1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The mean of $n$ observations is $\bar{x}$. If three observations $\mathrm{n}+1, \mathrm{n}-1,2 \mathrm{n}-1$ are added such that mean remains same, then value of $n$ is

A
$\frac{2 \bar{x}+1}{3}$
B
$\frac{3 \bar{x}-1}{4}$
C
$\frac{3 \bar{x}+1}{4}$
D
$\frac{\bar{x}+1}{4}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to

A
$\frac{-1}{\sqrt{2}}$
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
D
$\sqrt{2}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the concentric circle, with the circle $\mathrm{C}_1$ having equation $x^2+y^2-6 x-4 y-12=0$ and having double area compared to the area of $\mathrm{C}_1$, is

A
$x^2+y^2-6 x-4 y=27$
B
$x^2+y^2-6 x-4 y=13$
C
$x^2+y^2-6 x-4 y=50$
D
$x^2+y^2-6 x-4 y=37$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $$(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0$$ where $a>-1$ then $\lim _\limits{a \rightarrow 0^{+}} \alpha(a)$ and $\lim _\limits{a \rightarrow 0^{+}} \beta(a)$ respectively are

A
1 and $-\frac{5}{2}$
B
$-$1 and $-\frac{1}{2}$
C
2 and $-\frac{7}{2}$
D
3 and $-\frac{9}{2}$
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