1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

One end of the diameter of the circle $x^2+y^2-6 x-5 y-1=0$ is $(-1,3)$, then the equation of the tangent at the other end of the diameter is

A
$8 x+y-58=0$
B
$8 x-2 y-52=0$
C
$8 x-y-54=0$
D
$8 x+2 y-60=0$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\tan ^{-1}\left(\frac{x+1}{x-1}\right)+\tan ^{-1}\left(\frac{x-1}{x}\right)=\tan ^{-1}(-7)$, then $x$ is equal to

A
$-$1
B
1
C
2
D
4
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the normal to the curve $y=x \log x$ parallel to $2 x-2 y+3=0$ is

A
$x+y=3 \mathrm{e}^{-2}$
B
$x-y=3 \mathrm{e}^{-2}$
C
$x-y=3 \mathrm{e}^2$
D
$x+y=3 \mathrm{e}^2$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] \mathrm{d} x,$$ where $x>0$ is

A
$\left(\tan ^{-1} x\right) \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
B
$\left(\tan ^{-1} x\right)^2 \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
C
$2\left(\tan ^{-1} x\right) \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
D
$2\left(\tan ^{-1} x\right)^2 \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
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