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.
| 3001. |
Solution set of the inequality \[6\le -3(2x-5) |
| A. | \[(0,\,3/2)\] |
| B. | \[\left( 1/2,\,3/2 \right]\] |
| C. | \[\left[ 1/2,\,3/2 \right)\] |
| D. | \[\left[ 0,\,1/2 \right)\] |
| Answer» C. \[\left[ 1/2,\,3/2 \right)\] | |
| 3002. |
Solution set of the inequality \[4x-3\ge 3x-4\]is |
| A. | (-1, 0) |
| B. | (1, \[\infty \]) |
| C. | \[\left( -\infty ,\,0 \right]\] |
| D. | \[\left[ -1,\,\infty \right)\] |
| Answer» E. | |
| 3003. |
The solution set of \[\frac{5x+8}{4-x}\le 2\]is |
| A. | \[(4,\,\infty )\cup \left( -\infty ,\,0 \right]\] |
| B. | \[[4,\,\infty ]\cup \left( -\infty ,\,4 \right]\] |
| C. | \[\left( -\infty ,\,0 \right]\cup (4,\,\infty )\] |
| D. | \[[4,\,\infty ]\cup \left( -\infty ,\,0 \right]\] |
| Answer» D. \[[4,\,\infty ]\cup \left( -\infty ,\,0 \right]\] | |
| 3004. |
For the inequality \[\frac{x}{3}+\frac{x}{2} |
| A. | \[(-\infty ,\,6)\] |
| B. | \[(-\infty ,\,6]\] |
| C. | \[[-\infty ,\,6)\] |
| D. | \[[-\infty ,\,6]\] |
| Answer» B. \[(-\infty ,\,6]\] | |
| 3005. |
The set of values of x which satisfy the inequations\[5x+2 |
| A. | \[(-\infty ,\,1)\] |
| B. | (2, 3) |
| C. | \[(-\infty ,\,3)\] |
| D. | \[(-\infty ,\,1)\cup (2,3)\] |
| Answer» E. | |
| 3006. |
Which interval does the following number line represent? |
| A. | (1, 1) |
| B. | (-2, 3) |
| C. | \[\left( -1,\,4 \right]\] |
| D. | \[\left( -\infty ,\,-1 \right)\] |
| Answer» D. \[\left( -\infty ,\,-1 \right)\] | |
| 3007. |
Which of the following set does not satisfy \[\left| x-3 \right|>4\]? |
| A. | \[(-\infty ,-1)\] |
| B. | \[(7,-\infty )\] |
| C. | \[(-1,7)\] |
| D. | none of these |
| Answer» D. none of these | |
| 3008. |
\[\underset{n\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{n}^{2}}-n+1}{{{n}^{2}}-n-1} \right)}^{n(n-1)}}\]is equal to |
| A. | \[e\] |
| B. | \[{{e}^{2}}\] |
| C. | \[{{e}^{-1}}\] |
| D. | 1 |
| Answer» C. \[{{e}^{-1}}\] | |
| 3009. |
The value of \[\underset{m\to \infty }{\mathop{\lim }}\,{{\left( \cos \frac{x}{m} \right)}^{m}}\]is |
| A. | 1 |
| B. | \[e\] |
| C. | \[{{e}^{-1}}\] |
| D. | none of these |
| Answer» B. \[e\] | |
| 3010. |
\[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{x=1}^{20}{{{\cos }^{2n}}(x-10)}\]is equal to |
| A. | 0 |
| B. | 1 |
| C. | 19 |
| D. | 20 |
| Answer» C. 19 | |
| 3011. |
The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{{{2}^{x}}+{{2}^{3-x}}-6}{\sqrt{{{2}^{-x}}}-{{2}^{1-x}}}\]is |
| A. | 16 |
| B. | 8 |
| C. | 4 |
| D. | 2 |
| Answer» C. 4 | |
| 3012. |
The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}\] is |
| A. | \[\frac{1}{8\sqrt{3}}\] |
| B. | \[\frac{1}{4\sqrt{3}}\] |
| C. | 0 |
| D. | None of these |
| Answer» B. \[\frac{1}{4\sqrt{3}}\] | |
| 3013. |
If \[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}}\], then \[dy/dx\]is equal to |
| A. | \[\frac{y}{x}\] |
| B. | \[\frac{x+y}{xy}\] |
| C. | \[xy\] |
| D. | \[\frac{x}{y}\] |
| Answer» B. \[\frac{x+y}{xy}\] | |
| 3014. |
Let y be an implicit function of x defined by \[{{x}^{2x}}-2{{x}^{x}}\cot y-1=0\]. Then y'(1) equals |
| A. | -1 |
| B. | 1 |
| C. | \[log\text{ }2\] |
| D. | \[-log\text{ }2\] |
| Answer» B. 1 | |
| 3015. |
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\]is equal to |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | none of these |
| Answer» E. | |
| 3016. |
If then \[\frac{dy}{dx}\] is |
| A. | \[\frac{2xy}{2y-{{x}^{2}}}\] |
| B. | \[\frac{xy}{y+{{x}^{2}}}\] |
| C. | \[\frac{xy}{y-{{x}^{2}}}\] |
| D. | \[\frac{2xy}{2+{{\frac{x}{y}}^{2}}}\] |
| Answer» B. \[\frac{xy}{y+{{x}^{2}}}\] | |
| 3017. |
If \[y={{\tan }^{-1}}\sqrt{\frac{x+1}{x-1}}\]. Then \[\frac{dy}{dx}\]is |
| A. | \[\frac{-1}{2\left| x \right|\sqrt{{{x}^{2}}-1}}\] |
| B. | \[\frac{-1}{2x\sqrt{{{x}^{2}}-1}}\] |
| C. | \[\frac{1}{2x\sqrt{{{x}^{2}}-1}}\] |
| D. | none of these |
| Answer» B. \[\frac{-1}{2x\sqrt{{{x}^{2}}-1}}\] | |
| 3018. |
If \[y=1+x+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}+...+\frac{{{x}^{n}}}{n!}\], then \[\frac{dy}{dx}\]is equal to |
| A. | y |
| B. | \[y+\frac{{{x}^{n}}}{n!}\] |
| C. | \[y-\frac{{{x}^{n}}}{n!}\] |
| D. | \[y-1-\frac{{{x}^{n}}}{n!}\] |
| Answer» D. \[y-1-\frac{{{x}^{n}}}{n!}\] | |
| 3019. |
If \[y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+...\infty },}}\]then \[\frac{dy}{dx}\]is |
| A. | \[\frac{x}{2y-1}\] |
| B. | \[\frac{x}{2y+1}\] |
| C. | \[\frac{1}{x(2y-1)}\] |
| D. | \[\frac{1}{x(1-2y)}\] |
| Answer» D. \[\frac{1}{x(1-2y)}\] | |
| 3020. |
If \[y={{x}^{({{x}^{x}})}}\], then \[\frac{dy}{dx}\]is |
| A. | \[y\left[ {{x}^{x}}(logex)logx+{{x}^{x}} \right]\] |
| B. | \[y\left[ {{x}^{x}}(logex)logx+x \right]\] |
| C. | \[y\left[ {{x}^{x}}(logex)logx+{{x}^{x-1}} \right]\] |
| D. | \[y\left[ {{x}^{x}}(lo{{g}_{e}}x)logx+{{x}^{x-1}} \right]\] |
| Answer» D. \[y\left[ {{x}^{x}}(lo{{g}_{e}}x)logx+{{x}^{x-1}} \right]\] | |
| 3021. |
If \[y={{\left( x+\sqrt{{{x}^{2}}+{{a}^{2}}} \right)}^{n}}\], then \[\frac{dy}{dx}\]is |
| A. | \[\frac{ny}{\sqrt{{{x}^{2}}+{{a}^{2}}}}\] |
| B. | \[-\frac{ny}{\sqrt{{{x}^{2}}+{{a}^{2}}}}\] |
| C. | \[\frac{nx}{\sqrt{{{x}^{2}}+{{a}^{2}}}}\] |
| D. | \[-\frac{nx}{\sqrt{{{x}^{2}}+{{a}^{2}}}}\] |
| Answer» B. \[-\frac{ny}{\sqrt{{{x}^{2}}+{{a}^{2}}}}\] | |
| 3022. |
If \[\left| {{\sin }^{-1}}x \right|+\left| {{\cos }^{-1}}x \right|=\frac{\pi }{2}\], then x\[\in \] |
| A. | R |
| B. | \[\left[ -1,1 \right]\] |
| C. | \[\left[ 0,1 \right]\] |
| D. | \[\phi \] |
| Answer» D. \[\phi \] | |
| 3023. |
The number of integer x satisfying \[{{\sin }^{-1}}\left| x-2 \right|+{{\cos }^{-1}}(1-\left| 3-x \right|)=\frac{\pi }{2}\] is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 3024. |
If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2}\], then \[\frac{1+{{x}^{4}}+{{y}^{4}}}{{{x}^{2}}-{{x}^{2}}{{y}^{2}}+{{y}^{2}}}\] is equal to |
| A. | 1 |
| B. | 2 |
| C. | \[\frac{1}{2}\] |
| D. | none of these |
| Answer» C. \[\frac{1}{2}\] | |
| 3025. |
If\[a{{\sin }^{-1}}x-b{{\cos }^{-1}}x=c,\]then\[a{{\sin }^{-1}}x+b{{\cos }^{-1}}x\]is equal to |
| A. | 0 |
| B. | \[\frac{\pi ab+c(b-c)}{a+b}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{\pi ab+c(a-b)}{a+b}\] |
| Answer» E. | |
| 3026. |
The value of the expression \[{{\sin }^{-1}}\left( \sin \frac{22\pi }{7} \right)\]\[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)\]+\[{{\tan }^{-1}}\left( \tan \frac{5\pi }{3} \right)\]+\[{{\sin }^{-1}}(cos2)\]is |
| A. | \[\frac{17\pi }{42}-2\] |
| B. | \[-\,2\] |
| C. | \[\frac{-\pi }{21}-2\] |
| D. | none of these |
| Answer» B. \[-\,2\] | |
| 3027. |
If \[\alpha \in \left( -\frac{3\pi }{2},-\pi \right)\]then the value of \[{{\tan }^{-1}}(cot\alpha )\]-\[{{\cot }^{-1}}(tan\alpha )+si{{n}^{-1}}(sin\alpha )+co{{s}^{-1}}(cos\alpha )\]is equal to |
| A. | \[2\pi +a\] |
| B. | \[\pi +a\] |
| C. | 0 |
| D. | \[\pi -a\] |
| Answer» D. \[\pi -a\] | |
| 3028. |
The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\] is an increasing function in |
| A. | \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\] |
| B. | \[\left( -\frac{\pi }{2},\frac{\pi }{4} \right)\] |
| C. | \[\left( 0,\frac{\pi }{2} \right)\] |
| D. | \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] |
| Answer» C. \[\left( 0,\frac{\pi }{2} \right)\] | |
| 3029. |
The trigonometric equation \[{{\sin }^{-1}}x=2{{\sin }^{-1}}a\] has a solution for |
| A. | \[\frac{1}{2}<\left| a \right|<\frac{1}{\sqrt{2}}\] |
| B. | All real values of a |
| C. | \[\left| a \right|<1/2\] |
| D. | \[\left| a \right|\ge \frac{1}{\sqrt{2}}\] |
| Answer» D. \[\left| a \right|\ge \frac{1}{\sqrt{2}}\] | |
| 3030. |
The number of real solutions of the equation\[\sqrt{1+\cos 2x}=\sqrt{2}{{\sin }^{-1}}(sinx),-\pi \le x\le \pi \] is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | infinite |
| Answer» D. infinite | |
| 3031. |
\[{{\cot }^{-1}}(\sqrt{\cos \alpha })-ta{{n}^{-1}}(\sqrt{\cos \alpha })=x\], then sin x is equal to |
| A. | \[{{\tan }^{2}}\frac{\alpha }{2}\] |
| B. | \[{{\cot }^{2}}\frac{\alpha }{2}\] |
| C. | \[\tan \alpha \] |
| D. | \[\cot \frac{\alpha }{2}\] |
| Answer» B. \[{{\cot }^{2}}\frac{\alpha }{2}\] | |
| 3032. |
If \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha ,\] then \[4{{x}^{2}}-4xy\,\cos \,\alpha +{{y}^{2}}\] is equal to |
| A. | 4 |
| B. | \[2{{\sin }^{2}}\alpha \] |
| C. | \[-4{{\sin }^{2}}\alpha \] |
| D. | \[4{{\sin }^{2}}\alpha \] |
| Answer» E. | |
| 3033. |
The value \[2{{\tan }^{-1}}\left[ \sqrt{\frac{a-b}{a+b}}\tan \frac{\theta }{2} \right]\]is equal to |
| A. | \[{{\cos }^{-1}}\left( \frac{a\cos \theta +b}{a+b\cos \theta } \right)\] |
| B. | \[{{\cos }^{-1}}\left( \frac{a+b\cos \theta }{a\cos \theta +b} \right)\] |
| C. | \[{{\cos }^{-1}}\left( \frac{a\cos \theta }{a+b\cos \theta } \right)\] |
| D. | \[{{\cos }^{-1}}\left( \frac{b\cos \theta }{a\cos \theta +b} \right)\] |
| Answer» B. \[{{\cos }^{-1}}\left( \frac{a+b\cos \theta }{a\cos \theta +b} \right)\] | |
| 3034. |
If \[3{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-4{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)+2{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)=\frac{\pi }{3}\]where \[\left| x \right| |
| A. | \[\frac{1}{\sqrt{3}}\] |
| B. | \[-\frac{1}{\sqrt{3}}\] |
| C. | \[\sqrt{3}\] |
| D. | \[-\frac{\sqrt{3}}{4}\] |
| Answer» B. \[-\frac{1}{\sqrt{3}}\] | |
| 3035. |
If \[{{\cot }^{-1}}(\sqrt{\cos \alpha )}-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x\], then sin x is |
| A. | \[{{\tan }^{2}}\frac{\alpha }{2}\] |
| B. | \[{{\cot }^{2}}\frac{\alpha }{2}\] |
| C. | \[\tan \alpha \] |
| D. | \[\cot \frac{\alpha }{2}\] |
| Answer» B. \[{{\cot }^{2}}\frac{\alpha }{2}\] | |
| 3036. |
The sum of the solutions of the equation\[2{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}+{{\cos }^{-1}}\sqrt{{{x}^{2}}+x}=\frac{3\pi }{2}\]is |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 3037. |
If \[\int \frac{\sin x}{\sin (x-\alpha )}dx=Ax+B\,\,\log \sin (x-\alpha )+c,\] then the value of (A, B) is |
| A. | \[(sin\alpha ,\,cos\alpha )\] |
| B. | \[(cos\alpha ,\,\sin \alpha )\] |
| C. | \[(-\sin \alpha ,\,\cos \alpha )\] |
| D. | \[(-\cos \alpha ,\,\sin \alpha )\] |
| Answer» C. \[(-\sin \alpha ,\,\cos \alpha )\] | |
| 3038. |
\[\int \frac{\sqrt{x-1}}{x\sqrt{x+1}}dx\]is equal to |
| A. | \[\ln \,\left| x-\sqrt{{{x}^{2}}-1} \right|-{{\tan }^{-1}}x+c\] |
| B. | \[\ln \,\left| x+\sqrt{{{x}^{2}}-1} \right|-{{\tan }^{-1}}x+c\] |
| C. | \[\ln \,\left| x-\sqrt{{{x}^{2}}-1} \right|-{{\sec }^{-1}}x+c\] |
| D. | \[\ln \,\left| x+\sqrt{{{x}^{2}}-1} \right|-{{\sec }^{-1}}x+c\] |
| Answer» E. | |
| 3039. |
\[\int \frac{\cos 4x-1}{\cot x-\tan x}dx\]is equal to |
| A. | \[\frac{1}{2}\ln \left| \sec 2x \right|-\frac{1}{4}{{\cos }^{2}}2x+c\] |
| B. | \[\frac{1}{2}\ln \left| \sec 2x \right|+\frac{1}{4}{{\cos }^{2}}x+c\] |
| C. | \[\frac{1}{2}\ln \left| \cos 2x \right|-\frac{1}{4}{{\cos }^{2}}2x+c\] |
| D. | \[\frac{1}{2}\ln \left| \cos 2x \right|+\frac{1}{4}{{\cos }^{2}}x+c\] |
| Answer» D. \[\frac{1}{2}\ln \left| \cos 2x \right|+\frac{1}{4}{{\cos }^{2}}x+c\] | |
| 3040. |
If\[\int \frac{3\sin x+2\cos x}{3\cos x+2\sin x}dx=ax+b\] ln\[\left| 2\sin x+3\cos x \right|+C\], then |
| A. | \[a=-\frac{12}{13},b=\frac{15}{39}\] |
| B. | \[a=-\frac{7}{13},b=\frac{6}{13}\] |
| C. | \[a=\frac{12}{13},b=-\frac{15}{39}\] |
| D. | \[a=-\frac{7}{13},b=-\frac{6}{13}\] |
| Answer» D. \[a=-\frac{7}{13},b=-\frac{6}{13}\] | |
| 3041. |
\[\int \frac{2\sin x}{(3+sin2x)}dx\]is equal to |
| A. | \[\frac{1}{2}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\] |
| B. | \[\frac{1}{2}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\] |
| C. | \[\frac{1}{4}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\] |
| D. | none of these |
| Answer» D. none of these | |
| 3042. |
\[\int \frac{{{\sin }^{8}}x-{{\cos }^{8}}x}{1-2{{\sin }^{2}}x{{\cos }^{2}}x}dx\] is equal to |
| A. | \[\frac{1}{2}\sin 2x+C\] |
| B. | \[-\frac{1}{2}\sin 2x+C\] |
| C. | \[-\frac{1}{2}\sin x+C\] |
| D. | \[-{{\sin }^{2}}x+C\] |
| Answer» C. \[-\frac{1}{2}\sin x+C\] | |
| 3043. |
If \[A=\int_{0}^{\pi }{\frac{\operatorname{cosx}}{{{(x+2)}^{2}}}dx,}\] then \[A=\int_{0}^{\pi /2}{\frac{\sin 2x}{x+1}dx,}\] is equal to |
| A. | \[\frac{1}{2}+\frac{1}{\pi +2}-A\] |
| B. | \[\frac{1}{\pi +2}-A\] |
| C. | \[1+\frac{1}{\pi +2}-A\] |
| D. | \[A-\frac{1}{2}-\frac{1}{\pi +2}\] |
| Answer» B. \[\frac{1}{\pi +2}-A\] | |
| 3044. |
If \[\int_{1}^{2}{{{e}^{{{x}^{2}}}}dx=a}\], then \[\int_{e}^{{{e}^{4}}}{\sqrt{\ln x}}\,dx\] is equal to |
| A. | \[2{{e}^{4}}-2e-a\] |
| B. | \[2{{e}^{4}}-e-a\] |
| C. | \[2{{e}^{4}}-e-2a\] |
| D. | \[{{e}^{4}}-e-a\] |
| Answer» C. \[2{{e}^{4}}-e-2a\] | |
| 3045. |
If \[\int_{0}^{1}{{{\cot }^{-1}}(1-x+{{x}^{2}})dx=\lambda \int_{0}^{1}{{{\tan }^{-1}}xdx,}}\] then \[\lambda \] is equal to |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 3046. |
If \[f(x)=\frac{{{e}^{x}}}{1+{{e}^{x}}},\,\,\,{{I}_{1}}=\int\limits_{f(-a)}^{f(a)}{xg\,(x(1-x))dx,}\] and \[{{I}_{2}}=\int\limits_{f(-a)}^{f(a)}{g(x(1-x))dx,}\] then the value of \[\frac{{{I}_{2}}}{{{I}_{1}}}\]is |
| A. | \[-\,1\] |
| B. | \[-\,2\] |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 3047. |
Given \[\int\limits_{0}^{\pi /2}{\frac{dx}{1+\sin x+\cos x}=\log \,2.}\] Then the value of the definite integral \[\int\limits_{0}^{\pi /2}{\frac{\sin x}{1+\sin x+\cos x}dx}\]is equal to |
| A. | \[\frac{1}{2}\log 2\] |
| B. | \[\frac{\pi }{2}-\log 2\] |
| C. | \[\frac{\pi }{4}-\frac{1}{2}\log 2\] |
| D. | \[\frac{\pi }{2}+\log 2\] |
| Answer» D. \[\frac{\pi }{2}+\log 2\] | |
| 3048. |
Let \[f(0)=0\] and \[\int\limits_{0}^{2}{f'(2t){{e}^{f(2t)}}dt=5}\]. Then the value of f(4) is |
| A. | log 2 |
| B. | log 7 |
| C. | log 11 |
| D. | log 13 |
| Answer» D. log 13 | |
| 3049. |
\[\int \frac{dx}{\cos x+\sqrt{3}\sin x}\] is equal to |
| A. | \[\frac{1}{2}\log \,\tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+c\] |
| B. | \[\frac{1}{2}\log \,\,\tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+c\] |
| C. | \[\log \,\,\tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+c\] |
| D. | \[\log \,\tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+c\] |
| Answer» B. \[\frac{1}{2}\log \,\,\tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+c\] | |
| 3050. |
\[\int \frac{dx}{x({{x}^{n}}+1)}\] is equal to |
| A. | \[\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\] |
| B. | \[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c\] |
| C. | \[\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\] |
| D. | none of these |
| Answer» B. \[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c\] | |