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Recent questions tagged isi2018
0
votes
0
answers
1
ISI2018MMA25
The solution of the differential equation $(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is $xy = log\ x − log\ y + C$ $xy = log\ y − log\ x + C$ $x^2y^2 = 2(log\ x − log\ y) + C$ $x^2y^2 = 2(log\ y − log\ x) + C$
asked
May 11
in
Others
by
akash.dinkar12
Boss
(
41.4k
points)

16
views
isi2018
nongate
differentialequation
0
votes
1
answer
2
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
(
41.4k
points)

53
views
isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
3
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
(
41.4k
points)

39
views
isi2018
engineeringmathematics
calculus
maximaminima
0
votes
0
answers
4
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
(
41.4k
points)

47
views
isi2018
engineeringmathematics
calculus
integration
0
votes
1
answer
5
ISI2018MMA27
Number of real solutions of the equation $x^7 + 2x^5 + 3x^3 + 4x = 2018$ is $1$ $3$ $5$ $7$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

33
views
isi2018
generalaptitude
numericalability
+1
vote
1
answer
6
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
(
41.4k
points)

117
views
isi2018
engineeringmathematics
discretemathematics
generatingfunctions
+2
votes
1
answer
7
ISI2018MMA24
The sum of the infinite series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+….$ is $2$ $3$ $4$ $6$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

44
views
isi2018
generalaptitude
numericalability
0
votes
0
answers
8
ISI2018MMA23
For $n\geq 1$,let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + · · · + c_nr^n$,where $c_k \leq M$ for all integer $k$ and $r<1$.Then both $\{a_n\}$ and $\{b_n\}$ are Cauchy ... $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

7
views
isi2018
generalaptitude
numericalability
0
votes
0
answers
9
ISI2018MMA22
The xaxis divides the circle $x^2 + y^2 − 6x − 4y + 5 = 0$ into two parts. The area of the smaller part is $2\pi1$ $2(\pi1)$ $2\pi3$ $2(\pi2)$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

13
views
isi2018
generalaptitude
numericalability
0
votes
0
answers
10
ISI2018MMA21
The angle between the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 4x$ is $\pi /2$ $\pi /3$ $\pi /4$ $\pi /6$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

4
views
isi2018
generalaptitude
numericalability
0
votes
1
answer
11
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
(
41.4k
points)

92
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
12
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
(
41.4k
points)

28
views
isi2018
engineeringmathematics
calculus
limits
0
votes
2
answers
13
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
(
41.4k
points)

40
views
isi2018
engineeringmathematics
probability
0
votes
2
answers
14
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
(
41.4k
points)

51
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
15
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
(
41.4k
points)

46
views
isi2018
engineeringmathematics
probability
0
votes
1
answer
16
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
(
41.4k
points)

41
views
isi2018
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
1
answer
17
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
(
41.4k
points)

62
views
isi2018
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
1
answer
18
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
(
41.4k
points)

55
views
isi2018
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
19
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
(
41.4k
points)

78
views
isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
20
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
(
41.4k
points)

63
views
isi2018
engineeringmathematics
linearalgebra
systemofequations
0
votes
1
answer
21
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
(
41.4k
points)

44
views
isi2018
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
22
ISI2018MMA9
If $\alpha$ is a root of $x^2x+1$, then $\alpha^{2018} + \alpha^{2018}$ is $1$ $0$ $1$ $2$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

42
views
isi2018
generalaptitude
numericalability
0
votes
0
answers
23
ISI2018MMA8
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 $gcd(a, b)$ is same as $gcd(r_1,r_2)$ $gcd(k_1,k_2)$ $gcd(k_1,r_2)$ $gcd(r_1,k_2)$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

13
views
isi2018
generalaptitude
numericalability
0
votes
1
answer
24
ISI2018MMA7
The greatest common divisor of all numbers of the form $p^2 − 1$, where $p \geq 7$ is a prime, is $6$ $12$ $24$ $48$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

12
views
isi2018
generalaptitude
numericalability
0
votes
0
answers
25
ISI2018MMA5
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 $3$ $33$ $63$ $93$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

10
views
isi2018
generalaptitude
numericalability
+1
vote
1
answer
26
ISI2018MMA3
The number of trailing zeros in $100!$ is $21$ $23$ $24$ $25$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

16
views
isi2018
generalaptitude
numericalability
+2
votes
1
answer
27
ISI2018MMA2
The number of squares in the following figure is $\begin{array}{cccc}\hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \hline \text{} & & & \\\hline \end{array}$ $25$ $26$ $29$ $30$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

66
views
isi2018
generalaptitude
numericalability
+1
vote
0
answers
28
ISI2018MMA1
The number of isosceles (but not equilateral) triangles with integer sides and no side exceeding $10$ is $65$ $75$ $81$ $90$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.4k
points)

13
views
isi2018
generalaptitude
numericalability
0
votes
1
answer
29
ISI2018MMA6
The volume of the region $S=\{(x,y,z) :\left  x \right +\left  y \right +\left  z \right \leq 1\}$ is $\frac{1}{6}\\$ $\frac{1}{3}\\$ $\frac{2}{3}\\$ $\frac{4}{3}$
asked
May 14, 2018
in
Numerical Ability
by
Tesla!
Boss
(
18.1k
points)

212
views
isi2018
generalaptitude
numericalability
+3
votes
3
answers
30
ISI2018MMA4
The number of common terms in the two sequences $\{ 3,7,11, \ldots , 407\}$ and $\{2,9,16,\ldots ,709\}$ is $13$ $14$ $15$ $16$
asked
May 13, 2018
in
Numerical Ability
by
jjayantamahata
Active
(
1.4k
points)

330
views
isi2018
generalaptitude
numericalability
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