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Questions by jjayantamahata

0 votes
1 answer
61
ISI-2014-20
0 votes
1 answer
62
ISI-2014-18
Let $D_1 = det \begin{pmatrix}a & b & c\\x &y & z\\p& q & r\end{pmatrix}$ and $D_2 = det \begin{pmatrix}-x & a & -p\\y &-b & q\\z & -c & r\end{pmatrix}$ Then $D_1 = D_2$ $D_1 = 2D_2$ $D_1 = -D_2$ $D_2 = 2D_1$
Let $D_1 = det \begin{pmatrix}a & b & c\\x &y & z\\p& q & r\end{pmatrix}$ and $D_2 = det \begin{pmatrix}-x & a & -p\\y &-b & q\\z & -c & r\end{pmatrix}$Then$D_1 = D_2$$D_...
0 votes
0 answers
63
ISI-2014-17
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$? $0$ $1$ $2$ $3$
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$?$0$$1$$2$$3$
0 votes
1 answer
64
ISI-2014-07
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is $2\sqrt2\pi^2$ $\dfrac{\pi^2}{2\sqrt2}$ $\dfrac{\pi^2}{\sqrt2}$ $\sqrt2\pi^2$
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is$2\sqrt2\pi^2$$\dfrac{\pi^2}{2\sqrt2}$$\dfrac{\pi^2}{\sqrt2}$$\sqrt2\pi^2$
0 votes
2 answers
65
ISI-2014-06
The sum of an infinite geometric series of real numbers is $14$, and the sum of the cubes of the terms of this series is $392$. Then the first term of the series is $-14$ $10$ $7$ $-5$
The sum of an infinite geometric series of real numbers is $14$, and the sum of the cubes of the terms of this series is $392$. Then the first term of the series is$-14$$...
0 votes
2 answers
66
ISI-2014-5
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$ $\text{is 0}$ $\text{is 1}$ $\text{is 2}$ $\text{does not exist}$
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$$\text{is 0}$$\text{is 1}$$\text{is 2}$$\text{does not exist}$
1 votes
1 answer
67
ISI-2014-4
How many pair of positive integers of $(m,n)$ are there satisfying $\displaystyle{\sum_{i=1}^{n}i! = m!}$ $0$ $1$ $2$ $3$
How many pair of positive integers of $(m,n)$ are there satisfying$$\displaystyle{\sum_{i=1}^{n}i! = m!}$$$0$$1$$2$$3$
0 votes
1 answer
68
ISI-2014-3
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true $Re(z)=0$ $\mid z \mid =1$ $Re(z) = 1$ $\text{No such z exists}$
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true$Re(z)=0$$\mid z \mid =1$$Re(z) = 1$$\text{No such z exists}$
0 votes
2 answers
69
ISI-2014-2
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is $\dfrac{41}{81}$ $\dfrac{37}{81}$ $\dfrac{2}{3}$ $\dfrac{4}{9}$
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is$\dfrac{41}{81}...
0 votes
2 answers
70
ISI-2014-1
The four distinct points $(-a,-b),(0,0),(a,b),(a^2,ab)$ are vertices of parallelogram vertices of rectangle collinear lying on a circle
The four distinct points $(-a,-b),(0,0),(a,b),(a^2,ab)$ arevertices of parallelogramvertices of rectanglecollinearlying on a circle
0 votes
0 answers
71
ISI-2014-14
The locus of the center of a circle that passes through origin and cuts off a length $2a$ from the line $y=c$ is $x^2+2cx=a^2+c^2$ $x^2+2cy=a^2+c^2$ $y^2+cx=a^2+c^2$ $y^2+2cy=a^2+c^2$
The locus of the center of a circle that passes through origin and cuts off a length $2a$ from the line $y=c$ is$x^2+2cx=a^2+c^2$$x^2+2cy=a^2+c^2$$y^2+cx=a^2+c^2$$y^2+2cy...
0 votes
0 answers
72
ISI-2014-13
The area bounded by the curves $arg(z) = \pi/3, arg(z) = 2\pi/3$ and $arg(z-2-2\sqrt3i)=\pi$ on the complex plane is given by $2\sqrt3$ $4\sqrt3$ $\sqrt3$ $3\sqrt3$
The area bounded by the curves $arg(z) = \pi/3, arg(z) = 2\pi/3$ and $arg(z-2-2\sqrt3i)=\pi$ on the complex plane is given by$2\sqrt3$$4\sqrt3$$\sqrt3$$3\sqrt3$
2 votes
3 answers
73
ISI-2014-11
Let $X_1,X_2,X_3,X_4$ be i.i.d. random variables each assuming the value $1$ and $-1$ with probability $\dfrac{1}{2}$ each. Then, the probability that the matrix $\begin{pmatrix}X_1 &X_2\\ X_3 &X_4\end{pmatrix}$ is nonsingular equals $1/2$ $3/8$ $5/8$ $1/4$
Let $X_1,X_2,X_3,X_4$ be i.i.d. random variables each assuming the value $1$ and $-1$ with probability $\dfrac{1}{2}$ each. Then, the probability that the matrix $\begin{...
1 votes
0 answers
74
ISI 2014-10
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$. What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{complement of (E2)}})$? $\text{0 and 0.6}$ $\text{0.4 and 0.6}$ $\text{0.4 and 1}$ $\text{0.6 and 1}$
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$.What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{comp...
2 votes
1 answer
76
ISI 2014
Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is $0$ $7$ $8$ $11$
Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is$0$$7$$8$$11$
1 votes
3 answers
77
ISRO-2017-Q4
The function f:[0,3]->[1,29] defined by f(x)=2*X^3 -15*X^2+36*X+1 is a) injective and surjective b) injective but not surjective c) injective but not surjective d) neither injective nor surjective
The function f:[0,3]->[1,29] defined by f(x)=2*X^3 -15*X^2+36*X+1 isa) injective and surjectiveb) injective but not surjectivec) injective but not surjectived) neither in...
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