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
Recent questions in Engineering Mathematics
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
+1
vote
0
answers
1
Variation on Birthday Problem
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked
Nov 12
in
Probability
by
Ayush Upadhyaya
Boss
(
27.6k
points)

68
views
probability
+1
vote
0
answers
2
The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $
asked
Nov 1
in
Combinatory
by
Satbir
Boss
(
21.5k
points)

159
views
permutationandcombination
0
votes
0
answers
3
Gravner probability
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked
Oct 23
in
Probability
by
ajaysoni1924
Boss
(
10.5k
points)

58
views
gravner
probability
engineeringmathematics
+1
vote
2
answers
4
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\bigg( 1+\dfrac{C_0}{C_1} \bigg) \bigg( 1+\dfrac{C_1}{C_2} \bigg) \cdots \bigg( 1+\dfrac{C_{n1}}{C_n} \bigg)$ is $\bigg( \frac{n+1}{n+2} \bigg) ^n$ $ \frac{n^n}{n!} $ $\bigg( \frac{n}{n+1} \bigg) ^n$ $ \frac{(n+1)^n}{n!} $
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
424k
points)

128
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
5
ISI2014DCG2
Let $a_n=\bigg( 1 – \frac{1}{\sqrt{2}} \bigg) \cdots \bigg( 1 – \frac{1}{\sqrt{n+1}} \bigg), \: n \geq 1$. Then $\underset{n \to \infty}{\lim} a_n$ equals $1$ does not exist equals $\frac{1}{\sqrt{\pi}}$ equals $0$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

91
views
isi2014dcg
calculus
limits
+3
votes
4
answers
6
ISI2014DCG3
$\underset{x \to \infty}{\lim} \bigg( \frac{3x1}{3x+1} \bigg) ^{4x}$ equals $1$ $0$ $e^{8/3}$ $e^{4/9}$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

127
views
isi2014dcg
calculus
limits
+3
votes
2
answers
7
ISI2014DCG4
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

92
views
isi2014dcg
calculus
limits
summation
series
+1
vote
1
answer
8
ISI2014DCG5
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

79
views
isi2014dcg
calculus
functions
sets
+2
votes
1
answer
9
ISI2014DCG6
If $f(x)$ is a real valued function such that $2f(x)+3f(x)=154x$, for every $x \in \mathbb{R}$, then $f(2)$ is $15$ $22$ $11$ $0$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

51
views
isi2014dcg
calculus
functions
+2
votes
3
answers
10
ISI2014DCG7
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[1 , \sqrt{3}{/2}]$ the interval $[\sqrt{3}{/2}, 1]$ the interval $[1, 1]$ none of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

39
views
isi2014dcg
calculus
functions
range
+1
vote
3
answers
11
ISI2014DCG8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

66
views
isi2014dcg
linearalgebra
matrix
+1
vote
1
answer
12
ISI2014DCG9
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta=1, 2$ $\eta=1, 2$ $\eta=3, 3$ $\eta=1, 2$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

36
views
isi2014dcg
linearalgebra
systemofequations
0
votes
1
answer
13
ISI2014DCG12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

60
views
isi2014dcg
calculus
definiteintegrals
integration
+1
vote
1
answer
14
ISI2014DCG13
Let the function $f(x)$ be defined as $f(x)=\mid x1 \mid + \mid x2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

38
views
isi2014dcg
calculus
function
limitcontinuity
differentiable
+1
vote
1
answer
15
ISI2014DCG15
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

31
views
isi2014dcg
settheory
algebra
+2
votes
1
answer
16
ISI2014DCG17
$\underset{x \to 2}{\lim} \dfrac{1}{1+e^{\frac{1}{x2}}}$ is $0$ $1/2$ $1$ nonexistent
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

18
views
isi2014dcg
calculus
limits
+1
vote
3
answers
17
ISI2014DCG18
$^nC_0+2^nC_1+3^nC_2+\cdots+(n+1)^nC_n$ equals $2^n+n2^{n1}$ $2^nn2^{n1}$ $2^n$ none of these
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
424k
points)

42
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
18
ISI2014DCG19
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is $36$ $\infty$ $25$ $21$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

25
views
isi2014dcg
calculus
maximaminima
maximumvalues
+1
vote
0
answers
19
ISI2014DCG21
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

16
views
isi2014dcg
calculus
functions
maximaminima
convexconcave
0
votes
1
answer
20
ISI2014DCG24
Let $f(x) = \dfrac{2x}{x1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

12
views
isi2014dcg
calculus
functions
+1
vote
1
answer
21
ISI2014DCG25
The determinant $\begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix}$ equals $\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ ... $3\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ None of these
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

36
views
isi2014dcg
linearalgebra
determinant
+1
vote
1
answer
22
ISI2014DCG28
The area enclosed by the curve $\mid\: x \mid + \mid y \mid =1$ is $1$ $2$ $\sqrt{2}$ $4$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

12
views
isi2014dcg
calculus
areaunderthecurve
0
votes
1
answer
23
ISI2014DCG29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

28
views
isi2014dcg
calculus
limits
continuitydifferentiability
+2
votes
0
answers
24
ISI2014DCG31
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

18
views
isi2014dcg
calculus
integration
definiteintegration
+2
votes
0
answers
25
ISI2014DCG32
Consider $30$ multiplechoice questions, each with four options of which exactly one is correct. Then the number of ways one can get only the alternate questions correctly answered is $3^{15}$ $2^{31}$ $2 \times \begin{pmatrix} 30 \\ 15 \end{pmatrix}$ $2 \times 3^{15}$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
424k
points)

49
views
isi2014dcg
permutationandcombination
0
votes
0
answers
26
ISI2014DCG33
Let $f(x)$ be a continuous function from $[0,1]$ to $[0,1]$ satisfying the following properties. $f(0)=0$, $f(1)=1$, and $f(x_1)<f(x_2)$ for $x_1 < x_2$ with $0 < x_1, \: x_2<1$. Then the number of such functions is $0$ $1$ $2$ $\infty$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

16
views
isi2014dcg
calculus
functions
limits
+1
vote
1
answer
27
ISI2014DCG34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
424k
points)

33
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
0
votes
1
answer
28
ISI2014DCG35
Let $A$ and $B$ be disjoint sets containing $m$ and $n$ elements respectively, and let $C=A \cup B$. Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ pq \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

18
views
isi2014dcg
settheory
disjointsets
+1
vote
1
answer
29
ISI2014DCG37
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^}{2}$ and $f(x) \to – \infty$ as $x \to \dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{1} x$ $\sin x$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

15
views
isi2014dcg
calculus
functions
limits
continuity
+1
vote
0
answers
30
ISI2014DCG38
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then which one of the following is true? $A’=A$ $A’=A$ $AA’=I$ None of these
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

18
views
isi2014dcg
linearalgebra
matrices
realmatrix
Page:
1
2
3
4
5
6
...
251
next »
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Linear Algebra Important Points
GATE 2020
OFFICIAL GATE MOCK TEST RELEASED
IIITH: Winter Research Admissions 2019 (For Spring 2020)
TIFR and JEST exam
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Probability
1k
Linear Algebra
722
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.3k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.5k
Others
1.5k
Admissions
595
Exam Queries
576
Tier 1 Placement Questions
23
Job Queries
72
Projects
17
Follow @csegate
Recent questions in Engineering Mathematics
Recent Blog Comments
i also don't have any pdf, actually, I added the...
i don't have , if you have upload it
@mohan123 Do you have all standard book...
bro can be upload all standard book questions in...
it'll take 34 days but for most purpose you can...
50,648
questions
56,429
answers
195,217
comments
99,947
users