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Recent questions tagged isi2019
+1
vote
1
answer
1
ISI2019MMA30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and $2[h(i)h(i1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$ Then the value of $h(1)$ is $\frac{1}{2^91}\\$ $\frac{10}{2^9+1}\\$ $\frac{10}{2^{10}1}\\$ $\frac{1}{2^{10}+1}$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

347
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
+1
vote
1
answer
2
ISI2019MMA29
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 $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

381
views
isi2019
engineeringmathematics
calculus
integration
0
votes
1
answer
3
ISI2019MMA28
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 $1/4$ $1/6$ $1/8$ $1/24$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

640
views
isi2019
calculus
engineeringmathematics
0
votes
2
answers
4
ISI2019MMA27
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? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
7k
points)

2.8k
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
5
ISI2019MMA26
If $t = \begin{pmatrix} 200 \\ 100 \end{pmatrix}/4^{100} $, then $t < \frac{1}{3}$ $\frac{1}{3} < t < \frac{1}{2}$ $\frac{1}{2} < t < \frac{2}{3}$ $\frac{2}{3} < t < 1$
asked
May 7
in
Numerical Ability
by
Sayan Bose
Loyal
(
7k
points)

177
views
isi2019
generalaptitude
numericalability
0
votes
1
answer
6
ISI2019MMA25
Let $a,b,c$ be nonzero 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 $(0,2)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

222
views
isi2019
engineeringmathematics
calculus
integration
+1
vote
1
answer
7
ISI2019MMA24
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f''(x)$ exists for every $x \in \mathbb{R}$, where $f''(x) = f \circ f^{n1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

230
views
isi2019
engineeringmathematics
calculus
limits
0
votes
1
answer
8
ISI2019MMA23
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 skewsymmetric matrix None of the above must necessarily hold
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7k
points)

118
views
isi2019
engineeringmathematics
linearalgebra
0
votes
3
answers
9
ISI2019MMA22
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 $2/7$ $1/3$ $5/7$ $2/3$
asked
May 7
in
Probability
by
Sayan Bose
Loyal
(
7k
points)

133
views
isi2019
probability
0
votes
1
answer
10
ISI2019MMA21
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 $x_2$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

388
views
isi2019
engineeringmathematics
calculus
0
votes
2
answers
11
ISI2019MMA20
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? $164025$ $190951$ $194976$ $219049$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
7k
points)

322
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
12
ISI2019MMA19
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 $1$ $2$ $6$ $12$
asked
May 7
in
Set Theory & Algebra
by
Sayan Bose
Loyal
(
7k
points)

190
views
isi2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
+1
vote
1
answer
13
ISI2019MMA18
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 $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3e}{2} – \frac{1}{4} \bigg)$ $\text{ln} \bigg(\frac{3}{e} – \frac{1}{2} \bigg)$ $\text{ln} \bigg(\frac{3}{2e} – \frac{1}{4} \bigg)$
asked
May 7
in
Others
by
Sayan Bose
Loyal
(
7k
points)

3.6k
views
isi2019
nongate
engineeringmathematics
calculus
differentiableequation
0
votes
2
answers
14
ISI2019MMA17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is $(3,6)$ $(6,3)$ $(5,10)$ $(10,5)$
asked
May 7
in
Geometry
by
Sayan Bose
Loyal
(
7k
points)

129
views
isi2019
nongate
geometry
0
votes
1
answer
15
ISI2019MMA16
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 $P$
asked
May 7
in
Geometry
by
Sayan Bose
Loyal
(
7k
points)

74
views
isi2019
nongate
geometry
0
votes
2
answers
16
ISI2019MMA15
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 $t$
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7k
points)

149
views
isi2019
linearalgebra
engineeringmathematics
0
votes
1
answer
17
ISI2019MMA14
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 $\frac{1}{1a} + \frac{1}{1b} + \frac{1}{1c}$ is $1$ $1$ $3$ $3$
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7k
points)

119
views
isi2019
linearalgebra
systemofequations
0
votes
2
answers
18
ISI2019MMA13
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 $8$ $10$ $12$ $14$
asked
May 6
in
Linear Algebra
by
Sayan Bose
Loyal
(
7k
points)

178
views
isi2019
engineeringmathematics
linearalgebra
0
votes
2
answers
19
ISI2019MMA12
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 $f(n^31) = f(n1)$ $f(n^31) = f(n1) +1$ $f(n^31) = 2f(n1)$ None of the above is necessarily true
asked
May 6
in
Numerical Ability
by
Sayan Bose
Loyal
(
7k
points)

291
views
isi2019
generalaptitude
numericalability
0
votes
1
answer
20
ISI2019MMA11
How many triplets of real numbers $(x,y,z)$ are simultaneous solutions of the equations $x+y=2$ and $xyz^2=1$? $0$ $1$ $2$ infinitely many
asked
May 6
in
Numerical Ability
by
Sayan Bose
Loyal
(
7k
points)

162
views
isi2019
generalaptitude
numericalability
0
votes
1
answer
21
ISI2019MMA10
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 $A$? $3/5$ $5/7$ $10/13$ $15/19$
asked
May 6
in
Probability
by
Sayan Bose
Loyal
(
7k
points)

137
views
isi2019
engineeringmathematics
discretemathematics
probability
+1
vote
1
answer
22
ISI2019MMA9
$(\cos 100^\circ + i \sin 100^\circ)(\cos 0^\circ + i \sin 110^\circ)$ is equal to $\frac{1}{2}(\sqrt3 – i)$ $\frac{1}{2}(\sqrt3 – i)$ $\frac{1}{2}(\sqrt3 +i)$ $\frac{1}{2}(\sqrt3 + i)$
asked
May 6
in
Others
by
Sayan Bose
Loyal
(
7k
points)

97
views
isi2019
nongate
trignometry
0
votes
1
answer
23
ISI2019MMA8
For $0 \leq x \leq 2 \pi$, the number of solutions of the equation $\sin^2x + 2 \cos^2x + \sin x \cos x = 0$ is $1$ $2$ $3$ $4$
asked
May 6
in
Others
by
Sayan Bose
Loyal
(
7k
points)

98
views
isi2019
nongate
trignometry
+1
vote
1
answer
24
ISI2019MMA7
The value of $\frac{1}{2\sin10^\circ}$ – $2\sin70^\circ$ is $1/2$ $1$ $1/2$ $1$
asked
May 6
in
Others
by
Sayan Bose
Loyal
(
7k
points)

89
views
isi2019
nongate
trignometry
0
votes
1
answer
25
ISI2019MMA6
The solution of the differential equation $\frac{dy}{dx} = \frac{2xy}{x^2y^2}$ 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
asked
May 6
in
Others
by
Sayan Bose
Loyal
(
7k
points)

171
views
isi2019
nongate
engineeringmathematics
calculus
0
votes
1
answer
26
ISI2019MMA5
If $f(a)=2, \: f’(a) = 1, \: g(a) =1$ and $g’(a) =2$, then the value of $\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{xa}$ is $5$ $3$ $3$ $5$
asked
May 6
in
Calculus
by
Sayan Bose
Loyal
(
7k
points)

157
views
isi2019
calculus
limits
0
votes
1
answer
27
ISI2019MMA4
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 $120$ $180$ $240$ $360$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
7k
points)

198
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
28
ISI2019MMA3
The sum of all $3$ digit numbers that leave a remainder of $2$ when divided by $3$ is: $189700$ $164850$ $164750$ $149700$
asked
May 6
in
Numerical Ability
by
Sayan Bose
Loyal
(
7k
points)

150
views
isi2019
generalaptitude
numericalability
0
votes
1
answer
29
ISI2019MMA2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
7k
points)

237
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
+2
votes
1
answer
30
ISI2019MMA1
The highest power of $7$ that divides $100!$ is : $14$ $15$ $16$ $18$
asked
May 6
in
Numerical Ability
by
Sayan Bose
Loyal
(
7k
points)

124
views
isi2019
generalaptitude
numericalability
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