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Recent questions tagged isi2016-mmamma
0
votes
1
answer
1
ISI2016-MMA-2
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$? $0$ $1$ $2$ $3$
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asked
in
Others
Sep 13, 2018
by
go_editor
158
views
isi2016-mmamma
complex-number
non-gate
1
vote
2
answers
2
ISI2016-MMA-3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
324
views
isi2016-mmamma
trigonometry
quadratic-equations
roots
0
votes
1
answer
3
ISI2016-MMA-4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
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asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
227
views
isi2016-mmamma
linear-algebra
matrix
system-of-equations
0
votes
0
answers
4
ISI2016-MMA-5
Let $ f(x, y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x, y) \neq (0, 0) \\ 0 & \text{ if } (x, y) = (0, 0) \end{cases}$ Then $\lim_{(x, y) \rightarrow (0,0)}$f(x,y)$ equals $0$ equals $1$ equals $2$ does not exist
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asked
in
Calculus
Sep 13, 2018
by
go_editor
192
views
isi2016-mmamma
calculus
limits
non-gate
0
votes
1
answer
5
ISI2016-MMA-6
Find the centroid of the triangle whose sides are given by the following equations: $\begin{matrix} 4x & - & y & = &19 \\ x &- & y & = & 4 \\ x& + & 2y & = & -11 \end{matrix}$ $\left(\frac{11}{3}, -\frac{7}{3}\right)$ ... $\left(-\frac{11}{3}, -\frac{7}{3}\right)$ $\left(\frac{7}{3}, -\frac{11}{3}\right)$
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asked
in
Geometry
Sep 13, 2018
by
go_editor
227
views
isi2016-mmamma
triangle
centroid
non-gate
0
votes
0
answers
6
ISI2016-MMA-7
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$ is $\{1\}$ $\{1, -1\}$ $\{1, 2\}$ $\{-1, 2\}$
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asked
in
Calculus
Sep 13, 2018
by
go_editor
129
views
isi2016-mmamma
differential-equation
non-gate
2
votes
2
answers
7
ISI2016-MMA-8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
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asked
in
Calculus
Sep 13, 2018
by
go_editor
469
views
isi2016-mmamma
calculus
differentiation
2
votes
2
answers
8
ISI2016-MMA-9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
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asked
in
Probability
Sep 13, 2018
by
go_editor
609
views
isi2016-mmamma
probability
random-variable
poisson-distribution
expectation
0
votes
1
answer
9
ISI2016-MMA-10
If $A_1, A_2, \dots , A_n$ are independent events with probabilities $p_1, p_2, \dots , p_n$ respectively, then $P( \cup_{i=1}^n A_i)$ equals $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1-p_i)$ $1-\Pi_{i=1}^n \: \: (1-p_i)$
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asked
in
Probability
Sep 13, 2018
by
go_editor
208
views
isi2016-mmamma
probability
independent-events
0
votes
1
answer
10
ISI2016-MMA-11
Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability 4/5 and with water it would die with probability 3/20. The probability that Ravi's neighbor would remember to water the plant is 9/10. If the plant actually died, what is the probability that Ravi's neighbor forgot to water the plant? 4/5 27/43 16/43 2/25
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asked
in
Probability
Sep 13, 2018
by
go_editor
203
views
isi2016-mmamma
probability
0
votes
1
answer
11
ISI2016-MMA-12
Suppose there are $n$ positive real numbers such that their sum is 20 and the product is strictly greater than 1. What is the maximum possible value of n? 18 19 20 21
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
199
views
isi2016-mmamma
quantitative-aptitude
number-system
0
votes
2
answers
12
ISI2016-MMA-13
Which one of the following statements is correct regarding the elements and subsets of the set $\{1, 2, \{1, 2, 3\}\}$? $\{1, 2\} \in \{1, 2, \{1, 2, 3\} \}$ $\{1, 2\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $\{1, 2, 3\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $3 \in \{1, 2, \{1, 2, 3\} \}$
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asked
in
Set Theory & Algebra
Sep 13, 2018
by
go_editor
223
views
isi2016-mmamma
set-theory
subsets
0
votes
1
answer
13
ISI2016-MMA-15
The number of positive integers $n$ for which $n^2 +96$ is a perfect square $0$ $1$ $2$ $4$
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
188
views
isi2016-mmamma
quantitative-aptitude
number-system
0
votes
0
answers
14
ISI2016-MMA-16
Suppose a 6 digit number $N$ is formed by rearranging the digits of the number 123456. If $N$ is divisible by 5, then the set of all possible remainders when $N$ is divided by 45 is $\{30\}$ $\{15, 30\}$ $\{0, 15, 30\}$ $\{0, 5, 15, 30\}$
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
169
views
isi2016-mmamma
quantitative-aptitude
number-system
remainder-theorem
0
votes
0
answers
15
ISI2016-MMA-17
The number of positive integers $n$ for which $n^3 +(n+1)^3 +(n+2)^3 = (n+3)^3$ is $0$ $1$ $2$ $3$
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
181
views
isi2016-mmamma
quantitative-aptitude
number-system
3
votes
1
answer
16
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
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asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
194
views
isi2016-mmamma
linear-algebra
matrix
summation
1
vote
2
answers
17
ISI2016-MMA-19
Let $A$ be a real $2 \times 2$ matrix. If $5+3i$ is an eigenvalue of $A$, then $det(A)$ equals 4 equals 8 equals 16 cannot be determined from the given information
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asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
416
views
isi2016-mmamma
linear-algebra
matrix
eigen-value
2
votes
1
answer
18
ISI2016-MMA-20
Let $f : (0, \infty) \rightarrow (0, \infty)$ be a strictly decreasing function. Consider $h(x) = \dfrac{f(\frac{x}{1+x})}{1+f(\frac{x}{1+x})}$. Which one of the following is always true? $h$ is strictly decreasing $h$ is strictly increasing $h$ is strictly decreasing at first and then strictly increasing $h$ is strictly increasing at first and then strictly decreasing
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asked
in
Calculus
Sep 13, 2018
by
go_editor
198
views
isi2016-mmamma
calculus
functions
non-gate
1
vote
0
answers
19
ISI2016-MMA-21
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
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asked
in
Calculus
Sep 13, 2018
by
go_editor
202
views
isi2016-mmamma
functions
inequality
combinatory
0
votes
0
answers
20
ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
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asked
in
Others
Sep 13, 2018
by
go_editor
176
views
isi2016-mmamma
sequence-series
convergence-divergence
summation
non-gate
0
votes
0
answers
21
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
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asked
in
Calculus
Sep 13, 2018
by
go_editor
164
views
isi2016-mmamma
calculus
integration
definite-integral
0
votes
0
answers
22
ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true? The limits $\lim_{x \rightarrow a+} f(x) $ and $\lim_{x \rightarrow a-} f(x)$ exist for all real numbers $a$ If $f$ is differentiable at $a$ then ... such that $f(x)<B$ for all real $x$ There cannot be any real number $L$ such that $f(x)>L$ for all real $x$
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asked
in
Calculus
Sep 13, 2018
by
go_editor
256
views
isi2016-mmamma
calculus
continuity
differentiation
limits
0
votes
1
answer
23
ISI2016-MMA-25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$-digit palindrome and $12345$ is not a palindrome. How many $8$-digit palindromes are prime? $0$ $1$ $11$ $19$
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asked
in
Combinatory
Sep 13, 2018
by
go_editor
200
views
isi2016-mmamma
combinatory
2
votes
2
answers
24
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then $f$ is not continuous at some points $f$ is continuous everywhere, but not differentiable anywhere $f$ is continuous everywhere, but not differentiable at exactly one point $f$ is differentiable everywhere
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asked
in
Calculus
Sep 13, 2018
by
go_editor
268
views
isi2016-mmamma
calculus
continuity
differentiation
1
vote
1
answer
25
ISI2016-MMA-28
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true? $A \neq A^2$ Eigenvalues of $A^2$ are all zero rank($A$) > rank($A^2$) rank($A$) > trace($A$)
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asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
251
views
isi2016-mmamma
linear-algebra
matrix
eigen-value
rank-of-matrix
0
votes
0
answers
26
ISI2016-MMA-29
Suppose $a$ is a real number for which all the roots of the equation $x^4 -2ax^2+x+a^2-a=0$ are real. Then $a<-\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
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asked
in
Quantitative Aptitude
Sep 13, 2018
by
go_editor
137
views
isi2016-mmamma
quantitative-aptitude
quadratic-equations
roots
0
votes
0
answers
27
ISI2016-MMA-30
A club with $n$ members is organized into four committees so that each member belongs to exactly two committees and each pair of committees has exactly one member in common. Then $n=4$ $n=6$ $n=8$ $n$ cannot be determined from the given information
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asked
in
Combinatory
Sep 13, 2018
by
go_editor
140
views
isi2016-mmamma
combinatory
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