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Recent questions tagged isi2016mmamma
0
votes
1
answer
1
ISI2016MMA2
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$? $0$ $1$ $2$ $3$
asked
Sep 13, 2018
in
Others
by
jothee
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105k
points)

27
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isi2016mmamma
complexnumber
nongate
+1
vote
1
answer
2
ISI2016MMA3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{x}$ is $0$ $1$ $2$ $\infty$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
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105k
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29
views
isi2016mmamma
trigonometry
quadraticequations
roots
0
votes
1
answer
3
ISI2016MMA4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $4$ $0$ $16$ $16$
asked
Sep 13, 2018
in
Linear Algebra
by
jothee
Veteran
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105k
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32
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isi2016mmamma
linearalgebra
matrices
systemofequations
0
votes
0
answers
4
ISI2016MMA5
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
asked
Sep 13, 2018
in
Calculus
by
jothee
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105k
points)

22
views
isi2016mmamma
calculus
limits
nongate
0
votes
1
answer
5
ISI2016MMA6
Find the centroid of the triangle whose sides are given by the following equations: $\begin{matrix} 4x &  & y & = &19 \\ x & & y & = & 4 \\ x& + & 2y & = & 11 \end{matrix}$ $\left(\frac{11}{3}, \frac{7}{3}\right)$ ... $\left(\frac{11}{3}, \frac{7}{3}\right)$ $\left(\frac{7}{3}, \frac{11}{3}\right)$
asked
Sep 13, 2018
in
Geometry
by
jothee
Veteran
(
105k
points)

29
views
isi2016mmamma
triangles
centroid
nongate
0
votes
0
answers
6
ISI2016MMA7
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 $\{1\}$ $\{1, 1\}$ $\{1, 2\}$ $\{1, 2\}$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

14
views
isi2016mmamma
differentialequation
nongate
+2
votes
1
answer
7
ISI2016MMA8
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 $64/5$ $32/5$ $37/5$ $67/5$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

48
views
isi2016mmamma
calculus
differentiation
0
votes
1
answer
8
ISI2016MMA9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(XY)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
asked
Sep 13, 2018
in
Probability
by
jothee
Veteran
(
105k
points)

58
views
isi2016mmamma
probability
randomvariable
poissondistribution
expectation
0
votes
0
answers
9
ISI2016MMA10
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 $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1p_i)$ $1\Pi_{i=1}^n \: \: (1p_i)$
asked
Sep 13, 2018
in
Probability
by
jothee
Veteran
(
105k
points)

20
views
isi2016mmamma
probability
independentevents
0
votes
1
answer
10
ISI2016MMA11
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
asked
Sep 13, 2018
in
Probability
by
jothee
Veteran
(
105k
points)

27
views
isi2016mmamma
probability
0
votes
0
answers
11
ISI2016MMA12
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
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

18
views
isi2016mmamma
numericalability
numbersystem
0
votes
2
answers
12
ISI2016MMA13
Which one of the following statements is correct regarding the elements and subsets of the set $\{1, 2, \{1, 2, 3\}\}$? $\{1, 2\} \in \{1, 2, \{1, 2, 3\} \}$ $\{1, 2\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $\{1, 2, 3\} \subseteq \{1, 2, \{1, 2, 3\} \}$ $3 \in \{1, 2, \{1, 2, 3\} \}$
asked
Sep 13, 2018
in
Set Theory & Algebra
by
jothee
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(
105k
points)

23
views
isi2016mmamma
sets
subsets
0
votes
1
answer
13
ISI2016MMA15
The number of positive integers $n$ for which $n^2 +96$ is a perfect square $0$ $1$ $2$ $4$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

25
views
isi2016mmamma
numericalability
numbersystem
0
votes
0
answers
14
ISI2016MMA16
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 $\{30\}$ $\{15, 30\}$ $\{0, 15, 30\}$ $\{0, 5, 15, 30\}$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

16
views
isi2016mmamma
numericalability
numbersystem
remaindertheorem
0
votes
0
answers
15
ISI2016MMA17
The number of positive integers $n$ for which $n^3 +(n+1)^3 +(n+2)^3 = (n+3)^3$ is $0$ $1$ $2$ $3$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

16
views
isi2016mmamma
numericalability
numbersystem
+2
votes
1
answer
16
ISI2016MMA18
Let $A=\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
asked
Sep 13, 2018
in
Linear Algebra
by
jothee
Veteran
(
105k
points)

28
views
isi2016mmamma
linearalgebra
matrices
summation
+1
vote
0
answers
17
ISI2016MMA19
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
asked
Sep 13, 2018
in
Linear Algebra
by
jothee
Veteran
(
105k
points)

21
views
isi2016mmamma
linearalgebra
matrices
eigenvalue
+2
votes
0
answers
18
ISI2016MMA20
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
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
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19
views
isi2016mmamma
calculus
functions
nongate
+1
vote
0
answers
19
ISI2016MMA21
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

22
views
isi2016mmamma
functions
inequality
permutationandcombination
0
votes
0
answers
20
ISI2016MMA22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [1, 1)$ $a \in (1, 1]$ $a \in [1, 1]$ $a \in (\infty, \infty)$
asked
Sep 13, 2018
in
Others
by
jothee
Veteran
(
105k
points)

14
views
isi2016mmamma
sequenceseries
convergencedivergence
summation
nongate
0
votes
0
answers
21
ISI2016MMA23
Given that $\int_{\infty}^{\infty} e^{x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{ \infty}^{\infty} \mid x \mid ^{1/2} e^{ \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

13
views
isi2016mmamma
calculus
integration
definiteintegrals
0
votes
0
answers
22
ISI2016MMA24
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 $x$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

12
views
isi2016mmamma
calculus
continuity
differentiation
limits
0
votes
0
answers
23
ISI2016MMA25
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? $0$ $1$ $11$ $19$
asked
Sep 13, 2018
in
Combinatory
by
jothee
Veteran
(
105k
points)

17
views
isi2016mmamma
permutationandcombination
+2
votes
1
answer
24
ISI2016MMA27
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
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

21
views
isi2016mmamma
calculus
continuity
differentiation
+1
vote
0
answers
25
ISI2016MMA28
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($A$)
asked
Sep 13, 2018
in
Linear Algebra
by
jothee
Veteran
(
105k
points)

22
views
isi2016mmamma
linearalgebra
matrices
eigenvalue
rankofmatrix
0
votes
0
answers
26
ISI2016MMA29
Suppose $a$ is a real number for which all the roots of the equation $x^4 2ax^2+x+a^2a=0$ are real. Then $a<\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
asked
Sep 13, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

15
views
isi2016mmamma
numericalability
quadraticequations
roots
0
votes
0
answers
27
ISI2016MMA30
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
asked
Sep 13, 2018
in
Combinatory
by
jothee
Veteran
(
105k
points)

17
views
isi2016mmamma
permutationandcombination
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