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

If $$\cos x=\frac{25}{24}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$

A
$$\frac{6}{5 \sqrt{2}}$$
B
$$\frac{8}{5 \sqrt{2}}$$
C
$$\frac{7}{5 \sqrt{2}}$$
D
$$\frac{1}{5 \sqrt{2}}$$
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then

A
$$a=-e, b=2$$
B
$$a=e, b=-2$$
C
$$a=e, b=2$$
D
$$a=-e, b=-2$$
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is

A
$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$
B
$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$
C
$$\bar{r}=(2 \hat{i}+\hat{k})+\lambda(3 \hat{i}+4 \hat{j})$$
D
$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$$

A
$$\frac{1}{\sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$
B
$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$
C
$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$
D
$$\frac{1}{2} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$
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