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Recent questions tagged isi2016-mmamma

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1 answer
1
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 jothee 72 views
1 vote
2 answers
2
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 jothee 88 views
0 votes
1 answer
3
The $a, b, c$ and $d$ satisfy the equations$\begin{matrix} a & + & 7b & + & 3c & + & 5d & = &16 \\ 8a & + & 4b & + & 6c & + & 2d & = &-16 \\ 2a & + & 6b & + & 4c & + & 8d & = &16 \\ 5a & + & 7b & + & 3c & + & 5d & = &-16 \end{matrix}$Then $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
asked Sep 13, 2018 in Linear Algebra jothee 87 views
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0 answers
4
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 jothee 61 views
0 votes
1 answer
5
Find the centroid of the triangle whose sides are given by the following equations: $\begin{matrix} 4x & - & y & = &19 \\ x &- & y & = & 4 \\ x& + & 2y & = & -11 \end{matrix}$ $\left(\frac{11}{3}, -\frac{7}{3}\right)$ $\left(\frac{5}{3}, -\frac{7}{3}\right)$ $\left(-\frac{11}{3}, -\frac{7}{3}\right)$ $\left(\frac{7}{3}, -\frac{11}{3}\right)$
asked Sep 13, 2018 in Geometry jothee 84 views
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0 answers
6
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 jothee 56 views
2 votes
1 answer
7
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 jothee 131 views
0 votes
2 answers
8
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
asked Sep 13, 2018 in Probability jothee 165 views
0 votes
1 answer
9
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 $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1-p_i)$ $1-\Pi_{i=1}^n \: \: (1-p_i)$
asked Sep 13, 2018 in Probability jothee 96 views
0 votes
1 answer
10
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 jothee 83 views
0 votes
1 answer
11
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 jothee 65 views
0 votes
2 answers
12
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 jothee 74 views
0 votes
1 answer
13
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 jothee 61 views
0 votes
0 answers
14
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 jothee 59 views
0 votes
0 answers
15
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 jothee 50 views
2 votes
1 answer
16
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 jothee 80 views
1 vote
1 answer
17
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 jothee 112 views
2 votes
0 answers
18
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 jothee 64 views
1 vote
0 answers
19
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 jothee 81 views
0 votes
0 answers
20
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 jothee 70 views
0 votes
0 answers
21
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 jothee 61 views
0 votes
0 answers
22
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 $a$ ... number $B$ 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 jothee 109 views
0 votes
1 answer
23
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 jothee 66 views
2 votes
2 answers
24
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 jothee 95 views
1 vote
0 answers
25
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 jothee 81 views
0 votes
0 answers
26
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 $a<-\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
asked Sep 13, 2018 in Numerical Ability jothee 53 views
0 votes
0 answers
27
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 jothee 64 views
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