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Recent questions tagged isi2019-mma

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ISI2019-MMA-30
Consider the function $h$ defined on $\{0,1, .10\}$ with $h(0)=0, \: h(10)=10 $ and$2[h(i)-h(i-1)] = h(i+1) - h(i) \: \text{ for } i = 1,2, \dots ,9.$Then ... {1}{2^9-1}\\$\frac{10}{2^9+1}\\$\frac{10}{2^{10}-1}\\$\frac{1}{2^{10}+1}$
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ISI2019-MMA-29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$ ... }n \int_{0}^{100} f(x)\psi(nx)dx$ is$f(0)$f'(0)$f''(0)$f(100)$
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ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is$1/4$1/6$1/8$1/24$
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ISI2019-MMA-27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold ... {pmatrix} 30 \\ 5 \end{pmatrix}$\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
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ISI2019-MMA-26
If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then$t < \frac{1}{3}$\frac{1}{3} < t < \frac{1}{2}$\frac{1}{2} < t < \frac{2}{3}$\frac{2}{3} < t < 1$
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ISI2019-MMA-25
Let $a,b,c$ ... $(0,2)$two distinct real roots in $(0,2)$
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ISI2019-MMA-24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, ... the following is necessarily true?$S \subset T$T \subset S$S = T$None of the above
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ISI2019-MMA-23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ ... must be a symmetric matrixA must be a skew-symmetric matrixNone of the above must necessarily hold
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ISI2019-MMA-22
A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2/5$, then the value of $p$ is$2/7$1/3$5/7$2/3$
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ISI2019-MMA-21
A function $f:\mathbb{R^2} \rightarrow \mathbb{R}$ is called degenerate on $x_i$, if $f(x_1,x_2)$ remains constant when $x_i$ varies $(i=1,2)$ ... $ but not on $x_1$f$ is neither degenerate on $x_1$ nor on $x_2$
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ISI2019-MMA-20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $ O'$ ... $190951$194976$219049$
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ISI2019-MMA-19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is$1$2$6$12$
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ISI2019-MMA-18
For the differential equation $\frac{dy}{dx} + xe^{-y}+2x=0$It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ ... - \frac{1}{2} \bigg)$\text{ln} \bigg(\frac{3}{2e} - \frac{1}{4} \bigg)$
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ISI2019-MMA-17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is$(3,6)$(6,3)$(5,10)$(10,5)$
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ISI2019-MMA-16
If $S$ and $S’$ are the foci of the ellipse $3x^2 + 4y^2=12$ and $P$ is a point on the ellipse, then the perimeter of the triangle $PSS’$ is$4$6$8$dependent on the coordinates of $P$
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ISI2019-MMA-15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$2$ for any real number $t$2$ or $3$ depending on the value of $t$1,2$ or $3$ depending on the value of $t$
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ISI2019-MMA-14
If the system of equations$\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is$1$-1$3$-3$
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ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$10$12$14$
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ISI2019-MMA-12
Given a positive integer $m$, we define $f(m)$ as the highest power of $2$ that divides $m$. If $n$ is a prime number greater than $3$, then$f(n^3-1) = f(n-1)$f(n^3-1) = f(n-1) +1$f(n^3-1) = 2f(n-1)$None of the above is necessarily true
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ISI2019-MMA-11
How many triplets of real numbers $(x,y,z)$ are simultaneous solutions of the equations $x+y=2$ and $xy-z^2=1$?$0$1$2$infinitely many
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ISI2019-MMA-10
The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the student is ... $?$3/5$5/7$10/13$15/19$
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ISI2019-MMA-9
$(\cos 100^\circ + i \sin 100^\circ)(\cos 0^\circ + i \sin 110^\circ)$ is equal to$\frac{1}{2}(\sqrt3 – i)$\frac{1}{2}(-\sqrt3 – i)$\frac{1}{2}(-\sqrt3 +i)$\frac{1}{2}(\sqrt3 + i)$
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ISI2019-MMA-8
For $0 \leq x < 2 \pi$, the number of solutions of the equation$\sin^2x + 2 \cos^2x + 3\sin x \cos x = 0$is$1$2$3$4$
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ISI2019-MMA-7
The value of $\frac{1}{2\sin10^\circ}$ – $2\sin70^\circ$ is $-1/2$ $-1$1/2$1$
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ISI2019-MMA-6
The solution of the differential equation $\frac{dy}{dx} = \frac{2xy}{x^2-y^2}$is$x^2 + y^2 = cy$, where $c$ is a constant$x^2 + y^2 = cx$, where $c$ is a ... $c$ is a constant$x^2 - y^2 = cx$, where $c$ is a constant
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ISI2019-MMA-5
If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-a}$ is$-5$-3$3$5$
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ISI2019-MMA-4
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not divisible by $9$ is equal to$120$180$240$360$
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ISI2019-MMA-3
The sum of all $3$ digit numbers that leave a remainder of $2$ when divided by $3$ is:$189700$164850$164750$149700$
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ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is$21$22$27$28$
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ISI2019-MMA-1
The highest power of $7$ that divides $100!$ is : $14$15$16$18$
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