1
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \tan ^{-1}(\sec x+\tan x) d x=$$

A
$$\frac{\pi x}{4}+\frac{x^2}{4}+c$$
B
$$\sin x \cos x+c$$
C
$$\frac{\pi x}{2}+\frac{x^2}{2}+c$$
D
$$\sin x+\cos x+c$$
2
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$A(\propto)=\left[\begin{array}{cc}\cos \propto & \sin \propto \\ -\sin \propto & \cos \propto\end{array}\right]$$, then $$\left[A^2(\propto)\right]^{-1}=$$

A
$$\mathrm{A}(\propto)$$
B
$$\mathrm{A}^2(\propto)$$
C
$$\mathrm{A}(-2 \propto)$$
D
$$\mathrm{A}(2 \propto)$$
3
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

A
$$\frac{5}{11}$$
B
$$\frac{5}{12}$$
C
$$\frac{7}{12}$$
D
$$\frac{7}{11}$$
4
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4 h^2=}$$

A
$$(a+2 b)(a+3 b)$$
B
$$a^2+4 a b+b^2$$
C
$$a^2+6 a b+b^2$$
D
$$(a-2 b)(2 a+b)$$
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