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Recent questions tagged isi2016-mmamma

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1 answer
1
ISI2016-MMA-2
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid =5$? $0$ $1$ $2$ $3$
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$$3$
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1 votes
2 answers
2
ISI2016-MMA-3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is$0$$1$$2$$\infty$
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3
ISI2016-MMA-4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
The $a, b, c$ and $d$ satisfy the equations$$\begin{matrix} a & + & 7b & + & 3c & + & 5d & = &16 \\ 8a & + & 4b & + & 6c & + & 2d & = &-16 \\ 2a & + & 6b & + & 4c & + & 8...
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4
ISI2016-MMA-5
Let $ f(x, y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x, y) \neq (0, 0) \\ 0 & \text{ if } (x, y) = (0, 0) \end{cases}$ Then $\lim_{(x, y) \rightarrow (0,0)}$f(x,y)$ equals $0$ equals $1$ equals $2$ does not exist
Let $ f(x, y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x, y) \neq (0, 0) \\ 0 & \text{ if } (x, y) = (0, 0) \end{cases}$Then $\lim_{(x, y) \rightarrow (0,0)}...
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6
ISI2016-MMA-7
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$ is $\{1\}$ $\{1, -1\}$ $\{1, 2\}$ $\{-1, 2\}$
The set of value(s) of $\alpha$ for which $y(t)=t^{\alpha}$ is a solution to the differential equation $$t^2 \frac{d^2y}{dx^2}-2t \frac{dy}{dx}+2y =0 \: \text{ for } t>0$...
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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 $64/5$ $32/5$ $37/5$ $67/5$
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$$67/5$
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2 votes
2 answers
8
ISI2016-MMA-9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ?$\lambda$$2 \lambd...
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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 $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1-p_i)$ $1-\Pi_{i=1}^n \: \: (1-p_i)$
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$$\P...
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11
ISI2016-MMA-12
Suppose there are $n$ positive real numbers such that their sum is 20 and the product is strictly greater than 1. What is the maximum possible value of n? 18 19 20 21
Suppose there are $n$ positive real numbers such that their sum is 20 and the product is strictly greater than 1. What is the maximum possible value of n?18192021
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13
ISI2016-MMA-15
The number of positive integers $n$ for which $n^2 +96$ is a perfect square $0$ $1$ $2$ $4$
The number of positive integers $n$ for which $n^2 +96$ is a perfect square$0$$1$$2$$4$
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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 $\{30\}$ $\{15, 30\}$ $\{0, 15, 30\}$ $\{0, 5, 15, 30\}$
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 divid...
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15
ISI2016-MMA-17
The number of positive integers $n$ for which $n^3 +(n+1)^3 +(n+2)^3 = (n+3)^3$ is $0$ $1$ $2$ $3$
The number of positive integers $n$ for which $n^3 +(n+1)^3 +(n+2)^3 = (n+3)^3$ is$0$$1$$2$$3$
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3 votes
1 answer
16
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then$B^2 =1$$B^2 =0$$B^2 =A$$B^2 =B$
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1 votes
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
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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1 votes
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 $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
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}$$\begin{pm...
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20
ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if$a \in [-1, 1)$$a \in (-1, 1]$$a \in [-1, 1]$$a \in (-\infty, \infty)$
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21
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
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$$\sqrt{\pi}...
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0 votes
1 answer
23
ISI2016-MMA-25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$-digit palindrome and $12345$ is not a palindrome. How many $8$-digit palindromes are prime? $0$ $1$ $11$ $19$
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$-digit palindrome and $12345$ is not a ...
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2 votes
1 answer
25
ISI2016-MMA-28
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true? $A \neq A^2$ Eigenvalues of $A^2$ are all zero rank($A$) > rank($A^2$) rank($A$) > trace($A$)
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true?$A \neq A^2$Eigenvalues of $A^2$ are all z...
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26
ISI2016-MMA-29
Suppose $a$ is a real number for which all the roots of the equation $x^4 -2ax^2+x+a^2-a=0$ are real. Then $a<-\frac{2}{3}$ $a=0$ $0<a<\frac{3}{4}$ $a \geq \frac{3}{4}$
Suppose $a$ is a real number for which all the roots of the equation $x^4 -2ax^2+x+a^2-a=0$ are real. Then$a<-\frac{2}{3}$$a=0$$0<a<\frac{3}{4}$$a \geq \frac{3}{4}$
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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
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 comm...
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