1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=$$ _________, if $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$

A
$$\frac{-\sqrt{5}+1}{8}$$
B
$$\frac{\sqrt{5}-1}{8}$$
C
$$\frac{\sqrt{5}+1}{8}$$
D
$$\frac{-\sqrt{5}-1}{8}$$
2
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{k}}$$, then its variance is

A
$$\frac{\mathrm{k}^2-1}{12}$$
B
$$\frac{\mathrm{k}^2-1}{6}$$
C
$$\frac{\mathrm{k}^2+1}{12}$$
D
$$\frac{\mathrm{k}^2+1}{6}$$
3
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\tan y=\frac{x \sin \alpha}{1-x \cos \alpha}$$ and $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\mathrm{m}}{x^2+2 \mathrm{n} x+1}$$, then $$\mathrm{m}^2+\mathrm{n}^2$$ is

A
2
B
3
C
1
D
4
4
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides of the triangle (in units) are

A
$$3,4,5$$
B
$$4,5,6$$
C
$$5,6,7$$
D
$$2,3,4$$
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