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Search results for isi2016-dcg
0
votes
1
answer
1
ISI2016-DCG-56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals $-1$ $0$ $1$ Does not exist
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals$-1$$0$$1$Does not exist
gatecse
323
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
limits
+
–
2
votes
2
answers
2
ISI2016-DCG-45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan^{2}\:x-x\:\tan\:x}{\sin\:x}$ is $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $0$ None of these
The value of $\underset{x \to 0}{\lim} \dfrac{\tan^{2}\:x-x\:\tan\:x}{\sin\:x}$ is$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$0$None of these
gatecse
453
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
limits
+
–
0
votes
1
answer
3
ISI2016-DCG-13
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
For all the natural number $n\geq 3,\: n^{2}+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
gatecse
333
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
number-system
remainder-theorem
+
–
1
votes
1
answer
4
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
409
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
integration
non-gate
+
–
0
votes
1
answer
5
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}$$f(x)=\begin{cases} = x-2,x\leq-2 \\ =4,...
gatecse
434
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
functions
curves
non-gate
+
–
0
votes
1
answer
6
ISI2016-DCG-47
The Taylor series expansion of $f(x)=\ln(1+x^{2})$ about $x=0$ is $\sum_{n=1}^{\infty}(-1)^{n}\frac{x^{n}}{n}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n}}{n}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n+1}}{n+1}$ $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{n+1}}{n+1}$
The Taylor series expansion of $f(x)=\ln(1+x^{2})$ about $x=0$ is$\sum_{n=1}^{\infty}(-1)^{n}\frac{x^{n}}{n}$$\sum_{n=1}^{\infty}(-1)^{n+1}\frac{x^{2n}}{n}$$\sum_{n=1}^{\...
gatecse
409
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
taylor-series
non-gate
+
–
0
votes
1
answer
7
ISI2016-DCG-35
Let $A,B$ and $C$ be three non empty sets. Consider the two relations given below: $A-(B-C)=(A-B)\cup C$ $A-(B\cup C)=(A-B)-C$ Both (1) and (2) are correct. (1) is correct but (2) is not. (2) is correct but (1) is not. Both (1) and (2) are incorrect.
Let $A,B$ and $C$ be three non empty sets. Consider the two relations given below:$A-(B-C)=(A-B)\cup C$$A-(B\cup C)=(A-B)-C$Both (1) and (2) are correct.(1) is correct bu...
gatecse
373
views
gatecse
asked
Sep 18, 2019
Set Theory & Algebra
isi2016-dcg
set-theory
+
–
0
votes
1
answer
8
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
395
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
work-time
+
–
0
votes
1
answer
9
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$$\frac{13}{2}$...
gatecse
344
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
ellipse
quadrilateral
area
non-gate
+
–
0
votes
1
answer
10
ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y-5)^{2}=25$ $x^{2}+y^{2}=100$ $(x-5)^{2}+y^{2}=125$ $(x-5)^{2}+(y-5)^{2}=50$
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is$x^{2}+(y-5)^{2}=25$$x^{2}+y^{2}=100$...
gatecse
358
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
11
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)$$y=y...
gatecse
260
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
12
ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}-y^{2}=C$ $2x^{2}-y^{2}=C$ $2y^{2}-x^{2}=C$ $x^{2}+y^{2}=C$
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration)$x^{2}-y^{2}=C$$2x^{2}-y^{2}=C$$2y^{2}-x^{2}=C$$x^...
gatecse
270
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
differential-equation
non-gate
+
–
0
votes
1
answer
13
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
253
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
hyperbola
curves
non-gate
+
–
0
votes
1
answer
14
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}$$\frac{32}{3}$
gatecse
339
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
curves
area
non-gate
+
–
1
votes
2
answers
15
ISI2016-DCG-65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is$8$$9$$9.5$None of these
gatecse
339
views
gatecse
asked
Sep 18, 2019
Geometry
isi2016-dcg
trigonometry
non-gate
+
–
2
votes
1
answer
16
ISI2016-DCG-28
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then$(ac)^{\frac{n}{n+1}}+b=0$$(ac)^{\frac{n+1}{n}}+b=0$$(ac^{n})^{\frac{1}{n...
gatecse
632
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
2
votes
1
answer
17
ISI2016-DCG-21
The value of the term independent of $x$ in the expansion of $(1-x)^{2}(x+\frac{1}{x})^{7}$ is $-70$ $70$ $35$ None of these
The value of the term independent of $x$ in the expansion of $(1-x)^{2}(x+\frac{1}{x})^{7}$ is$-70$$70$$35$None of these
gatecse
468
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2016-dcg
combinatory
binomial-theorem
+
–
1
votes
1
answer
18
ISI2016-DCG-31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=-1,0\:\text{or}\:1$ $\mid\:(A)\mid=-1\:\text{or}\:1$
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then$\mid\:(A)\mid=1$$\mid\:(A)\mid=0\:\text{or}\...
gatecse
385
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2016-dcg
linear-algebra
matrix
determinant
+
–
0
votes
1
answer
19
ISI2016-DCG-30
Let $p,q,r,s$ be real numbers such that $pr=2(q+s).$ Consider the equations $x^{2}+px+q=0$ and $x^{2}+rx+s=0.$ Then at least one of the equations has real roots. both these equations have real roots. neither of these equations have real roots. given data is not sufficient to arrive at any conclusion.
Let $p,q,r,s$ be real numbers such that $pr=2(q+s).$ Consider the equations $x^{2}+px+q=0$ and $x^{2}+rx+s=0.$ Thenat least one of the equations has real roots.both these...
gatecse
380
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
1
votes
2
answers
20
ISI2016-DCG-2
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then $a<b$ $a>b$ $a=b$ None of these
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then$a<b$$a>b$$a=b$None of these
gatecse
661
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
summation
inequality
+
–
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