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Recent questions tagged isi2015-dcg

1 votes
1 answer
61
ISI2015-DCG-61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is $\tan ^6 \frac{\pi}{81}$ $0$ $-1$ None of these
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is$\tan ^6 \frac{\pi}{81}$$0$$-1$None of these
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0 votes
0 answers
62
ISI2015-DCG-62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is$1$$2$$3$more than $3$
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1 votes
1 answer
63
ISI2015-DCG-63
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $ \sin^ {-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$ \sin^ ...
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0 votes
2 answers
64
ISI2015-DCG-64
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$None of these
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2 votes
1 answer
65
ISI2015-DCG-65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is$8$$9$$9.5$None of these
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0 votes
1 answer
66
ISI2015-DCG-66
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals$1$$\frac{2}{5}$$\frac{3}{5}$None of these
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