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Recent questions tagged engineering-mathematics
3
votes
3
answers
151
ISI2018-MMA-15
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.
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 evenThe number of elements of ord...
akash.dinkar12
3.1k
views
akash.dinkar12
asked
May 11, 2019
Set Theory & Algebra
isi2018-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
+
–
0
votes
1
answer
152
ISI2018-MMA-14
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 $-4$ $-2$ $2$ $4$
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$$4$
akash.dinkar12
1.6k
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
eigen-value
determinant
+
–
1
votes
2
answers
153
ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is$2$$2(1+i)$$0$$2^{10}$
akash.dinkar12
884
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
determinant
+
–
3
votes
4
answers
154
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
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$
akash.dinkar12
1.5k
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
+
–
1
votes
1
answer
155
ISI2018-MMA-11
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is $2$ $-2$ $3$ $-3$
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is$2$$-2$$3$$-3$
akash.dinkar12
840
views
akash.dinkar12
asked
May 11, 2019
Quantitative Aptitude
isi2018-mma
engineering-mathematics
linear-algebra
system-of-equations
+
–
1
votes
1
answer
156
ISI2018-MMA-10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done s...
akash.dinkar12
1.5k
views
akash.dinkar12
asked
May 11, 2019
Combinatory
isi2018-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
4
votes
1
answer
157
ISI2019-MMA-30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^9-1}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}-1}\\$ $\frac{1}{2^{10}+1}$
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and$$2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$$Then t...
Sayan Bose
1.8k
views
Sayan Bose
asked
May 7, 2019
Calculus
isi2019-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
functions
+
–
2
votes
1
answer
158
ISI2019-MMA-29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rig...
Sayan Bose
1.9k
views
Sayan Bose
asked
May 7, 2019
Calculus
isi2019-mma
engineering-mathematics
calculus
integration
+
–
1
votes
1
answer
159
ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is $1/4$ $1/6$ $1/8$ $1/24$
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$$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...
Sayan Bose
2.1k
views
Sayan Bose
asked
May 7, 2019
Calculus
isi2019-mma
calculus
engineering-mathematics
integration
+
–
3
votes
3
answers
160
ISI2019-MMA-27
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}$
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 el...
Sayan Bose
5.0k
views
Sayan Bose
asked
May 7, 2019
Combinatory
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
0
votes
1
answer
161
ISI2019-MMA-25
Let $a,b,c$ be non-zero 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)$
Let $a,b,c$ be non-zero 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...
Sayan Bose
1.2k
views
Sayan Bose
asked
May 7, 2019
Calculus
isi2019-mma
engineering-mathematics
calculus
integration
+
–
1
votes
2
answers
162
ISI2019-MMA-24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f \circ f^{n-1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f ...
Sayan Bose
1.6k
views
Sayan Bose
asked
May 7, 2019
Calculus
isi2019-mma
engineering-mathematics
calculus
limits
+
–
1
votes
1
answer
163
ISI2019-MMA-23
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 skew-symmetric matrix None of the above must necessarily hold
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, the...
Sayan Bose
1.7k
views
Sayan Bose
asked
May 7, 2019
Linear Algebra
isi2019-mma
engineering-mathematics
linear-algebra
matrix
+
–
0
votes
3
answers
164
ISI2019-MMA-20
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$
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 ...
Sayan Bose
2.5k
views
Sayan Bose
asked
May 7, 2019
Combinatory
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
2
votes
3
answers
165
ISI2019-MMA-19
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$
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$
Sayan Bose
2.0k
views
Sayan Bose
asked
May 7, 2019
Set Theory & Algebra
isi2019-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
+
–
1
votes
1
answer
166
ISI2019-MMA-18
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 $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3e}{2} – \frac{1}{4} \bigg)$ $\text{ln} \bigg(\frac{3}{e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{4} \bigg)$
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}{...
Sayan Bose
4.5k
views
Sayan Bose
asked
May 6, 2019
Others
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
+
–
1
votes
2
answers
167
ISI2019-MMA-15
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 $t$
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 o...
Sayan Bose
1.3k
views
Sayan Bose
asked
May 6, 2019
Linear Algebra
isi2019-mma
linear-algebra
engineering-mathematics
matrix
+
–
1
votes
2
answers
168
ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$$10$$12$$1...
Sayan Bose
2.3k
views
Sayan Bose
asked
May 6, 2019
Linear Algebra
isi2019-mma
engineering-mathematics
linear-algebra
vector-space
non-gate
+
–
0
votes
1
answer
169
ISI2019-MMA-10
The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the student is told that he has been admitted to at least one of these colleges, what is the probability that he has got admitted to college $A$? $3/5$ $5/7$ $10/13$ $15/19$
The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the studen...
Sayan Bose
2.7k
views
Sayan Bose
asked
May 6, 2019
Probability
isi2019-mma
engineering-mathematics
discrete-mathematics
probability
+
–
0
votes
1
answer
170
ISI2019-MMA-6
The solution of the differential equation $\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$ is $x^2 + y^2 = cy$, where $c$ is a constant $x^2 + y^2 = cx$, where $c$ is a constant $x^2 – y^2 = cy$ , where $c$ is a constant $x^2 - y^2 = cx$, where $c$ is a constant
The solution of the differential equation $$\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$$is$x^2 + y^2 = cy$, where $c$ is a constant$x^2 + y^2 = cx$, where $c$ is a constant$x^2 ...
Sayan Bose
1.1k
views
Sayan Bose
asked
May 6, 2019
Calculus
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
+
–
1
votes
1
answer
171
ISI2019-MMA-4
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not...
Sayan Bose
2.0k
views
Sayan Bose
asked
May 5, 2019
Combinatory
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
0
votes
1
answer
172
ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is$21$$22$$27$$28$
Sayan Bose
3.4k
views
Sayan Bose
asked
May 5, 2019
Combinatory
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
0
votes
1
answer
173
Gate 2002 - ME
Which of the following functions is not differentiable in the domain $[-1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x-1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,-x)$
Which of the following functions is not differentiable in the domain $[-1,1]$ ?(a) $f(x) = x^2$(b) $f(x) = x-1$(c) $f(x) = 2$(d) $f(x) = Maximum (x,-x)$
balchandar reddy san
2.6k
views
balchandar reddy san
asked
May 4, 2019
Calculus
engineering-mathematics
usergate2002
usermod
calculus
differentiation
+
–
4
votes
1
answer
174
Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
Hirak
1.2k
views
Hirak
asked
Apr 25, 2019
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
1
votes
1
answer
175
ISI2017-PCB-CS-1(b)
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.
akash.dinkar12
846
views
akash.dinkar12
asked
Apr 8, 2019
Graph Theory
isi2017-pcb-cs
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
descriptive
+
–
0
votes
2
answers
176
Probability - Independent Events
What is the probability that, in six throws of a die, there will be exactly one each of “1”, “2”, “3”, “4”, “5” and “6”? $0.00187220$ $0.01432110$ $0.01176210$ $0.01543210$
What is the probability that, in six throws of a die, there will be exactly one each of “1”, “2”, “3”, “4”, “5” and “6”?$0.00187220$$0.01432110$$0...
zeeshanmohnavi
579
views
zeeshanmohnavi
asked
Mar 8, 2019
Probability
probability
engineering-mathematics
+
–
0
votes
1
answer
177
Ace Test Series: Set Theory & Algebra - Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________ Ans given 48 but I got 8 Please verify
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________Ans given 48but I got 8Please verify
srestha
851
views
srestha
asked
Mar 7, 2019
Set Theory & Algebra
ace-test-series
engineering-mathematics
discrete-mathematics
set-theory&algebra
relations
+
–
1
votes
1
answer
178
ISI MMA-2015
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$(A) equals $1$...
ankitgupta.1729
1.3k
views
ankitgupta.1729
asked
Feb 21, 2019
Calculus
engineering-mathematics
calculus
userisi2015
usermod
sequence-series
limits
+
–
2
votes
1
answer
179
ISI MMA-2015
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy $f(x^{2}+1) = f(x)g(x)$ $,$ for every $x\in \mathbb{R}$ , then (A) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) \neq 0$ (B) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) = 0$ (C) $f$ has $m$ distinct real roots (D) $f$ has no real root.
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy $f(x^{2}+1)...
ankitgupta.1729
1.2k
views
ankitgupta.1729
asked
Feb 20, 2019
Calculus
engineering-mathematics
calculus
userisi2015
usermod
+
–
0
votes
0
answers
180
Discrete random variable
Na462
482
views
Na462
asked
Feb 20, 2019
Probability
probability
random-variable
engineering-mathematics
+
–
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