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Recent questions tagged non-gate
0
votes
2
answers
241
ISI2015-DCG-47
The Taylor series expansion of $f(x)= \text{ln}(1+x^2)$ about $x=0$ is $\sum _{n=1}^{\infty} (-1)^n \frac{x^n}{n}$ $\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n}}{n}$ $\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n+1}}{n+1}$ $\sum _{n=0}^{\infty} (-1)^{n+1} \frac{x^{n+1}}{n+1}$
The Taylor series expansion of $f(x)= \text{ln}(1+x^2)$ about $x=0$ is$\sum _{n=1}^{\infty} (-1)^n \frac{x^n}{n}$$\sum _{n=1}^{\infty} (-1)^{n+1} \frac{x^{2n}}{n}$$\sum _...
gatecse
833
views
gatecse
asked
Sep 18, 2019
Calculus
isi2015-dcg
calculus
taylor-series
non-gate
+
–
0
votes
2
answers
242
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is$2p$$p^{2}$$(p+1)(p-1)$$\frac{2p}{p^{2}-1}$
gatecse
435
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
0
answers
243
ISI2016-DCG-15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
The shaded region in the following diagram represents the relation$y\:\leq\: x$$\mid \:y\mid \:\leq\: \mid x\:\mid $$y\:\leq\: \mid x\:\mid$$\mid \:y\mid\: \leq\: x$
gatecse
361
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
area
curves
non-gate
+
–
0
votes
1
answer
244
ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
gatecse
275
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
curves
area
non-gate
+
–
0
votes
0
answers
245
ISI2016-DCG-38
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2),(3,-4)$ and $(5,6)$ is $12$ $14$ $16$ $18$
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2),(3,-4)$ and $(5,6)$ is$12$$14$$16$$18$
gatecse
189
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
lines
non-gate
+
–
0
votes
1
answer
246
ISI2016-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $a=\pm\sqrt{2}b$ $b=-\sqrt{2}a$ $b=a$
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$a=\pm\sqrt{2}b$$b=-\sqrt{2}a$$b=a$
gatecse
302
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
triangles
non-gate
+
–
0
votes
0
answers
247
ISI2016-DCG-40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ represent a circle a parabola an ellipse a hyperbola
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ representa circlea parabolaan ellipsea...
gatecse
272
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
curves
non-gate
+
–
0
votes
0
answers
248
ISI2016-DCG-41
A straight line touches the circle $x^{2}+y^{2}=2a^{2}$ and also the parabola $y^{2}=8ax.$ Then the equation of the straight line is $y=\pm x$ $y=\pm(x+a)$ $y=\pm(x+2a)$ $y=\pm(x-21)$
A straight line touches the circle $x^{2}+y^{2}=2a^{2}$ and also the parabola $y^{2}=8ax.$ Then the equation of the straight line is$y=\pm x$$y=\pm(x+a)$$y=\pm(x+2a)$$y=...
gatecse
178
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
lines
parabola
non-gate
+
–
0
votes
0
answers
249
ISI2016-DCG-42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is $\frac{4}{5}$ $\frac{1}{\sqrt{52}}$ $\frac{3}{5}$ $\frac{1}{2}$
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is$\frac{4}{5}$$\frac{1}{\sqrt{52}}$$\frac{3}{5}$$\frac{1}{2}$
gatecse
162
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
ellipse
non-gate
+
–
0
votes
1
answer
250
ISI2016-DCG-43
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is $27$ $\frac{13}{2}$ $\frac{15}{4}$ $45$
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\frac{13}{2}$...
gatecse
331
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
ellipse
quadrilateral
area
non-gate
+
–
0
votes
1
answer
251
ISI2016-DCG-44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then the equation of the hyperbola is $y^{2}-x^{2}=32$ $x^{2}-y^{2}=16$ $y^{2}-x^{2}=16$ $x^{2}-y^{2}=32$
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then the equation of the hyperbola is$y^{2}-x^{2}=32$$x^{2}-y^{2}=16$$y^{2}-x^...
gatecse
243
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
hyperbola
curves
non-gate
+
–
1
votes
1
answer
252
ISI2016-DCG-46
Let $I=\int(\sin\:x-\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin\:x+\cos\:x)^{4}+K$ $(\sin\:x+\cos\:x)^{2}+K$ $-\frac{1}{4}(\sin\:x+\cos\:x)^{4}+K$ None of these
Let $I=\int(\sin\:x-\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is$(\sin\:x+\cos\:x)^{4}+K$$(\sin\:x+\cos\:x)^{2}+K$$-\fr...
gatecse
389
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
integration
non-gate
+
–
0
votes
1
answer
253
ISI2016-DCG-47
The Taylor series expansion of $f(x)=\ln(1+x^{2})$ about $x=0$ is $\sum_{n=1}^{\infty}(-1)^{n}\frac{x^{n}}{n}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n}}{n}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n+1}}{n+1}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{n+1}}{n+1}$
The Taylor series expansion of $f(x)=\ln(1+x^{2})$ about $x=0$ is$\sum_{n=1}^{\infty}(-1)^{n}\frac{x^{n}}{n}$$\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n}}{n}$$\sum_{n=1}^{\...
gatecse
397
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
taylor-series
non-gate
+
–
0
votes
1
answer
254
ISI2016-DCG-48
The piecewise linear function for the following graph is $f(x)=\begin{cases} = x,x\leq-2 \\ =4,-2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = x-2,x\leq-2 \\ =4,-2<x<3 \\ = x-1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq-2 \\ =x,-2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2-x,x\leq-2 \\ =4,-2<x<3 \\ = x+1,x\geq 3\end{cases}$
The piecewise linear function for the following graph is$f(x)=\begin{cases} = x,x\leq-2 \\ =4,-2<x<3 \\ = x+1,x\geq 3\end{cases}$$f(x)=\begin{cases} = x-2,x\leq-2 \\ =4,...
gatecse
417
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
functions
curves
non-gate
+
–
0
votes
1
answer
255
ISI2016-DCG-52
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is$\frac{64}{3}$$6$$\frac{16}{3}$$\frac{32}{3}$
gatecse
324
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
curves
area
non-gate
+
–
0
votes
0
answers
256
ISI2016-DCG-59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in$\left[\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:\frac{3}{...
gatecse
339
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
geometry
triangles
trigonometry
non-gate
+
–
0
votes
0
answers
257
ISI2016-DCG-60
Which of the following relations is true for the following figure? $b^{2}=c(c+a)$ $c^{2}=a(a+b)$ $a^{2}=b(b+c)$ All of these
Which of the following relations is true for the following figure?$b^{2}=c(c+a)$$c^{2}=a(a+b)$$a^{2}=b(b+c)$All of these
gatecse
352
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
triangles
non-gate
+
–
0
votes
1
answer
258
ISI2016-DCG-61
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}-1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is $\tan^{6}\frac{\pi}{81}$ $0$ $-1$ None of these
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}-1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is$\tan^{6}\frac{\pi}{81}$$0$$-1$None of these
gatecse
241
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
0
answers
259
ISI2016-DCG-62
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$$2$$3$more than $3$
gatecse
173
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
260
ISI2016-DCG-63
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$\sin^{-1}\f...
gatecse
361
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
261
ISI2016-DCG-64
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$None of these
gatecse
273
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
1
votes
2
answers
262
ISI2016-DCG-65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is$8$$9$$9.5$None of these
gatecse
320
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
263
ISI2016-DCG-66
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is$1$$\frac{2}{5}$$\frac{3}{5}$None of these
gatecse
284
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
inverse
non-gate
+
–
0
votes
1
answer
264
ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}-y^{2}=C$ $2x^{2}-y^{2}=C$ $2y^{2}-x^{2}=C$ $x^{2}+y^{2}=C$
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$$2x^{2}-y^{2}=C$$2y^{2}-x^{2}=C$$x^...
gatecse
260
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
265
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)$$y=y...
gatecse
253
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
266
ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y-5)^{2}=25$ $x^{2}+y^{2}=100$ $(x-5)^{2}+y^{2}=125$ $(x-5)^{2}+(y-5)^{2}=50$
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$$x^{2}+y^{2}=100$...
gatecse
349
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
0
answers
267
ISI2017-DCG-24
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ has unique solution no solution infinite number of solutions none of these
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ hasunique solutionno solutioninfinite number of solutionsnone of these
gatecse
310
views
gatecse
asked
Sep 18, 2019
Others
isi2017-dcg
engineering-mathematics
calculus
non-gate
differential-equation
+
–
1
votes
1
answer
268
ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [...
gatecse
553
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2017-dcg
linear-algebra
determinant
definite-integral
non-gate
+
–
0
votes
1
answer
269
ISI2017-DCG-29
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is $2$ $4$ $6$ $8$
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$
gatecse
431
views
gatecse
asked
Sep 18, 2019
Geometry
isi2017-dcg
non-gate
geometry
area
+
–
1
votes
1
answer
270
ISI2018-DCG-18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as$2 \: \text{cosec} \: x$$\text{cosec} \: x + \text{cosec} \: y$$2 \: \sin x$$\sin x+\...
gatecse
285
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
trigonometry
non-gate
+
–
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