1
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$. The equation of the hyperbola with eccentricity 2 is

A
$\frac{x^2}{12}-\frac{y^2}{4}=1$
B
$\frac{x^2}{4}-\frac{y^2}{12}=1$
C
$\frac{x^2}{12}-\frac{y^2}{16}=1$
D
$\frac{x^2}{16}-\frac{y^2}{12}=1$
2
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$. The equation of the hyperbola with eccentricity 2 is

A
$\frac{x^2}{12}-\frac{y^2}{4}=1$
B
$\frac{x^2}{4}-\frac{y^2}{12}=1$
C
$\frac{x^2}{12}-\frac{y^2}{16}=1$
D
$\frac{x^2}{16}-\frac{y^2}{12}=1$
3
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet, hung in the open air, loses half its moisture during the first hour, then $90 \%$ of the moisture will be lost in ________ hours.

A
$2 \log _2 10$
B
$\frac{4 \log 10}{\log 2}$
C
$\quad \log _2 10$
D
$\frac{3 \log 10}{\log 2}$
4
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If a random variable $X$ has p.d.f. $f(x)=\left\{\begin{array}{ll}\frac{a x^2}{2}+b x & , \text { if } 1 \leqslant x \leqslant 3 \\ 0 & , \text { otherwise }\end{array}\right.$ and $f(2)=2$, then the values of $a$ and $b$ are, respectively

A
$11,-10$
B
$\quad-9,10$
C
$\frac{1}{6}, \frac{5}{6}$
D
$9,-8$
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