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Recent questions tagged isi2019-mma
4
votes
1
answer
1
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 the value of $h(1)$ is $\frac{1}{2^9-1}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}-1}\\$ $\frac{1}{2^{10}+1}$
Sayan Bose
asked
in
Calculus
May 7, 2019
by
Sayan Bose
1.4k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
functions
1
vote
1
answer
2
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 $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
Sayan Bose
asked
in
Calculus
May 7, 2019
by
Sayan Bose
1.5k
views
isi2019-mma
engineering-mathematics
calculus
integration
1
vote
1
answer
3
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 $1/4$ $1/6$ $1/8$ $1/24$
Sayan Bose
asked
in
Calculus
May 7, 2019
by
Sayan Bose
1.7k
views
isi2019-mma
calculus
engineering-mathematics
integration
3
votes
3
answers
4
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 the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
Sayan Bose
asked
in
Combinatory
May 7, 2019
by
Sayan Bose
4.5k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
1
vote
1
answer
5
ISI2019-MMA-26
If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then $t < \frac{1}{3}$ $\frac{1}{3} < t < \frac{1}{2}$ $\frac{1}{2} < t < \frac{2}{3}$ $\frac{2}{3} < t < 1$
Sayan Bose
asked
in
Quantitative Aptitude
May 7, 2019
by
Sayan Bose
1.2k
views
isi2019-mma
general-aptitude
quantitative-aptitude
0
votes
1
answer
6
ISI2019-MMA-25
Let $a,b,c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$
Sayan Bose
asked
in
Calculus
May 7, 2019
by
Sayan Bose
888
views
isi2019-mma
engineering-mathematics
calculus
integration
1
vote
2
answers
7
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 $x \in \mathbb{R}$, where $f^n(x) = f \circ f^{n-1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
Sayan Bose
asked
in
Calculus
May 7, 2019
by
Sayan Bose
1.3k
views
isi2019-mma
engineering-mathematics
calculus
limits
1
vote
1
answer
8
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 $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skew-symmetric matrix None of the above must necessarily hold
Sayan Bose
asked
in
Linear Algebra
May 7, 2019
by
Sayan Bose
1.3k
views
isi2019-mma
engineering-mathematics
linear-algebra
matrix
0
votes
3
answers
9
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 $2/7$ $1/3$ $5/7$ $2/3$
Sayan Bose
asked
in
Probability
May 7, 2019
by
Sayan Bose
625
views
isi2019-mma
probability
0
votes
1
answer
10
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 $(i=1,2)$. Define $f(x_1,x_2) = \mid 2^{\pi _i/x_1} \mid ^{x_2} \text{ for } x_1 \neq 0$, where $i = \sqrt {-1}$. ... $x_1$ but not on $x_2$ $f$ is degenerate on $x_2$ but not on $x_1$ $f$ is neither degenerate on $x_1$ nor on $x_2$
Sayan Bose
asked
in
Others
May 7, 2019
by
Sayan Bose
1.1k
views
isi2019-mma
complex-number
0
votes
3
answers
11
ISI2019-MMA-20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
Sayan Bose
asked
in
Combinatory
May 7, 2019
by
Sayan Bose
2.0k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
2
votes
3
answers
12
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 $1$ $2$ $6$ $12$
Sayan Bose
asked
in
Set Theory & Algebra
May 7, 2019
by
Sayan Bose
1.7k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1
vote
1
answer
13
ISI2019-MMA-18
For the differential equation $\frac{dy}{dx} + xe^{-y}+2x=0$ It is given that $y=0$ when $x=0$. When $x=1$, $\:y$ is given by $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3e}{2} – \frac{1}{4} \bigg)$ $\text{ln} \bigg(\frac{3}{e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{4} \bigg)$
Sayan Bose
asked
in
Others
May 7, 2019
by
Sayan Bose
4.2k
views
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
1
vote
2
answers
14
ISI2019-MMA-17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is $(3,6)$ $(6,3)$ $(5,10)$ $(10,5)$
Sayan Bose
asked
in
Geometry
May 7, 2019
by
Sayan Bose
966
views
isi2019-mma
non-gate
geometry
1
vote
1
answer
15
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 $P$
Sayan Bose
asked
in
Geometry
May 7, 2019
by
Sayan Bose
669
views
isi2019-mma
non-gate
geometry
1
vote
2
answers
16
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 $t$
Sayan Bose
asked
in
Linear Algebra
May 7, 2019
by
Sayan Bose
1.1k
views
isi2019-mma
linear-algebra
engineering-mathematics
matrix
2
votes
1
answer
17
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 $1$ $-1$ $3$ $-3$
Sayan Bose
asked
in
Linear Algebra
May 7, 2019
by
Sayan Bose
772
views
isi2019-mma
linear-algebra
system-of-equations
1
vote
2
answers
18
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 $8$ $10$ $12$ $14$
Sayan Bose
asked
in
Linear Algebra
May 6, 2019
by
Sayan Bose
1.5k
views
isi2019-mma
engineering-mathematics
linear-algebra
vector-space
non-gate
0
votes
3
answers
19
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
Sayan Bose
asked
in
Quantitative Aptitude
May 6, 2019
by
Sayan Bose
1.5k
views
isi2019-mma
general-aptitude
quantitative-aptitude
0
votes
3
answers
20
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
Sayan Bose
asked
in
Quantitative Aptitude
May 6, 2019
by
Sayan Bose
1.2k
views
isi2019-mma
general-aptitude
quantitative-aptitude
0
votes
1
answer
21
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 told that he has been admitted to at least one of these colleges, what is the probability that he has got admitted to college $A$? $3/5$ $5/7$ $10/13$ $15/19$
Sayan Bose
asked
in
Probability
May 6, 2019
by
Sayan Bose
2.2k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
probability
1
vote
1
answer
22
ISI2019-MMA-9
$(\cos 100^\circ + i \sin 100^\circ)(\cos 0^\circ + i \sin 110^\circ)$ is equal to $\frac{1}{2}(\sqrt3 – i)$ $\frac{1}{2}(-\sqrt3 – i)$ $\frac{1}{2}(-\sqrt3 +i)$ $\frac{1}{2}(\sqrt3 + i)$
Sayan Bose
asked
in
Others
May 6, 2019
by
Sayan Bose
750
views
isi2019-mma
non-gate
trignometry
1
vote
1
answer
23
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 $1$ $2$ $3$ $4$
Sayan Bose
asked
in
Others
May 6, 2019
by
Sayan Bose
935
views
isi2019-mma
non-gate
trignometry
1
vote
1
answer
24
ISI2019-MMA-7
The value of $\frac{1}{2\sin10^\circ}$ – $2\sin70^\circ$ is $-1/2$ $-1$ $1/2$ $1$
Sayan Bose
asked
in
Others
May 6, 2019
by
Sayan Bose
576
views
isi2019-mma
non-gate
trignometry
0
votes
1
answer
25
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 constant $x^2 – y^2 = cy$ , where $c$ is a constant $x^2 - y^2 = cx$, where $c$ is a constant
Sayan Bose
asked
in
Calculus
May 6, 2019
by
Sayan Bose
780
views
isi2019-mma
non-gate
engineering-mathematics
calculus
differential-equation
0
votes
1
answer
26
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 $-5$ $-3$ $3$ $5$
Sayan Bose
asked
in
Calculus
May 6, 2019
by
Sayan Bose
617
views
isi2019-mma
calculus
limits
1
vote
1
answer
27
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 $120$ $180$ $240$ $360$
Sayan Bose
asked
in
Combinatory
May 6, 2019
by
Sayan Bose
1.6k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
2
votes
1
answer
28
ISI2019-MMA-3
The sum of all $3$ digit numbers that leave a remainder of $2$ when divided by $3$ is: $189700$ $164850$ $164750$ $149700$
Sayan Bose
asked
in
Quantitative Aptitude
May 6, 2019
by
Sayan Bose
742
views
isi2019-mma
general-aptitude
quantitative-aptitude
0
votes
1
answer
29
ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
Sayan Bose
asked
in
Combinatory
May 6, 2019
by
Sayan Bose
2.6k
views
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
3
votes
1
answer
30
ISI2019-MMA-1
The highest power of $7$ that divides $100!$ is : $14$ $15$ $16$ $18$
Sayan Bose
asked
in
Quantitative Aptitude
May 6, 2019
by
Sayan Bose
3.1k
views
isi2019-mma
general-aptitude
quantitative-aptitude
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Please upload 4th Mock Test, due date was 4th Dec.
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