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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.
| 3901. |
If \[{{\sin }^{-1}}(1-x)-2{{\sin }^{-1}}x=\pi /2\], then x equals [Orissa JEE 2005] |
| A. | \[\left( 0,\,-\frac{1}{2} \right)\] |
| B. | \[\left( \frac{1}{2},\,0 \right)\] |
| C. | {0} |
| D. | (-1, 0) |
| Answer» D. (-1, 0) | |
| 3902. |
If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\frac{\pi }{4}\] then [Karnataka CET 2005] |
| A. | \[x+y+xy=1\] |
| B. | \[x+y-xy=1\] |
| C. | \[x+y+xy+1=0\] |
| D. | \[x+y-xy+1=0\] |
| Answer» C. \[x+y+xy+1=0\] | |
| 3903. |
If \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha \], then \[4{{x}^{2}}-4xy\cos \alpha +{{y}^{2}}\] is equal to [AIEEE 2005] |
| A. | \[4{{\sin }^{2}}\alpha \] |
| B. | \[-4{{\sin }^{2}}\alpha \] |
| C. | \[2\sin 2\alpha \] |
| D. | \[4\] |
| Answer» B. \[-4{{\sin }^{2}}\alpha \] | |
| 3904. |
\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal to [Kerala (Engg.) 2005] |
| A. | \[{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\] |
| B. | \[2{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\] |
| C. | \[\frac{1}{2}{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\] |
| D. | \[2{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\] |
| E. | \[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\] |
| Answer» E. \[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\] | |
| 3905. |
\[{{\tan }^{-1}}\frac{1}{\sqrt{{{x}^{2}}-1}}=\] |
| A. | \[\frac{\pi }{2}+\text{cose}{{\text{c}}^{-1}}x\] |
| B. | \[\frac{\pi }{2}+{{\sec }^{-1}}x\] |
| C. | \[\text{cose}{{\text{c}}^{-1}}x\] |
| D. | \[{{\sec }^{-1}}x\] |
| Answer» D. \[{{\sec }^{-1}}x\] | |
| 3906. |
The value of \[{{\cos }^{-1}}(\cos 12)-{{\sin }^{-1}}(\sin 14)\] is [J & K 2005] |
| A. | -2 |
| B. | \[8\pi -26\] |
| C. | \[4\pi +2\] |
| D. | None of these |
| Answer» B. \[8\pi -26\] | |
| 3907. |
\[\sin \left( \frac{1}{2}{{\cos }^{-1}}\frac{4}{5} \right)=\] [Karnataka CET 2003] |
| A. | \[\frac{1}{\sqrt{10}}\] |
| B. | \[-\frac{1}{\sqrt{10}}\] |
| C. | \[\frac{1}{10}\]. |
| D. | \[-\frac{1}{10}\] |
| Answer» B. \[-\frac{1}{\sqrt{10}}\] | |
| 3908. |
The value of \[\sin \left( 2{{\tan }^{-1}}\left( \frac{1}{3} \right) \right)+\cos ({{\tan }^{-1}}2\sqrt{2})=\] [AMU 1999] |
| A. | \[\frac{16}{15}\] |
| B. | \[\frac{14}{15}\] |
| C. | \[\frac{12}{15}\] |
| D. | \[\frac{11}{15}\] |
| Answer» C. \[\frac{12}{15}\] | |
| 3909. |
If \[3{{\sin }^{-1}}\frac{2x}{1-{{x}^{2}}}-4{{\cos }^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}}+2{{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}=\frac{\pi }{3}\] then \[x\] = |
| A. | \[\sqrt{3}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 3910. |
\[4{{\tan }^{-1}}\frac{1}{5}-{{\tan }^{-1}}\frac{1}{239}\]is equal to [MNR 1995] |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | \[\frac{\pi }{4}\] |
| Answer» E. | |
| 3911. |
\[3{{\tan }^{-1}}a\]is equal to [MP PET 1993] |
| A. | \[{{\tan }^{-1}}\frac{3a+{{a}^{3}}}{1+3{{a}^{2}}}\] |
| B. | \[{{\tan }^{-1}}\frac{3a-{{a}^{3}}}{1+3{{a}^{2}}}\] |
| C. | \[{{\tan }^{-1}}\frac{3a+{{a}^{3}}}{1-3{{a}^{2}}}\] |
| D. | \[{{\tan }^{-1}}\frac{3a-{{a}^{3}}}{1-3{{a}^{2}}}\] |
| Answer» E. | |
| 3912. |
\[\sin \left( 4{{\tan }^{-1}}\frac{1}{3} \right)=\] |
| A. | \[\frac{12}{25}\] |
| B. | \[\frac{24}{25}\] |
| C. | \[\frac{1}{5}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{5}\] | |
| 3913. |
\[\frac{1}{2}{{\cos }^{-1}}\left( \frac{1-x}{1+x} \right)=\] |
| A. | \[{{\cot }^{-1}}\sqrt{x}\] |
| B. | \[{{\tan }^{-1}}\sqrt{x}\] |
| C. | \[{{\tan }^{-1}}x\] |
| D. | \[{{\cot }^{-1}}x\] |
| Answer» C. \[{{\tan }^{-1}}x\] | |
| 3914. |
\[\tan \left[ \frac{1}{2}{{\cos }^{-1}}\left( \frac{\sqrt{5}}{3} \right) \right]=\] [Roorkee 1986] |
| A. | \[\frac{3-\sqrt{5}}{2}\] |
| B. | \[\frac{3+\sqrt{5}}{2}\] |
| C. | \[\frac{2}{3-\sqrt{5}}\] |
| D. | \[\frac{2}{3+\sqrt{5}}\] |
| Answer» B. \[\frac{3+\sqrt{5}}{2}\] | |
| 3915. |
If \[2{{\cos }^{-1}}\sqrt{\frac{1+x}{2}}=\frac{\pi }{2},\]then \[x=\] |
| A. | 1 |
| B. | 0 |
| C. | -0.5 |
| D. | 44228 |
| Answer» C. -0.5 | |
| 3916. |
\[{{\tan }^{-1}}\left[ \frac{\cos x}{1+\sin x} \right]=\] |
| A. | \[\frac{\pi }{4}-\frac{x}{2}\] |
| B. | \[\frac{\pi }{4}+\frac{x}{2}\] |
| C. | \[\frac{x}{2}\] |
| D. | \[\frac{\pi }{4}-x\] |
| Answer» B. \[\frac{\pi }{4}+\frac{x}{2}\] | |
| 3917. |
\[\tan \left[ 2{{\tan }^{-1}}\left( \frac{1}{5} \right)-\frac{\pi }{4} \right]=\] [IIT 1984] |
| A. | \[\frac{17}{7}\] |
| B. | \[-\frac{17}{7}\] |
| C. | \[\frac{7}{17}\] |
| D. | \[-\frac{7}{17}\] |
| Answer» E. | |
| 3918. |
\[\tan \left( 2{{\cos }^{-1}}\frac{3}{5} \right)=\] |
| A. | \[\frac{7}{25}\] |
| B. | \[\frac{24}{25}\] |
| C. | \[-\frac{24}{7}\] |
| D. | \[\frac{8}{3}\] |
| Answer» D. \[\frac{8}{3}\] | |
| 3919. |
If \[2{{\tan }^{-1}}(\cos x)={{\tan }^{-1}}(2\text{cosec }x),\] then x = |
| A. | \[\frac{3\pi }{4}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | None of these |
| Answer» C. \[\frac{\pi }{3}\] | |
| 3920. |
If \[\cos (2{{\sin }^{-1}}x)=\frac{1}{9},\]then \[x=\] [Roorkee 1975] |
| A. | Only 2/3 |
| B. | Only -2/3 |
| C. | 2/3, -2/3 |
| D. | Neither 2/3 nor -2/3 |
| Answer» D. Neither 2/3 nor -2/3 | |
| 3921. |
If \[A={{\tan }^{-1}}x\], then \[\sin 2A=\] [MNR 1988; UPSEAT 2000] |
| A. | \[\frac{2x}{\sqrt{1-{{x}^{2}}}}\] |
| B. | \[\frac{2x}{1-{{x}^{2}}}\] |
| C. | \[\frac{2x}{1+{{x}^{2}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3922. |
If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi ,\] then \[\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=\] [MP PET 1991] |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{1}{xyz}\] |
| D. | \[xyz\] |
| Answer» C. \[\frac{1}{xyz}\] | |
| 3923. |
\[{{\cot }^{-1}}[{{(\cos \alpha )}^{1/2}}]-{{\tan }^{-1}}[{{(\cos \alpha )}^{1/2}}]=x,\]then \[\sin x=\] [AIEEE 2002] |
| A. | \[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\] |
| B. | \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\] |
| C. | \[\tan \alpha \] |
| D. | \[\cot \left( \frac{\alpha }{2} \right)\] |
| Answer» B. \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\] | |
| 3924. |
The value of \[\tan \left( {{\tan }^{-1}}\frac{1}{2}-{{\tan }^{-1}}\frac{1}{3} \right)\]is [AMU 2001] |
| A. | \[5/6\] |
| B. | \[7/6\] |
| C. | \[1/6\] |
| D. | \[1/7\] |
| Answer» E. | |
| 3925. |
\[{{\sec }^{-1}}[\sec (-{{30}^{o}})]=\] [MP PET 1992] |
| A. | \[-{{60}^{o}}\] |
| B. | \[-{{30}^{o}}\] |
| C. | \[{{30}^{o}}\] |
| D. | \[{{150}^{o}}\] |
| Answer» D. \[{{150}^{o}}\] | |
| 3926. |
The value of \[\tan \left[ {{\sin }^{-1}}\left( \frac{3}{5} \right)+{{\cos }^{-1}}\left( \frac{3}{\sqrt{13}} \right) \right]\]is [AMU 2001] |
| A. | \[\frac{6}{17}\] |
| B. | \[\frac{6}{\sqrt{13}}\] |
| C. | \[\frac{\sqrt{13}}{5}\] |
| D. | \[\frac{17}{6}\] |
| Answer» E. | |
| 3927. |
\[\cos \text{ }\left[ {{\cos }^{-1}}\text{ }\left( \frac{-1}{7} \right)+{{\sin }^{-1}}\text{ }\left( \frac{-1}{7} \right) \right]=\] [EAMCET 2003] |
| A. | \[-1/3\] |
| B. | 0 |
| C. | \[1/3\] |
| D. | \[4/9\] |
| Answer» C. \[1/3\] | |
| 3928. |
If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi ,\]then \[xy+yz+zx=\] [Karnataka CET 2003] |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | -3 |
| Answer» D. -3 | |
| 3929. |
The value of \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)-{{\sin }^{-1}}\left( \frac{1}{2} \right)\]is [MP PET 2003] |
| A. | \[{{45}^{o}}\] |
| B. | \[{{90}^{o}}\] |
| C. | \[{{15}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» E. | |
| 3930. |
The value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \cos \frac{5\pi }{3} \right)\]is [UPSEAT 2003] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{5\pi }{3}\] |
| C. | \[\frac{10\pi }{3}\] |
| D. | \[0\] |
| Answer» B. \[\frac{5\pi }{3}\] | |
| 3931. |
\[\sin \left\{ {{\tan }^{-1}}\left( \frac{1-{{x}^{2}}}{2x} \right)+{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right) \right\}\]is equal to [Kurukshetra CEE 2001] |
| A. | 0 |
| B. | 1 |
| C. | \[\sqrt{2}\] |
| D. | \[\frac{1}{\sqrt{2}}\] |
| Answer» C. \[\sqrt{2}\] | |
| 3932. |
If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\]then\[x\]is equal to [UPSEAT 2001] |
| A. | 0 |
| B. | \[\frac{1}{2}\] |
| C. | \[-\frac{\sqrt{3}}{2}\] |
| D. | \[\frac{1}{\sqrt{2}}\] |
| Answer» C. \[-\frac{\sqrt{3}}{2}\] | |
| 3933. |
The value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right)\]is [Roorkee 2000] |
| A. | 0 |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{2\pi }{3}\] |
| D. | \[\frac{10\pi }{3}\] |
| Answer» B. \[\frac{\pi }{2}\] | |
| 3934. |
If \[{{\sin }^{-1}}a+{{\sin }^{-1}}b+{{\sin }^{-1}}c=\pi ,\] then the value of \[a\sqrt{(1-{{a}^{2}})}+b\sqrt{(1-{{b}^{2}})}+c\sqrt{(1-{{c}^{2}})}\] will be [UPSEAT 1999] |
| A. | \[2abc\] |
| B. | \[abc\] |
| C. | \[\frac{1}{2}abc\] |
| D. | \[\frac{1}{3}abc\] |
| Answer» B. \[abc\] | |
| 3935. |
If \[{{\cos }^{-1}}\left( \frac{1}{x} \right)=\theta \], then \[\tan \theta \]= [MNR 1978; MP PET 1989] |
| A. | \[\frac{1}{\sqrt{{{x}^{2}}-1}}\] |
| B. | \[\sqrt{{{x}^{2}}+1}\] |
| C. | \[\sqrt{1-{{x}^{2}}}\] |
| D. | \[\sqrt{{{x}^{2}}-1}\] |
| Answer» E. | |
| 3936. |
\[\int_{{}}^{{}}{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}\ }dx=\] [AISSE 1990] |
| A. | \[-\sqrt{2}{{\tan }^{-1}}x+\sqrt{3}{{\tan }^{-1}}x+c\] |
| B. | \[-\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\] |
| C. | \[\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\] |
| D. | None of these |
| Answer» C. \[\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\] | |
| 3937. |
\[\int_{{}}^{{}}{\frac{{{x}^{2}}+x-1}{{{x}^{2}}+x-6}\ dx=}\] [AISSE 1988] |
| A. | \[x+\log (x+3)+\log (x-2)+c\] |
| B. | \[x-\log (x+3)+\log (x-2)+c\] |
| C. | \[x-\log (x+3)-\log (x-2)+c\] |
| D. | None of these |
| Answer» C. \[x-\log (x+3)-\log (x-2)+c\] | |
| 3938. |
\[\int_{{}}^{{}}{\frac{1}{(x-1)({{x}^{2}}+1)}dx}=\] [Roorkee 1984] |
| A. | \[\frac{1}{2}\log (x-1)-\frac{1}{4}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c\] |
| B. | \[\frac{1}{2}\log (x-1)+\frac{1}{4}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c\] |
| C. | \[\frac{1}{2}\log (x-1)-\frac{1}{2}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c\] |
| D. | None of these |
| Answer» B. \[\frac{1}{2}\log (x-1)+\frac{1}{4}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c\] | |
| 3939. |
Correct evaluation of \[\int_{{}}^{{}}{\frac{x}{(x-2)(x-1)}\ dx}\] is [MP PET 1993] |
| A. | \[{{\log }_{e}}\frac{{{(x-2)}^{2}}}{(x-1)}+p\] |
| B. | \[{{\log }_{e}}\frac{(x-1)}{(x-2)}+p\] |
| C. | \[\frac{x-1}{x-2}+p\] |
| D. | \[2{{\log }_{e}}\left( \frac{x-2}{x-1} \right)+p\] (where p is an arbitrary constant) |
| Answer» B. \[{{\log }_{e}}\frac{(x-1)}{(x-2)}+p\] | |
| 3940. |
If \[\int{\frac{2{{x}^{2}}+3.dx}{({{x}^{2}}-1)({{x}^{2}}-4)}}=\log {{\left( \frac{x-2}{x+2} \right)}^{a}}{{\left( \frac{x+1}{x-1} \right)}^{b}}+c\] then the values of a and b respectively are [AMU 2005] |
| A. | \[\frac{11}{12},\frac{5}{6}\] |
| B. | \[\frac{11}{12},\frac{-5}{6}\] |
| C. | \[-\frac{11}{12},\frac{5}{6}\] |
| D. | None of these |
| Answer» B. \[\frac{11}{12},\frac{-5}{6}\] | |
| 3941. |
\[\int_{{}}^{{}}{\frac{1}{\cos x(1+\cos x)}}\ dx=\] |
| A. | \[\log (\sec x+\tan x)+2\tan \frac{x}{2}+c\] |
| B. | \[\log (\sec x+\tan x)-2\tan \frac{x}{2}+c\] |
| C. | \[\log (\sec x+\tan x)+\tan \frac{x}{2}+c\] |
| D. | \[\log (\sec x+\tan x)-\tan \frac{x}{2}+c\] |
| Answer» E. | |
| 3942. |
\[\int{\frac{x\,\,dx}{{{x}^{2}}+4x+5}=}\] [RPET 2002] |
| A. | \[\frac{1}{2}\log ({{x}^{2}}+4x+5)+2{{\tan }^{-1}}(x)+c\] |
| B. | \[\frac{1}{2}\log ({{x}^{2}}+4x+5)-{{\tan }^{-1}}(x+2)+c\] |
| C. | \[\frac{1}{2}\log ({{x}^{2}}+4x+5)+{{\tan }^{-1}}(x+2)+c\] |
| D. | \[\frac{1}{2}\log ({{x}^{2}}+4x+5)-2{{\tan }^{-1}}(x+2)+c\] |
| Answer» E. | |
| 3943. |
\[\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}\] [AISSE 1990] |
| A. | \[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2x} \right)+c\] |
| B. | \[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2x}} \right)+c\] |
| C. | \[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2\sqrt{x}} \right)+c\] |
| D. | \[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2}x} \right)+c\] |
| Answer» E. | |
| 3944. |
\[\int_{{}}^{{}}{\frac{{{x}^{2}}-1}{{{x}^{4}}+{{x}^{2}}+1}\ dx=}\] [AISSE 1990] |
| A. | \[\frac{1}{2}\log \left( \frac{{{x}^{2}}+x+1}{{{x}^{2}}-x+1} \right)+c\] |
| B. | \[\frac{1}{2}\log \left( \frac{{{x}^{2}}-x-1}{{{x}^{2}}+x+1} \right)+c\] |
| C. | \[\log \left( \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right)+c\] |
| D. | \[\frac{1}{2}\log \left( \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right)+c\] |
| Answer» E. | |
| 3945. |
\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{7}}+1)}}=\] [Karnataka CET 2004] |
| A. | \[\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\] |
| B. | \[\frac{1}{7}\log \left( \frac{{{x}^{7}}}{{{x}^{7}}+1} \right)+c\] |
| C. | \[\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\] |
| D. | \[\frac{1}{7}\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\] |
| Answer» C. \[\log \left( \frac{{{x}^{7}}+1}{{{x}^{7}}} \right)+c\] | |
| 3946. |
\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{5}}+1)}}=\] [UPSEAT 2004] |
| A. | \[\frac{1}{5}\log {{x}^{5}}({{x}^{5}}+1)+c\] |
| B. | \[\frac{1}{5}\log {{x}^{5}}\left( \frac{1+{{x}^{5}}}{{{x}^{5}}} \right)+c\] |
| C. | \[\frac{1}{5}\log {{x}^{5}}\left( \frac{{{x}^{5}}}{{{x}^{5}}+1} \right)+c\] |
| D. | None of these |
| Answer» E. | |
| 3947. |
\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}\] [Roorkee 1979] |
| A. | \[n\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\] |
| B. | \[n\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\] |
| C. | \[\frac{1}{n}\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\] |
| D. | \[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\] |
| Answer» D. \[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\] | |
| 3948. |
\[\int_{{}}^{{}}{\frac{3\sin x+2\cos x}{3\cos x+2\sin x}\ dx=}\] |
| A. | \[\frac{12}{13}x-\frac{5}{13}\log (3\cos x+2\sin x)\] |
| B. | \[\frac{12}{13}x+\frac{5}{13}\log (3\cos x+2\sin x)\] |
| C. | \[\frac{13}{12}x+\frac{5}{13}\log (3\cos x+2\sin x)\] |
| D. | None of these |
| Answer» B. \[\frac{12}{13}x+\frac{5}{13}\log (3\cos x+2\sin x)\] | |
| 3949. |
\[\int_{{}}^{{}}{\frac{dx}{\cos x-\sin x}}\] is equal to [AIEEE 2004] |
| A. | \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}+\frac{3\pi }{8} \right)\, \right|+c\] |
| B. | \[\frac{1}{\sqrt{2}}\log \left| \cot \left( \frac{x}{2} \right)\, \right|+c\] |
| C. | \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{3\pi }{8} \right)\, \right|+c\] |
| D. | \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{\pi }{8} \right)\, \right|+c\] |
| Answer» B. \[\frac{1}{\sqrt{2}}\log \left| \cot \left( \frac{x}{2} \right)\, \right|+c\] | |
| 3950. |
\[\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}+2x+2}=}\] [Karnataka CET 2004] |
| A. | \[{{\sin }^{-1}}(x+1)+c\] |
| B. | \[{{\sinh }^{-1}}(x+1)+c\] |
| C. | \[{{\tanh }^{-1}}(x+1)+c\] |
| D. | \[{{\tan }^{-1}}(x+1)+c\] |
| Answer» E. | |