1
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The vectors are $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\bar{a} \cdot \bar{c}=|\bar{c}|$$ and $$|\bar{c}-\bar{a}|=2 \sqrt{2}$$, angle between $$\bar{a} \times \bar{b}$$ and $$\bar{c}$$ is $$\frac{\pi}{4}$$, then $$|(\bar{a} \times \bar{b}) \times \bar{c}|$$ is

A
3
B
$$\frac{3}{\sqrt{2}}$$
C
$$3 \sqrt{2}$$
D
1
2
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1}{7-6 x-x^2} d x=$$

A
$$\frac{1}{4} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{1}{8} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\frac{1}{16} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\frac{1}{32} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
3
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{d x}{\sin x+\cos x}=$$

A
$$\sqrt{2} \log \tan \left(x+\frac{\pi}{4}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{1}{\sqrt{2}} \log \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+c$$, where c is a constant of integration.
C
$$\frac{1}{\sqrt{2}} \log \left(\frac{\tan \frac{x}{2}-\sqrt{2}+1}{\tan \frac{x}{2}+\sqrt{2}+1}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$-\frac{1}{\sqrt{2}} \log \left(\frac{\tan \frac{x}{2}-(\sqrt{2}+1)}{\tan \frac{x}{2}+\sqrt{2}-1}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
4
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A ladder of length $$17 \mathrm{~m}$$ rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of $$1 \mathrm{~m} / \mathrm{sec}$$., then when it is $$8 \mathrm{~m}$$ away from the wall, its upper end is coming down at the rate of

A
$$\frac{5}{8} \mathrm{~m} / \mathrm{sec}$$.
B
$$\frac{8}{15} \mathrm{~m} / \mathrm{sec}$$.
C
$$\frac{-8}{15} \mathrm{~m} / \mathrm{sec}$$.
D
$$\frac{15}{8} \mathrm{~m} / \mathrm{sec}$$.
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