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Recent questions tagged isi2018-mma
0
votes
1
answer
1
ISI2018-MMA-25
The solution of the differential equation $(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is $xy = \log\ x − \log\ y + C$ $xy = \log\ y − \log\ x + C$ $x^2y^2 = 2(\log\ x − \log\ y) + C$ $x^2y^2 = 2(\log\ y − \log\ x) + C$
akash.dinkar12
asked
in
Others
May 11, 2019
by
akash.dinkar12
382
views
isi2018-mma
non-gate
differential-equation
1
vote
2
answers
2
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
akash.dinkar12
asked
in
Calculus
May 11, 2019
by
akash.dinkar12
877
views
isi2018-mma
engineering-mathematics
calculus
continuity
0
votes
1
answer
3
ISI2018-MMA-30
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.
akash.dinkar12
asked
in
Calculus
May 11, 2019
by
akash.dinkar12
811
views
isi2018-mma
engineering-mathematics
calculus
maxima-minima
2
votes
1
answer
4
ISI2018-MMA-29
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 $-2$ $-1$ $1$ $2$
akash.dinkar12
asked
in
Calculus
May 11, 2019
by
akash.dinkar12
718
views
isi2018-mma
engineering-mathematics
calculus
integration
1
vote
1
answer
5
ISI2018-MMA-27
Number of real solutions of the equation $x^7 + 2x^5 + 3x^3 + 4x = 2018$ is $1$ $3$ $5$ $7$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
683
views
isi2018-mma
general-aptitude
quantitative-aptitude
3
votes
1
answer
6
ISI2018-MMA-26
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 $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
akash.dinkar12
asked
in
Combinatory
May 11, 2019
by
akash.dinkar12
1.2k
views
isi2018-mma
engineering-mathematics
discrete-mathematics
generating-functions
2
votes
1
answer
7
ISI2018-MMA-24
The sum of the infinite series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots $ is $2$ $3$ $4$ $6$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
601
views
isi2018-mma
general-aptitude
quantitative-aptitude
0
votes
1
answer
8
ISI2018-MMA-23
For $n\geq 1$, let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ \dots +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + \dots + c_nr^n$,where $\mid c_k \mid \leq M$ for all integer $k$ and $\mid r \mid <1$. Then both $\{a_n\}$ ... $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
akash.dinkar12
asked
in
Others
May 11, 2019
by
akash.dinkar12
434
views
isi2018-mma
sequence-series
non-gate
0
votes
1
answer
9
ISI2018-MMA-22
The $x$-axis divides the circle $x^2 + y^2 − 6x − 4y + 5 = 0$ into two parts. The area of the smaller part is $2\pi-1$ $2(\pi-1)$ $2\pi-3$ $2(\pi-2)$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
533
views
isi2018-mma
general-aptitude
quantitative-aptitude
0
votes
1
answer
10
ISI2018-MMA-21
The angle between the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 4x$ is $\pi /2$ $\pi /3$ $\pi /4$ $\pi /6$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
546
views
isi2018-mma
general-aptitude
quantitative-aptitude
1
vote
1
answer
11
ISI2018-MMA-20
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 $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n-1}{m-1}/n^m\\$ $\binom{m+n-1}{m}/m^n$
akash.dinkar12
asked
in
Probability
May 11, 2019
by
akash.dinkar12
1.5k
views
isi2018-mma
engineering-mathematics
probability
0
votes
1
answer
12
ISI2018-MMA-19
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 $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 1-2p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
akash.dinkar12
asked
in
Calculus
May 11, 2019
by
akash.dinkar12
566
views
isi2018-mma
engineering-mathematics
calculus
limits
0
votes
2
answers
13
ISI2018-MMA-18
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 $0$ $1/16$ $1/8$ $1/4$
akash.dinkar12
asked
in
Probability
May 11, 2019
by
akash.dinkar12
812
views
isi2018-mma
engineering-mathematics
probability
0
votes
2
answers
14
ISI2018-MMA-17
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 $1/2$ $1/3$ $1/4$ $1/6$
akash.dinkar12
asked
in
Probability
May 11, 2019
by
akash.dinkar12
897
views
isi2018-mma
engineering-mathematics
probability
0
votes
2
answers
15
ISI2018-MMA-16
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
akash.dinkar12
asked
in
Probability
May 11, 2019
by
akash.dinkar12
1.0k
views
isi2018-mma
engineering-mathematics
probability
3
votes
3
answers
16
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.
akash.dinkar12
asked
in
Set Theory & Algebra
May 11, 2019
by
akash.dinkar12
2.7k
views
isi2018-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
0
votes
1
answer
17
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 $-4$ $-2$ $2$ $4$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
1.2k
views
isi2018-mma
engineering-mathematics
linear-algebra
eigen-value
determinant
1
vote
2
answers
18
ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
644
views
isi2018-mma
engineering-mathematics
linear-algebra
determinant
2
votes
3
answers
19
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
1.1k
views
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
1
vote
1
answer
20
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 $2$ $-2$ $3$ $-3$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
594
views
isi2018-mma
engineering-mathematics
linear-algebra
system-of-equations
1
vote
1
answer
21
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? $120$ $324$ $424$ $576$
akash.dinkar12
asked
in
Combinatory
May 11, 2019
by
akash.dinkar12
1.1k
views
isi2018-mma
engineering-mathematics
discrete-mathematics
combinatory
2
votes
1
answer
22
ISI2018-MMA-9
If $\alpha$ is a root of $x^2-x+1$, then $\alpha^{2018} + \alpha^{-2018}$ is $-1$ $0$ $1$ $2$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
668
views
isi2018-mma
general-aptitude
quantitative-aptitude
0
votes
2
answers
23
ISI2018-MMA-8
Let $a$ and $b$ be two positive integers such that $a = k_1b + r_1$ and $b = k_2r_1 + r_2,$ where $k_1,k_2,r_1,r_2$ are positive integers with $r_2 < r_1 < b$ Then $\text{gcd}(a, b)$ is same as $\text{gcd}(r_1,r_2)$ $\text{gcd}(k_1,k_2)$ $\text{gcd}(k_1,r_2)$ $\text{gcd}(r_1,k_2)$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
880
views
isi2018-mma
general-aptitude
quantitative-aptitude
0
votes
2
answers
24
ISI2018-MMA-7
The greatest common divisor of all numbers of the form $p^2 − 1$, where $p \geq 7$ is a prime, is $6$ $12$ $24$ $48$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
1.0k
views
isi2018-mma
general-aptitude
quantitative-aptitude
2
votes
5
answers
25
ISI2018-MMA-3
The number of trailing zeros in $100!$ is $21$ $23$ $24$ $25$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
519
views
isi2018-mma
general-aptitude
quantitative-aptitude
number-theory
3
votes
1
answer
26
ISI2018-MMA-2
The number of squares in the following figure is $\begin{array}{|c|c|c|c|}\hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \end{array}$ $25$ $26$ $29$ $30$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
483
views
isi2018-mma
general-aptitude
quantitative-aptitude
1
vote
2
answers
27
ISI2018-MMA-1
The number of isosceles (but not equilateral) triangles with integer sides and no side exceeding $10$ is $65$ $75$ $81$ $90$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
1.5k
views
isi2018-mma
general-aptitude
quantitative-aptitude
1
vote
3
answers
28
ISI2018-MMA-5
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
jjayantamahata
asked
in
Combinatory
May 20, 2018
by
jjayantamahata
1.9k
views
isi2018-mma
general-aptitude
quantitative-aptitude
1
vote
1
answer
29
ISI2018-MMA-6
The volume of the region $S=\{(x,y,z) : \mid x \mid +\mid y \mid + \mid z \mid \leq 1\}$ is $\frac{1}{6}\\$ $\frac{1}{3}\\$ $\frac{2}{3}\\$ $\frac{4}{3}$
Tesla!
asked
in
Quantitative Aptitude
May 14, 2018
by
Tesla!
819
views
isi2018-mma
general-aptitude
quantitative-aptitude
7
votes
3
answers
30
ISI2018-MMA-4
The number of common terms in the two sequences $\{ 3,7,11, \ldots , 407\}$ and $\{2,9,16,\ldots ,709\}$ is $13$ $14$ $15$ $16$
jjayantamahata
asked
in
Quantitative Aptitude
May 13, 2018
by
jjayantamahata
1.1k
views
isi2018-mma
general-aptitude
quantitative-aptitude
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