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Recent questions tagged isi2016-mmamma

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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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583
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2 answers
1 votes
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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454
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ISI2016-MMA-4
The $a, b, c$ and $d$ ... & + & 3c & + & 5d & = &-16 \end{matrix}$Then $(a+d)(b+c)$ equals$-4$0$16$-16$
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476
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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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ISI2016-MMA-6
Find the centroid of the triangle whose sides are given by the following equations: ... {11}{3}, -\frac{7}{3}\right)$\left(\frac{7}{3}, -\frac{11}{3}\right)$
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235
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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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956
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2 answers
2 votes
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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920
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2 answers
2 votes
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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333
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1 answers
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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 ... $1-\Pi_{i=1}^n \: \: (1-p_i)$
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392
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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 that Ravi's neighbor forgot to water the plant?4/527/4316/432/25
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359
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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?18192021
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361
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2 answers
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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\} \}$3 \in \{1, 2, \{1, 2, 3\} \}$
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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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276
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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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295
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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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331
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1 answers
3 votes
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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688
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2 answers
1 votes
ISI2016-MMA-19
Let $A$ be a real $2 \times 2$ matrix. If $5+3i$ is an eigenvalue of $A$, then $det(A)$equals 4equals 8equals 16cannot be determined from the given information
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483
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1 answers
2 votes
ISI2016-MMA-20
Let $f : (0, \infty) \rightarrow (0, \infty)$ ... at first and then strictly increasing$h$ is strictly increasing at first and then strictly decreasing
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350
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0 answers
1 votes
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 $f(1)< f(2) < f(3)$ ... $\frac{8!}{3!}$
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268
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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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463
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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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578
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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 ... cannot be any real number $L$ such that $f(x)>L$ for all real $x$
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407
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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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616
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3 answers
3 votes
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$ ... differentiable anywhere$f$ is continuous everywhere, but not differentiable at exactly one point$f$ is differentiable everywhere
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528
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1 answers
2 votes
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 zerorank($A$) > rank($A^2$)rank($A$) > trace($A$)
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252
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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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356
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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 ... $n=6$n=8$n$ cannot be determined from the given information
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