1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is

A
$$\left(\frac{1}{3}\right)^{1 / 2}$$
B
$$\left(\frac{2}{3}\right)^{1 / 2}$$
C
$$\left(\frac{3}{2}\right)^{1 / 2}$$
D
$$(3)^{1 / 2}$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is

A
$$(-\infty, \infty)$$
B
$$(-\infty, 2) \cup(3, \infty)$$
C
$$(2,3)$$
D
None of these
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}$$ and $$\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ are coplanar, then $$\lambda$$ is the root of the equation

A
$$\mathrm{x}^2+3 \mathrm{x}=6$$
B
$$x^2+2 x=4$$
C
$$x^2+3 x=4$$
D
$$x^2+2 x=6$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area of the triangle $$\mathrm{ABC}$$ is $$10 \sqrt{3} \mathrm{~cm}^2$$, angle $$\mathrm{B}$$ is $$60^{\circ}$$ and its perimeter is $$20 \mathrm{~cm}$$, then $$\ell(\mathrm{AC})=$$

A
10 cm
B
8 cm
C
5 cm
D
7 cm
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