1
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$

The $P\left(\frac{1}{4}< x<\frac{1}{3}\right)=\ldots$

A
$\frac{179}{864}$
B
$\frac{159}{864}$
C
$\frac{169}{864}$
D
$\frac{189}{864}$
2
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The eccentricity of the hyperbola $25 x^2-9 y^2=225$ is .......

A
$\frac{\sqrt{34}}{3}$
B
4
C
$\sqrt{34}$
D
$\frac{\sqrt{34}}{5}$
3
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $f(x)=x+\frac{1}{x}, x \neq 0$, then local maximum and minimum values of function $f$ are respectively.......

A
$-1$ and 1
B
$-2$ and 2
C
2 and $-2$
D
1 and $-1$
4
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Derivative of $\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right)$ is

A
1
B
cot t
C
tan t
D
0
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