{({{e}^{x}}+x+c)}}=0\] |
| B. | \[\log y={{e}^{x}}+x+c\] |
| C. | \[\log y+{{e}^{x}}=x+c\] |
| D. | None of these |
| Answer» C. \[\log y+{{e}^{x}}=x+c\] | |
| 8234. |
The solution of the differential equation \[(1+{{x}^{2}})\frac{dy}{dx}=x(1+{{y}^{2}})\]is [AISSE 1983] |
| A. | \[2{{\tan }^{-1}}y=\log (1+{{x}^{2}})+c\] |
| B. | \[{{\tan }^{-1}}y=\log (1+{{x}^{2}})+c\] |
| C. | \[2{{\tan }^{-1}}y+\log (1+{{x}^{2}})+c=0\] |
| D. | None of these |
| Answer» B. \[{{\tan }^{-1}}y=\log (1+{{x}^{2}})+c\] | |
| 8235. |
The solution of the differential equation \[(1+\cos x)dy=(1-\cos x)dx\]is |
| A. | \[y=2\tan \frac{x}{2}-x+c\] |
| B. | \[y=2\tan x+x+c\] |
| C. | \[y=2\tan \frac{x}{2}+x+c\] |
| D. | \[y=x-2\tan \frac{x}{2}+c\] |
| Answer» B. \[y=2\tan x+x+c\] | |
| 8236. |
The solution of the differential equation \[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\] is [Pb. CET 2003] |
| A. | \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+c\] |
| B. | \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+c\] |
| C. | \[\log \left( xy \right)=\frac{1}{x}+\frac{1}{y}+c\] |
| D. | \[\log \left( xy \right)+\frac{1}{x}+\frac{1}{y}=c\] |
| Answer» B. \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+c\] | |
| 8237. |
The solution of the differential equation \[\frac{dy}{dx}=(1+x)(1+{{y}^{2}})\] is |
| A. | \[y=\tan ({{x}^{2}}+x+c)\] |
| B. | \[y=\tan (2{{x}^{2}}+x+c)\] |
| C. | \[y=\tan ({{x}^{2}}-x+c)\] |
| D. | \[y=\tan \left( \frac{{{x}^{2}}}{2}+x+c \right)\] |
| Answer» E. | |
| 8238. |
Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible? |
| A. | (3, 2) |
| B. | (2, 3/2) |
| C. | (2, 4) |
| D. | (2, 2) |
| Answer» C. (2, 4) | |
| 8239. |
What is the solution of the differential equation\[(x+y)(dx-dy)=dx+dy\]? |
| A. | \[x+y+ln\,\,(x+y)=c\] |
| B. | \[x-y+ln\,\,(x+y)=c\] |
| C. | \[y-x+ln\,\,(x+y)=c\] |
| D. | \[y-x-ln\,\,(x-y)=c\] |
| Answer» D. \[y-x-ln\,\,(x-y)=c\] | |
| 8240. |
The solution to the differential equation\[\frac{dy}{dx}=\frac{yf'(x)-{{y}^{2}}}{f(x)}\]Where \[f(x)\] is a given function is |
| A. | \[f(x)=y(x+c)\] |
| B. | \[f(x)=cxy\] |
| C. | \[f(x)=c(x+y)\] |
| D. | \[yf(x)=cx\] |
| Answer» B. \[f(x)=cxy\] | |
| 8241. |
What is the solution of the differential equation\[\frac{dx}{dy}+\frac{x}{y}-{{y}^{2}}=0\]? |
| A. | \[xy={{x}^{4}}+c\] |
| B. | \[xy={{y}^{4}}+c\] |
| C. | \[4xy={{y}^{4}}+c\] |
| D. | \[3xy={{y}^{3}}+c\] where c is an arbitrary constant. |
| Answer» D. \[3xy={{y}^{3}}+c\] where c is an arbitrary constant. | |
| 8242. |
If \[y+x\frac{dy}{dx}=x\frac{\phi (xy)}{\phi '(xy)}\] then \[\phi (xy)\] is equation to |
| A. | \[k{{e}^{{{x}^{2}}/2}}\] |
| B. | \[k{{e}^{{{y}^{2}}/2}}\] |
| C. | \[k{{e}^{xy/2}}\] |
| D. | \[k{{e}^{xy}}\] |
| Answer» B. \[k{{e}^{{{y}^{2}}/2}}\] | |
| 8243. |
What are the order and degree respectively of the differential equation\[y=x\frac{dy}{dx}+\frac{dx}{dy}\]? |
| A. | 1, 1 |
| B. | 1, 2 |
| C. | 2, 1 |
| D. | 2, 2 |
| Answer» C. 2, 1 | |
| 8244. |
What is the solution of the equation\[\ln \,\left( \frac{dy}{dx} \right)+x=0\]? |
| A. | \[y+{{e}^{x}}=c\] |
| B. | \[y-{{e}^{-x}}=c\] |
| C. | \[y+{{e}^{-x}}=c\] |
| D. | \[y-{{e}^{x}}=c\] |
| Answer» D. \[y-{{e}^{x}}=c\] | |
| 8245. |
What is the solution of the differential equation\[\sin \left( \frac{dy}{dx} \right)-a=0\]? |
| A. | \[y=x{{\sin }^{-1}}a+c\] |
| B. | \[x=y{{\sin }^{-1}}a+c\] |
| C. | \[y=x+x{{\sin }^{-1}}a+c\] |
| D. | \[y=\,{{\sin }^{-1}}a+c\] where c is an arbitrary constant. |
| Answer» B. \[x=y{{\sin }^{-1}}a+c\] | |
| 8246. |
Solution of the differential equation\[x=1+xy\frac{dy}{dx}+\frac{{{x}^{2}}{{y}^{2}}}{2!}{{\left( \frac{dy}{dx} \right)}^{2}}+\]\[\frac{{{x}^{3}}{{y}^{3}}}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}+............\] |
| A. | \[y=ln\,(x)+c\] |
| B. | \[y=\,{{(ln\,x)}^{2}}+c\] |
| C. | \[y=\pm \,ln\,(x)+c\] |
| D. | \[xy={{x}^{y}}+c\] |
| Answer» D. \[xy={{x}^{y}}+c\] | |
| 8247. |
The solution of the equation\[x\int\limits_{0}^{x}{y(t)dt=(x+1)\int_{0}^{x}{ty(t)dt,x>0}}\] is |
| A. | \[y=\frac{c}{{{x}^{3}}}{{e}^{{{x}^{3}}}}\] |
| B. | \[y=c{{x}^{3}}{{e}^{-{{x}^{3}}}}\] |
| C. | \[\frac{c}{{{x}^{3}}}{{e}^{-x}}\] |
| D. | None of these |
| Answer» E. | |
| 8248. |
The solution of the differential equation\[x\sin x\frac{dy}{dx}+(x\cos x+\sin x)y=\sin x\]. When \[y(0)=0\] is |
| A. | \[xy\sin x=1-\cos x\] |
| B. | \[xy\sin x+\cos x=0\] |
| C. | \[x\sin x+y\cos x=0\] |
| D. | \[x\sin x+y\cos x=1\] |
| Answer» B. \[xy\sin x+\cos x=0\] | |
| 8249. |
A continuously differentiable function \[\phi \,(x)\],\[x\in [0,\pi ]-\left\{ \frac{\pi }{2} \right\}\] satisfying \[y'=1+{{y}^{2}},y(0)=0=y(\pi )\] is |
| A. | \[\tan x\] |
| B. | \[x(x-\pi )\] |
| C. | \[(x-\pi )(1-{{e}^{x}})\] |
| D. | \[{{\sec }^{2}}x\] |
| Answer» B. \[x(x-\pi )\] | |
| 8250. |
The solution of \[\frac{dy}{dx}=\frac{{{e}^{x}}({{\sin }^{2}}x+\sin 2x)}{y(2\,\,\log \,\,y+1)}\] is |
| A. | \[{{y}^{2}}(\log \,y)-{{e}^{x}}{{\sin }^{2}}x+c=0\] |
| B. | \[{{y}^{2}}(\log \,y)-{{e}^{x}}{{\cos }^{2}}x+c=0\] |
| C. | \[{{y}^{2}}(\log \,y)+{{e}^{x}}{{\cos }^{2}}x+c=0\] |
| D. | None of these |
| Answer» B. \[{{y}^{2}}(\log \,y)-{{e}^{x}}{{\cos }^{2}}x+c=0\] | |