The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Questions by Arjun
User Arjun
Wall
Recent activity
All questions
All answers
Exams Taken
All Blogs
User Arjun
Wall
Recent activity
All questions
All answers
Exams Taken
All Blogs
0
votes
1
answer
1
ISI2015MMA49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
asked
Sep 23, 2019
in
Geometry

17
views
isi2015mma
trigonometry
nongate
+2
votes
2
answers
2
ISI2015MMA50
Let ... $V_3<V_2<V_1$ $V_3<V_1<V_2$ $V_1<V_2<V_3$ $V_2<V_3<V_1$
asked
Sep 23, 2019
in
Others

30
views
isi2015mma
inequality
nongate
0
votes
1
answer
3
ISI2015MMA51
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n1}$ $\frac{1}{n2}$
asked
Sep 23, 2019
in
Probability

61
views
isi2015mma
probability
randomvariable
permutationandcombination
+1
vote
1
answer
4
ISI2015MMA52
Two coins are tossed independently where $P$(head occurs when coin $i$ is tossed) $=p_i, \: i=1,2$. Given that at least one head has occurred, the probability that coins produced different outcomes is $\frac{2p_1p_2}{p_1+p_22p_1p_2}$ $\frac{p_1+p_22p_1p_2}{p_1+p_2p_1p_2}$ $\frac{2}{3}$ none of the above
asked
Sep 23, 2019
in
Probability

41
views
isi2015mma
probability
independentevents
+1
vote
1
answer
5
ISI2015MMA53
The number of cars $(X)$ arriving at a service station per day follows a Poisson distribution with mean $4$. The service station can provide service to a maximum of $4$ cars per day. Then the expected number of cars that do not get service per day equals $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i4)$
asked
Sep 23, 2019
in
Probability

41
views
isi2015mma
poissondistribution
expectation
+1
vote
1
answer
6
ISI2015MMA54
If $0 <x<1$, then the sum of the infinite series $\frac{1}{2}x^2+\frac{2}{3}x^3+\frac{3}{4}x^4+ \cdots$ is $\log \frac{1+x}{1x}$ $\frac{x}{1x} + \log(1+x)$ $\frac{1}{1x} + \log(1x)$ $\frac{x}{1x} + \log(1x)$
asked
Sep 23, 2019
in
Others

20
views
isi2015mma
summation
nongate
0
votes
0
answers
7
ISI2015MMA55
Let $\{a_n\}$ be a sequence of real numbers. Then $\underset{n \to \infty}{\lim} a_n$ exists if and only if $\underset{n \to \infty}{\lim} a_{2n}$ and $\underset{n \to \infty}{\lim} a_{2n+2}$ exists $\underset{n \to \infty}{\lim} a_{2n}$ ... $\underset{n \to \infty}{\lim} a_{3n}$ exist none of the above
asked
Sep 23, 2019
in
Calculus

12
views
isi2015mma
calculus
limits
0
votes
0
answers
8
ISI2015MMA56
Let $\{a_n\}$ be a sequence of nonnegative real numbers such that the series $\Sigma_{n=1}^{\infty} a_n$ is convergent. If $p$ is a real number such that the series $\Sigma \frac{\sqrt{a_n}}{n^p}$ diverges, then $p$ must be strictly less than $\frac{1}{2}$ ... but can be greater than$\frac{1}{2}$ $p$ must be strictly less than $1$ but can be greater than or equal to $\frac{1}{2}$
asked
Sep 23, 2019
in
Others

11
views
isi2015mma
convergencedivergence
nongate
0
votes
0
answers
9
ISI2015MMA57
Suppose $a>0$. Consider the sequence $a_n = n \{ \sqrt[n]{ea} – \sqrt[n]{a}, \:\:\:\:\: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ does not exist $\underset{n \to \infty}{\lim} a_n=e$ $\underset{n \to \infty}{\lim} a_n=0$ none of the above
asked
Sep 23, 2019
in
Calculus

14
views
isi2015mma
calculus
limits
0
votes
0
answers
10
ISI2015MMA58
Let $\{a_n\}, n \geq 1$, be a sequence of real numbers satisfying $\mid a_n \mid \leq 1$ for all $n$. Define $A_n = \frac{1}{n}(a_1+a_2+\cdots+a_n)$, for $n \geq 1$. Then $\underset{n \to \infty}{\lim} \sqrt{n}(A_{n+1}A_n)$ is equal to $0$ $1$ $1$ none of these
asked
Sep 23, 2019
in
Calculus

13
views
isi2015mma
calculus
limits
nongate
0
votes
0
answers
11
ISI2015MMA59
In the Taylor expansion of the function $f(x)=e^{x/2}$ about $x=3$, the coefficient of $(x3)^5$ is $e^{3/2} \frac{1}{5!}$ $e^{3/2} \frac{1}{2^5 5!}$ $e^{3/2} \frac{1}{2^5 5!}$ none of the above
asked
Sep 23, 2019
in
Calculus

10
views
isi2015mma
calculus
taylorseries
nongate
0
votes
0
answers
12
ISI2015MMA60
Let $\sigma$ be the permutation: $\begin{array} {}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 3 & 5 & 6 & 2 & 4 & 9 & 8 & 7 & 1, \end{array}$ $I$ be the identity permutation and $m$ be the order of $\sigma$ i.e. $m=\text{min}\{\text{positive integers }n: \sigma ^n=I \}$. Then $m$ is $8$ $12$ $360$ $2520$
asked
Sep 23, 2019
in
Combinatory

19
views
isi2015mma
permutationandcombination
+1
vote
1
answer
13
ISI2015MMA61
Let $ A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix} \text{ and } B=\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}.$ Then there exists a matrix $C$ ... no matrix $C$ such that $A=BC$ there exists a matrix $C$ such that $A=BC$, but $A \neq CB$ there is no matrix $C$ such that $A=CB$
asked
Sep 23, 2019
in
Linear Algebra

37
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
14
ISI2015MMA62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
asked
Sep 23, 2019
in
Linear Algebra

47
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
15
ISI2015MMA63
Let $\theta=2\pi/67$. Now consider the matrix $A = \begin{pmatrix} \cos \theta & \sin \theta \\  \sin \theta & \cos \theta \end{pmatrix}$. Then the matrix $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
asked
Sep 23, 2019
in
Linear Algebra

24
views
isi2015mma
linearalgebra
matrices
0
votes
0
answers
16
ISI2015MMA64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $t=0$ and $t=2 \pi$ is $2 \pi$ $2 \sqrt{2 \pi}$ $\sqrt{2 \pi}$ none of the above
asked
Sep 23, 2019
in
Geometry

9
views
isi2015mma
trigonometry
curves
nongate
0
votes
0
answers
17
ISI2015MMA65
Let $n$ be a positive real number and $p$ be a positive integer. Which of the following inequalities is true? $n^p > \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ $n^p < \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ $(n+1)^p < \frac{(n+1)^{p+1} – n^{p+1}}{p+1}$ none of the above
asked
Sep 23, 2019
in
Others

8
views
isi2015mma
inequality
nongate
0
votes
0
answers
18
ISI2015MMA66
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid xy \mid$ holds for all $x$ and $y$ is $2$ $1$ $\frac{\pi}{2}$ there is no smallest positive value of $K$; any $K>0$ will make the inequality hold.
asked
Sep 23, 2019
in
Others

10
views
isi2015mma
inequality
trigonometry
nongate
0
votes
0
answers
19
ISI2015MMA67
Given two real numbers $a<b$, let $d(x,[a,b]) = \text{min} \{ \mid xy \mid : a \leq y \leq b \} \text{ for }  \infty < x < \infty$. Then the function $f(x) = \frac{d(x,[0,1])}{d(x,[0,1]) + d(x,[2,3])}$ satisfies $0 \leq f(x) < \frac{1}{2}$ for every $x$ ... $f(x)=1$ if $ 0 \leq x \leq 1$ $f(x)=0$ if $0 \leq x \leq 1$ and $f(x)=1$ if $ 2 \leq x \leq 3$
asked
Sep 23, 2019
in
Others

11
views
isi2015mma
functions
nongate
0
votes
0
answers
20
ISI2015MMA68
Let $f(x,y) = \begin{cases} e^{1/(x^2+y^2)} & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0). \end{cases}$Then $f(x,y)$ is not continuous at $(0,0)$ continuous at $(0,0)$ but does not have first order partial derivatives continuous at $(0,0)$ and has first order partial derivatives, but not differentiable at $(0,0)$ differentiable at $(0,0)$
asked
Sep 23, 2019
in
Others

13
views
isi2015mma
partialderivatives
nongate
0
votes
0
answers
21
ISI2015MMA69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
asked
Sep 23, 2019
in
Calculus

19
views
isi2015mma
calculus
continuity
differentiation
definiteintegrals
nongate
0
votes
0
answers
22
ISI2015MMA70
Let $w=\log(u^2 +v^2)$ where $u=e^{(x^2+y)}$ and $v=e^{(x+y^2)}$. Then $\frac{\partial w }{\partial x} \mid _{x=0, y=0}$ is $0$ $1$ $2$ $4$
asked
Sep 23, 2019
in
Others

11
views
isi2015mma
partialderivatives
nongate
0
votes
0
answers
23
ISI2015MMA71
Let $f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ does not exist
asked
Sep 23, 2019
in
Others

9
views
isi2015mma
continuity
partialderivatives
nongate
0
votes
0
answers
24
ISI2015MMA72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
asked
Sep 23, 2019
in
Calculus

12
views
isi2015mma
calculus
differentiation
0
votes
0
answers
25
ISI2015MMA73
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then $\alpha$ must be $0$ $\alpha$ need not be $0$, but $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < 1$
asked
Sep 23, 2019
in
Calculus

13
views
isi2015mma
calculus
limits
differentiation
0
votes
0
answers
26
ISI2015MMA74
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Then if $f(1) \geq g(1)$, then $f(x) \geq g(x)$ for all $x$ if $f(1) \leq g(1)$, then $f(x) \leq g(x)$ for all $x$ $f(1) \leq g(1)$ $f(1) \geq g(1)$
asked
Sep 23, 2019
in
Calculus

10
views
isi2015mma
calculus
differentiation
0
votes
0
answers
27
ISI2015MMA75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}1$ $8(5 \sqrt{5}1)$
asked
Sep 23, 2019
in
Geometry

14
views
isi2015mma
curves
nongate
0
votes
0
answers
28
ISI2015MMA76
Given that $\int_{\infty}^{\infty} e^{x^2} dx = \sqrt{\pi}$, the value of $ \int_{\infty}^{\infty} \int_{\infty}^{\infty} e^{(x^2+xy+y^2)} dxdy$ is $\sqrt{\pi/3}$ $\pi/\sqrt{3}$ $\sqrt{2 \pi/3}$ $2 \pi / \sqrt{3}$
asked
Sep 23, 2019
in
Calculus

13
views
isi2015mma
calculus
definiteintegrals
nongate
+1
vote
0
answers
29
ISI2015MMA77
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$axis, the line $y=x$, and the line $x=1$. The value of the double integral $ \int \int_R \frac{\sin x}{x}\: dxdy$ is $1\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$
asked
Sep 23, 2019
in
Calculus

16
views
isi2015mma
integration
nongate
0
votes
1
answer
30
ISI2015MMA78
The value of $\displaystyle \lim_{n \to \infty} \left[ (n+1) \int_0^1 x^n \ln(1+x) dx \right]$ is $0$ $\ln 2$ $\ln 3$ $\infty$
asked
Sep 23, 2019
in
Calculus

18
views
isi2015mma
calculus
limits
definiteintegrals
nongate
Page:
« prev
1
2
3
4
5
6
7
8
9
10
...
45
next »
50,737
questions
57,292
answers
198,224
comments
104,909
users