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Recent questions tagged engineeringmathematics
0
votes
1
answer
1
ISI2018PCBB3
An $n$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
asked
May 12
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

10
views
isi2018pcbb
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
0
votes
1
answer
2
ISI2018PCBA4
Let $A$ and $B$ are two nonempty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $A+B\geq A +B 1 $, where $S$ denotes the cardinality of finite set $S$.
asked
May 12
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

16
views
isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
descriptive
+1
vote
1
answer
3
ISI2018PCBA1
Consider a $n \times n$ matrix $A=I_n\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
asked
May 12
in
Linear Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

30
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
0
answers
4
ISI2018MMA28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ x \leq 1 \\ 0 & ,if\ x>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

19
views
isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
5
ISI2018MMA30
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ ... at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

74
views
isi2018
engineeringmathematics
calculus
maximaminima
0
votes
0
answers
6
ISI2018MMA29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $2$ $1$ $1$ $2$
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

33
views
isi2018
engineeringmathematics
calculus
integration
+1
vote
1
answer
7
ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
asked
May 11
in
Combinatory
by
akash.dinkar12
Boss
(
40.5k
points)

99
views
isi2018
engineeringmathematics
discretemathematics
generatingfunctions
0
votes
1
answer
8
ISI2018MMA20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n1}{m1}/n^m\\$ $\binom{m+n1}{m}/m^n$
asked
May 11
in
Probability
by
akash.dinkar12
Boss
(
40.5k
points)

22
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
9
ISI2018MMA19
Let $X_1,X_2, . . . ,X_n$ be independent and identically distributed with $P(X_i = 1) = P(X_i = −1) = p\ $and$ P(X_i = 0) = 1 − 2p$ for all $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 12p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
40.5k
points)

23
views
isi2018
engineeringmathematics
calculus
limits
0
votes
1
answer
10
ISI2018MMA18
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent ... $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is $0$ $1/16$ $1/8$ $1/4$
asked
May 11
in
Probability
by
akash.dinkar12
Boss
(
40.5k
points)

18
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
11
ISI2018MMA17
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same ... as before. The probability that the coin will be identified at the second draw is $1/2$ $1/3$ $1/4$ $1/6$
asked
May 11
in
Probability
by
akash.dinkar12
Boss
(
40.5k
points)

22
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
12
ISI2018MMA16
Consider a large village, where only two newspapers $P_1$ and $P_2$ are available to the families. It is known that the proportion of families not taking $P_1$ is $0.48$, not taking $P_2$ is $0.58$, taking only $P_2$ is $0.30$. The probability that a randomly chosen family from the village takes only $P_1$ is $0.24$ $0.28$ $0.40$ can not be determined
asked
May 11
in
Probability
by
akash.dinkar12
Boss
(
40.5k
points)

34
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
13
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
asked
May 11
in
Set Theory & Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

11
views
isi2018
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
1
answer
14
ISI2018MMA14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $4$ $2$ $2$ $4$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

38
views
isi2018
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
1
answer
15
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

27
views
isi2018
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
16
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
40.5k
points)

49
views
isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
17
ISI2018MMA11
The value of $\lambda$ for which the system of linear equations $2xyz=12$, $x2y+z=4$ and $x+y+\lambda z=4$ has no solution is $2$ $2$ $3$ $3$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
40.5k
points)

21
views
isi2018
engineeringmathematics
linearalgebra
systemofequations
0
votes
1
answer
18
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
asked
May 11
in
Combinatory
by
akash.dinkar12
Boss
(
40.5k
points)

21
views
isi2018
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
1
answer
19
ISI2019MMA30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)h(i1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^91}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}1}\\$ $\frac{1}{2^{10}+1}$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

316
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
0
votes
1
answer
20
ISI2019MMA29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

347
views
isi2019
engineeringmathematics
calculus
integration
0
votes
1
answer
21
ISI2019MMA28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{1}$ and $g^{1}$ is $1/4$ $1/6$ $1/8$ $1/24$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

616
views
isi2019
calculus
engineeringmathematics
0
votes
2
answers
22
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

2.7k
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
0
votes
1
answer
23
ISI2019MMA25
Let $a,b,c$ be nonzero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

203
views
isi2019
engineeringmathematics
calculus
integration
+1
vote
1
answer
24
ISI2019MMA24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f''(x)$ exists for every $x \in \mathbb{R}$, where $f''(x) = f \circ f^{n1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

213
views
isi2019
engineeringmathematics
calculus
limits
0
votes
1
answer
25
ISI2019MMA23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skewsymmetric matrix None of the above must necessarily hold
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
6.9k
points)

100
views
isi2019
engineeringmathematics
linearalgebra
0
votes
1
answer
26
ISI2019MMA21
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {1}$. ... $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
6.9k
points)

372
views
isi2019
engineeringmathematics
calculus
0
votes
2
answers
27
ISI2019MMA20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter ‘O’ and the digit ‘0’ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

281
views
isi2019
engineeringmathematics
discretemathematics
permutationsandcombinations
+1
vote
1
answer
28
ISI2019MMA19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is $1$ $2$ $6$ $12$
asked
May 7
in
Set Theory & Algebra
by
Sayan Bose
Loyal
(
6.9k
points)

163
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
+1
vote
1
answer
29
ISI2019MMA18
For the differential equation $\frac{dy}{dx} + xe^{y}+2x=0$ It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ is given by $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3e}{2} – \frac{1}{4} \bigg)$ $\text{ln} \bigg(\frac{3}{e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{4} \bigg)$
asked
May 7
in
Others
by
Sayan Bose
Loyal
(
6.9k
points)

3.5k
views
isi2019
nongate
engineeringmathematics
calculus
differentiableequation
0
votes
2
answers
30
ISI2019MMA15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & 1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
6.9k
points)

136
views
isi2019
linearalgebra
engineeringmathematics
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