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

The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are $2,4,10,12,14$, then the product of remaining two observations is

A
45
B
44
C
48
D
40
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\tan ^{-1}\left(\frac{2+3 x}{3-2 x}\right)+\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)$, then $\frac{d y}{d x}=$

A
$\frac{1}{1+25 x^2}$
B
$\frac{5}{1+25 x^2}$
C
$\frac{1}{1+5 x^2}$
D
$\frac{5}{1+5 x^2}$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x}$ is decreasing for all $x$ then

A
$\mathrm{ad}-\mathrm{bc}>0$
B
$ad - bc <0$
C
$a b-c d>0$
D
$\mathrm{ab }-\mathrm{cd}<0$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If a discrete random variable X is defined as follows

$\mathrm{P}[\mathrm{X}=x]=\left\{\begin{array}{cl}\frac{\mathrm{k}(x+1)}{5^x}, & \text { if } x=0,1,2 \ldots \ldots . \\ 0, & \text { otherwise }\end{array}\right.$

then $\mathrm{k}=$

A
$\frac{19}{25}$
B
$\frac{18}{25}$
C
$\frac{16}{25}$
D
$\frac{7}{25}$
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