1
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\int \frac{x^2 \mathrm{~d} x}{\left(1+x^2\right)\left(1+\sqrt{1+x^2}\right)}$$ and $$\mathrm{f}(0)=0$$, then $$\mathrm{f}(1)$$ is

A
$$\log (1+\sqrt{2})$$
B
$$\log (1+\sqrt{2})-\frac{\pi}{4}$$
C
$$\log (1+\sqrt{2})+\frac{\pi}{4}$$
D
$$\log (1-\sqrt{2})$$
2
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A line $$\mathrm{L}_1$$ passes through the point, whose p. v. (position vector) $$3 \hat{i}$$, is parallel to the vector $$-\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$$. Another line $$\mathrm{L}_2$$ passes through the point having p.v. $$\hat{i}+\hat{j}$$ is parallel to vector $$\hat{i}+\hat{k}$$, then the point of intersection of lines $$L_1$$ and $$L_2$$ has p.v.

A
$$2 \hat{i}+2 \hat{j}+\hat{k}$$
B
$$2 \hat{i}+\hat{j}+\hat{k}$$
C
$$2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$$
D
$$2 \hat{i}-2 \hat{j}+\hat{k}$$
3
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\tan ^{-1}\left(\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right)$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)$$ at $$x=0$$ is

A
3
B
5
C
8
D
1
4
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The expression $$(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$$ is equivalent to

A
$$\sim \mathrm{p} \vee \mathrm{q}$$
B
$$p \wedge q$$
C
$$\mathrm{p} \vee \mathrm{q}$$
D
$$p \vee \sim q$$
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