TS EAMCET MATHS PRACTICE MCQ
1)➤\(\int \frac{x^2-1}{\left( x^4+3x^2+1\right) tan^{-1}\left( x+\frac{1}{x}\right) }dx \:is\:equal\:to\)
A. \(tan^{-1}\left( x+\frac{1}{x}\right)\)
B.\(cot^{-1}\left( x+\frac{1}{x}\right)\)
C.\(log\left( x+\frac{1}{x}\right)\)
D.\(log[tan^{-1}\left( x+\frac{1}{x}\right)]\)
A. \(tan^{-1}\left( x+\frac{1}{x}\right)\)
B.\(cot^{-1}\left( x+\frac{1}{x}\right)\)
C.\(log\left( x+\frac{1}{x}\right)\)
D.\(log[tan^{-1}\left( x+\frac{1}{x}\right)]\)
2)➤\(\int \frac{e^x}{\left( 2+e^x\right) \left( e^x+1\right) }dx \:is\: equal \:to\)
A.\(log\left( \frac{e^x+1}{e^x+2}\right) \)
B.\(log\left( \frac{e^x+2}{e^x+1}\right)+C \)
C.\(\left( \frac{e^x+1}{e^x+2}\right) \)
D.\(\left( \frac{e^x+2}{e^x+1}+C\right) \)
A.\(log\left( \frac{e^x+1}{e^x+2}\right) \)
B.\(log\left( \frac{e^x+2}{e^x+1}\right)+C \)
C.\(\left( \frac{e^x+1}{e^x+2}\right) \)
D.\(\left( \frac{e^x+2}{e^x+1}+C\right) \)
3)➤\(\int tan\left( sin^{-1}x\right) dx \: is \: equal\:to\)
A.\(\frac{1}{\sqrt{1-x^2}}+c\)
B.\(\sqrt{1-x^2}+c\)
C.\( \frac{-x}{\sqrt{1-x^2}}+c\)
D.\(-\sqrt{1-x^2}+c\)
A.\(\frac{1}{\sqrt{1-x^2}}+c\)
B.\(\sqrt{1-x^2}+c\)
C.\( \frac{-x}{\sqrt{1-x^2}}+c\)
D.\(-\sqrt{1-x^2}+c\)
4)➤\(\int \frac{\left( x^3+3x^2+3x+1\right) }{\left( x+1\right) ^5}dx\: is\:equal\:to\)
A.\(-\frac{1}{\left( x+1\right) }+c\)
B.\(\frac{1}{5}log\left( x+1\right) +c\)
C.\(log\left( x+1\right)+c\)
D. \(tan^{-1}x+c\)
A.\(-\frac{1}{\left( x+1\right) }+c\)
B.\(\frac{1}{5}log\left( x+1\right) +c\)
C.\(log\left( x+1\right)+c\)
D. \(tan^{-1}x+c\)
5)➤\(If \int \frac{2e^x+3e^{-x}}{3e^x+4e^{-x}}dx\\=Ax+B log\left( 3e^x+4\right)+c\\ then\)
A.\(A=\frac{-3}{4},B=\frac{1}{24}\)
B.\(A=\frac{3}{4},B=\frac{-1}{4}\)
C.\(A=\frac{1}{4},B=\frac{1}{24}\)
D.\(A=\frac{-3}{4},B=\frac{1}{4}\)
A.\(A=\frac{-3}{4},B=\frac{1}{24}\)
B.\(A=\frac{3}{4},B=\frac{-1}{4}\)
C.\(A=\frac{1}{4},B=\frac{1}{24}\)
D.\(A=\frac{-3}{4},B=\frac{1}{4}\)
6)➤\(\int \frac{x^2+1}{x^4-x^2+1}dx\)
A.\(tan^{-1}\left( 2x^2-1\right) +c\)
B.\(tan^{-1}\left( \frac{x^2+1}{x}\right) +c\)
C.\(sin^{-1}\left( x-\frac{1}{x}\right) +c\)
D.\(tan^{-1}\left( \frac{x^2-1}{x}\right) +c\)
A.\(tan^{-1}\left( 2x^2-1\right) +c\)
B.\(tan^{-1}\left( \frac{x^2+1}{x}\right) +c\)
C.\(sin^{-1}\left( x-\frac{1}{x}\right) +c\)
D.\(tan^{-1}\left( \frac{x^2-1}{x}\right) +c\)
7)➤\(\int \frac{10x^9+10^xlog_e10}{10^x+x^{10}}dx\)
A.\(10^x-x^{10}+c\)
B.\(10^x+x^{10}+c\)
C.\(\left( 10^x-x^{10}\right) ^{-1}+c\)
D.\(log\left( 10^x+x^{10}\right) +c\)
A.\(10^x-x^{10}+c\)
B.\(10^x+x^{10}+c\)
C.\(\left( 10^x-x^{10}\right) ^{-1}+c\)
D.\(log\left( 10^x+x^{10}\right) +c\)
8)➤\(\int \frac{2dx}{\sqrt{1-4x^2}}dx\)
A.\(tan^{-1}\left( 2x\right) +c\)
B.\(cot^{-1}\left( 2x\right) +c\)
C.\(cos^{-1}\left( 2x\right) +c\)
D.\(sin^{-1}\left( 2x\right) +c\)
A.\(tan^{-1}\left( 2x\right) +c\)
B.\(cot^{-1}\left( 2x\right) +c\)
C.\(cos^{-1}\left( 2x\right) +c\)
D.\(sin^{-1}\left( 2x\right) +c\)
9)➤\(\int \left( \frac{x+2}{x+4}\right) ^2e^xdx\)
A.\(\frac{2xe^x}{x+4}+c\)
B.\(e^x\left( \frac{x-2}{x+4}\right) +c\)
C.\(e^x\left( \frac{x+2}{x+4}\right) +c\)
D.\(e^x\left( \frac{x}{x+4}\right) +c\)
A.\(\frac{2xe^x}{x+4}+c\)
B.\(e^x\left( \frac{x-2}{x+4}\right) +c\)
C.\(e^x\left( \frac{x+2}{x+4}\right) +c\)
D.\(e^x\left( \frac{x}{x+4}\right) +c\)
10)➤\(\int f\left( x\right) dx=g\left( x\right) +c,\\then\:\int f^{-1}\left( x\right) dx\:is\:equal\:to\)
A.\( xf^{-1}\left( x\right) +c\)
B. \(f\left\{ \left. g^{-1}\left( x\right) \right\} \right. +c\)
C.\( xf^{-1}\left( x\right) -g\left\{ f^{-1}\left( x\right) \right\}+c\)
D.\(g^{-1}\left( x\right) +c\)
A.\( xf^{-1}\left( x\right) +c\)
B. \(f\left\{ \left. g^{-1}\left( x\right) \right\} \right. +c\)
C.\( xf^{-1}\left( x\right) -g\left\{ f^{-1}\left( x\right) \right\}+c\)
D.\(g^{-1}\left( x\right) +c\)
If you have any doubt,let me know.