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1
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\tan ^4 \sqrt{x} \cdot \sec ^2 \sqrt{x}}{\sqrt{x}} d x=$$

A
$$\frac{-5}{2}[\tan \sqrt{x}]^5+c$$
B
$$[\tan \sqrt{\mathrm{x}}]^5+c$$
C
$$\frac{2}{5}[\tan \sqrt{x}]^5+c$$
D
$$\frac{5}{2}[\tan \sqrt{x}]^5+c$$
2
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos ^{-1} x d x=$$

A
$$x \cos ^{-1} x+\sqrt{1-x^2}+c$$
B
$$-x \cos ^{-1} x+\sqrt{1+x^2}+c$$
C
$$x \cos ^{-1} x-\sqrt{1+x^2}+c$$
D
$$x \cos ^{-1} x-\sqrt{1-x^2}+c$$
3
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$

A
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
B
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
C
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
D
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$

A
$$\sqrt{\mathrm{x}}-\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}-\log |\sqrt[6]{\mathrm{x}}+1|+c$$
B
$$2 \sqrt{\mathrm{x}}-3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}-6 \log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
C
$$2 \sqrt{\mathrm{x}}+3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}+6 \log |\sqrt[6]{\mathrm{x}}+1|+c$$
D
$$\sqrt{\mathrm{x}}+\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}+\log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
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Straight Lines and Pair of Straight Lines Circle Parabola
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