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ISI2016DCG50
The domain of the function $\ln(3x^{2}4x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

24
views
isi2016dcg
functions
0
votes
1
answer
2
ISI2016DCG53
$\underset{x\rightarrow1}{\lim}\dfrac{1+\sqrt[3]{x}}{1+\sqrt[5]{x}}$ equals $\frac{3}{5}$ $\frac{5}{3}$ $1$ $\infty$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

17
views
isi2016dcg
calculus
limits
0
votes
0
answers
3
ISI2016DCG54
$\underset{x\rightarrow 0}{\lim}x\sin\left(\dfrac{1}{x}\right)$ equals $1$ $0$ $1$ Does not exist
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
calculus
limits
0
votes
0
answers
4
ISI2016DCG55
$\underset{x\rightarrow 0}{\lim}\sin\left(\dfrac{1}{x}\right)$ equals $1$ $0$ $1$ Does not exist
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

15
views
isi2016dcg
calculus
limits
0
votes
0
answers
5
ISI2016DCG56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals $1$ $0$ $1$ Does not exist
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

13
views
isi2016dcg
calculus
limits
0
votes
0
answers
6
ISI2016DCG57
$\underset{x\rightarrow 1}{\lim} \dfrac{x^{16}1}{\mid x1\mid}$ equals $1$ $0$ $1$ Does not exist
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

36
views
isi2016dcg
calculus
limits
0
votes
0
answers
7
ISI2016DCG58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and manyone. $y$ is not differentiable and manyone. $y$ is not differentiable. $y$ is differentiable and manyone.
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

15
views
isi2016dcg
calculus
continuity
differentiation
functions
0
votes
0
answers
8
ISI2016DCG67
The general solution of the differential equation $2y{y}'x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}y^{2}=C$ $2x^{2}y^{2}=C$ $2y^{2}x^{2}=C$ $x^{2}+y^{2}=C$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

14
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
0
answers
9
ISI2016DCG68
The general solution of the differential equation $x+yx{y}'=0$ is (assuming $C$ as an arbitrary constant of integration) $y=x(\log x+C)$ $x=y(\log y+C)$ $y=x(\log y+C)$ $y=y(\log x+C)$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
0
answers
10
ISI2016DCG69
Consider the differential equation $(x^{2}y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y5)^{2}=25$ $x^{2}+y^{2}=100$ $(x5)^{2}+y^{2}=125$ $(x5)^{2}+(y5)^{2}=50$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

13
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
11
ISI2017DCG3
If $2f(x)3f(\frac{1}{x})=x^2 \: (x \neq0)$, then $f(2)$ is $\frac{2}{3}$ $ – \frac{3}{2}$ $ – \frac{7}{4}$ $\frac{5}{4}$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

27
views
isi2017dcg
calculus
functions
0
votes
1
answer
12
ISI2017DCG4
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +AI= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is $A$ $O$ $I$ none of these
asked
Sep 18, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

24
views
isi2017dcg
linearalgebra
matrices
0
votes
1
answer
13
ISI2017DCG6
Let $f(x) = \dfrac{x1}{x+1}, \: f^{k+1}(x)=f\left(f^k(x)\right)$ for all $k=1, 2, 3, \dots , 99$. Then $f^{100}(10)$ is $1$ $10$ $100$ $101$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

49
views
isi2017dcg
calculus
functions
+1
vote
1
answer
14
ISI2017DCG7
If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is $1$ $2$ $3$ $4$
asked
Sep 18, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

36
views
isi2017dcg
linearalgebra
determinant
+1
vote
1
answer
15
ISI2017DCG11
The coefficient of $x^6y^3$ in the expression $(x+2y)^9$ is $84$ $672$ $8$ none of these
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

22
views
isi2017dcg
permutationandcombination
binomialtheorem
0
votes
1
answer
16
ISI2017DCG12
Two sets have $m$ and $n$ elements. The number of subsets of the first set is $96$ more than that of the second set. Then the values of $m$ and $n$ are $8$ and $6$ $7$ and $6$ $7$ and $5$ $6$ and $5$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

18
views
isi2017dcg
sets
+1
vote
1
answer
17
ISI2017DCG22
Let $A_1,A_2,A_3, \dots , A_n$ be $n$ independent events such that $P(A_i) = \frac{1}{i+1}$ for $i=1,2,3, \dots , n$. The probability that none of $A_1, A_2, A_3, \dots , A_n$ occurs is $\frac{n}{n+1}$ $\frac{1}{n+1}$ $\frac{n1}{n+1}$ none of these
asked
Sep 18, 2019
in
Probability
by
gatecse
Boss
(
17.5k
points)

37
views
isi2017dcg
probability
independentevents
+1
vote
3
answers
18
ISI2017DCG23
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a nonzero determinant is $\frac{3}{16}$ $\frac{3}{8}$ $\frac{1}{4}$ none of these
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

61
views
isi2017dcg
probability
determinants
0
votes
1
answer
19
ISI2017DCG25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
asked
Sep 18, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

40
views
isi2017dcg
linearalgebra
determinant
definiteintegrals
nongate
0
votes
1
answer
20
ISI2017DCG26
The value of $\underset{n \to \infty}{\lim} \bigg( \dfrac{1}{1n^2} + \dfrac{2}{1n^2} + \dots + \dfrac{n}{1n^2} \bigg)$ is $0$ $ – \frac{1}{2}$ $\frac{1}{2}$ none of these
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

24
views
isi2017dcg
calculus
limits
0
votes
1
answer
21
ISI2017DCG27
The limit of the sequence $\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, \dots$ is $1$ $2$ $2\sqrt{2}$ $\infty$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

21
views
isi2017dcg
calculus
limits
0
votes
2
answers
22
ISI2017DCG28
A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a blue marble is $0.2$. The probability of selecting a white marble in the first draw is $0.5$. What is the ... blue marble in the second draw, given that the first marble drawn was white? $0.1$ $0.4$ $0.5$ $0.2$
asked
Sep 18, 2019
in
Probability
by
gatecse
Boss
(
17.5k
points)

60
views
isi2017dcg
probability
ballsinbins
0
votes
2
answers
23
ISI2017DCG30
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals $38$ $8$ $4$ $0$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

21
views
isi2017dcg
calculus
differentiation
functions
+2
votes
1
answer
24
ISI2018DCG2
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$? $0.25$ $0.50$ $0.48$ none of these
asked
Sep 18, 2019
in
Probability
by
gatecse
Boss
(
17.5k
points)

56
views
isi2018dcg
probability
numbersystem
+2
votes
1
answer
25
ISI2018DCG4
The number of terms with integral coefficients in the expansion of $\left(17^\frac{1}{3}+19^\frac{1}{2}x\right)^{600}$ is $99$ $100$ $101$ $102$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

53
views
isi2018dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
26
ISI2018DCG5
Let $A$ be the set of all prime numbers, $B$ be the set of all even prime numbers, and $C$ be the set of all odd prime numbers. Consider the following three statements in this regard: $A=B\cup C$. $B$ ... statements is true. Exactly one of the above statements is true. Exactly two of the above statements are true. All the above three statements are true.
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

31
views
isi2018dcg
sets
+1
vote
1
answer
27
ISI2018DCG6
A die is thrown thrice. If the first throw is a $4$ then the probability of getting $15$ as the sum of three throws is $\frac{1}{108}$ $\frac{1}{6}$ $\frac{1}{18}$ none of these
asked
Sep 18, 2019
in
Probability
by
gatecse
Boss
(
17.5k
points)

42
views
isi2018dcg
probability
+1
vote
2
answers
28
ISI2018DCG7
You are given three sets $A,B,C$ in such a way that the set $B \cap C$ consists of $8$ elements, the set $A\cap B$ consists of $7$ elements, and the set $C\cap A$ consists of $7$ elements. The minimum number of elements in the set $A\cup B\cup C$ is $8$ $14$ $15$ $22$
asked
Sep 18, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

50
views
isi2018dcg
sets
+1
vote
2
answers
29
ISI2018DCG8
A Pizza Shop offers $6$ different toppings, and they do not take an order without any topping. I can afford to have one pizza with a maximum of $3$ toppings. In how many ways can I order my pizza? $20$ $35$ $41$ $21$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

37
views
isi2018dcg
permutationandcombination
+1
vote
1
answer
30
ISI2018DCG9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

54
views
isi2018dcg
calculus
functions
differentiation
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