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Recent questions tagged isi2016-dcg
0
votes
1
answer
61
ISI2016-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
gatecse
250
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
0
answers
62
ISI2016-DCG-62
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$$2$$3$more than $3$
gatecse
189
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
63
ISI2016-DCG-63
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ 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 $\left[0,\frac{\pi}{2}\right],$ their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$\sin^{-1}\f...
gatecse
391
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
64
ISI2016-DCG-64
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$None of these
gatecse
284
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
1
votes
2
answers
65
ISI2016-DCG-65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is$8$$9$$9.5$None of these
gatecse
346
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
66
ISI2016-DCG-66
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is$1$$\frac{2}{5}$$\frac{3}{5}$None of these
gatecse
310
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
inverse
non-gate
+
–
0
votes
1
answer
67
ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}-y^{2}=C$ $2x^{2}-y^{2}=C$ $2y^{2}-x^{2}=C$ $x^{2}+y^{2}=C$
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$$2x^{2}-y^{2}=C$$2y^{2}-x^{2}=C$$x^...
gatecse
274
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
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–
0
votes
1
answer
68
ISI2016-DCG-68
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration) $y=x(\log x+C)$ $x=y(\log y+C)$ $y=x(\log y+C)$ $y=y(\log x+C)$
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration)$y=x(\log x+C)$$x=y(\log y+C)$$y=x(\log y+C)$$y=y...
gatecse
262
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
69
ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y-5)^{2}=25$ $x^{2}+y^{2}=100$ $(x-5)^{2}+y^{2}=125$ $(x-5)^{2}+(y-5)^{2}=50$
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$$x^{2}+y^{2}=100$...
gatecse
360
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
70
ISI2016-DCG-70
Water pours into a rectangular tank of $20\:metres$ depth which was initially half-filled. The rate at which the height of the water rises is inversely proportional to the height of the water at that instant. If the height of the water after an hour is observed to be $12\:metres$, ... hours, will be required to fill up the tank? $\frac{75}{11}$ $\frac{125}{11}$ $\frac{25}{3}$ $5$
Water pours into a rectangular tank of $20\:metres$ depth which was initially half-filled. The rate at which the height of the water rises is inversely proportional to th...
gatecse
401
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
work-time
+
–
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