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Recent questions tagged isi2018dcg
+2
votes
2
answers
1
ISI2018DCG1
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

73
views
isi2018dcg
numericalability
numbersystem
unitdigit
+2
votes
1
answer
2
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)

50
views
isi2018dcg
probability
numbersystem
0
votes
1
answer
3
ISI2018DCG3
If the coefficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is true? $n^2+4(4p+1)+4p^22=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n2p)^2=n+2$ $(n+2p)^2=n+2$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

43
views
isi2018dcg
numericalability
sequenceseries
arithmeticseries
+2
votes
1
answer
4
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)

51
views
isi2018dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
5
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)

29
views
isi2018dcg
sets
+1
vote
1
answer
6
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)

38
views
isi2018dcg
probability
+1
vote
2
answers
7
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)

47
views
isi2018dcg
sets
+1
vote
2
answers
8
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)

36
views
isi2018dcg
permutationandcombination
+1
vote
1
answer
9
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)

50
views
isi2018dcg
calculus
functions
differentiation
0
votes
1
answer
10
ISI2018DCG10
Let $f’(x)=4x^33x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^43x^3+2x^2+x+1$ $x^4x^3+x^2+2x+1$ $x^4x^3+x^2+2(x+1)$ none of these
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

21
views
isi2018dcg
calculus
differentiation
polynomials
+1
vote
0
answers
11
ISI2018DCG11
The sum of $99^{th}$ power of all the roots of $x^71=0$ is equal to $1$ $2$ $1$ $0$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

24
views
isi2018dcg
numericalability
polynomials
roots
+1
vote
1
answer
12
ISI2018DCG12
Let $A=\{10,11,12,13, \dots ,99\}$. How many pairs of numbers $x$ and $y$ are possible so that $x+y\geq 100$ and $x$ and $y$ belong to $A$? $2405$ $2455$ $1200$ $1230$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

49
views
isi2018dcg
permutationandcombination
0
votes
1
answer
13
ISI2018DCG13
In a certain town, $20\%$ families own a car, $90\%$ own a phone, $5 \%$ own neither a car nor a phone and $30, 000$ families own both a car and a phone. Consider the following statements in this regard: $10 \%$ families own both a car and a phone. $95 \%$ ... (iii) are correct and (ii) is wrong. (ii) & (iii) are correct and (i) is wrong. (i), (ii) & (iii) are correct.
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

47
views
isi2018dcg
numericalability
percentage
+1
vote
1
answer
14
ISI2018DCG14
In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way that every team has exactly $2$ ... of such $4$team combinations is $\frac{8!}{2^4}$ $\frac{8!}{2^4(4!)}$ $\frac{8!}{4!}$ $\frac{8!}{(4!)^2}$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

35
views
isi2018dcg
permutationandcombination
+1
vote
1
answer
15
ISI2018DCG15
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is $6$ $9$ $12$ $18$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

19
views
isi2018dcg
numericalability
numbersystem
geometry
parallelograms
+1
vote
1
answer
16
ISI2018DCG16
Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{1}$ does not exist if $(a,b)$ is equal to $(1,1)$ $(1,0)$ $(1,1)$ $(0,1)$
asked
Sep 18, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

26
views
isi2018dcg
linearalgebra
matrices
inverse
+2
votes
1
answer
17
ISI2018DCG17
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is $4096$ $4083$ $2^{13}1$ $2^{12}1$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

32
views
isi2018dcg
permutationandcombination
binomialtheorem
0
votes
1
answer
18
ISI2018DCG18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

13
views
isi2018dcg
trigonometry
nongate
0
votes
0
answers
19
ISI2018DCG19
The area of the region formed by line segments joining the points of intersection of the circle $x^2+y^210x6y+9=0$ with the two axes in succession in a definite order (clockwise or anticlockwise) is $16$ $9$ $3$ $12$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

14
views
isi2018dcg
circle
intersection
nongate
+2
votes
1
answer
20
ISI2018DCG20
The value of $\tan \left(\sin^{1}\left(\frac{3}{5}\right)+\cot^{1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

23
views
isi2018dcg
trigonometry
inverse
nongate
0
votes
0
answers
21
ISI2018DCG21
A box with a square base of length $x$ and height $y$ has an open top and its volume is $32$ cubic centimetres, as shown in the figure below. The values of $x$ and $y$ that minimize the surface area of the box are $x=4$ cm $\&$ $y=2 $ cm $x=3$ cm $\&$ $y=\frac{32}{9} $ cm $x=2$ cm $\&$ $y=8 $ cm none of these.
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

12
views
isi2018dcg
cubes
nongate
0
votes
1
answer
22
ISI2018DCG22
Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+bc)=ab,$ then the angle $C$ is $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2\pi}{3}$
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

13
views
isi2018dcg
triangles
nongate
0
votes
0
answers
23
ISI2018DCG23
Let $A$ be the point of intersection of the lines $3xy=1$ and $y=1$. Let $B$ be the point of reflection of the point $A$ with respect to the $y$axis. Then the equation of the straight line through $B$ that produces a right angled triangle $ABC$ with $\angle ABC=90^{\circ}$, and $C$ lies on the line $3xy=1$, is $3x3y=2$ $2x+3=0$ $3x+2=0$ $3y2=0$
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

9
views
isi2018dcg
lines
triangles
nongate
0
votes
1
answer
24
ISI2018DCG24
Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not differentiable, is $0$ $3$ $5$ $7$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

14
views
isi2018dcg
calculus
differentiation
0
votes
1
answer
25
ISI2018DCG25
There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The straight line $PR$ is a tangent to the third circle at $C$ ... $B$ as shown in the figure.Then the length of the line segment $AB$ is $6$ units $7$ units $8$ units $9$ units
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

29
views
isi2018dcg
circle
lines
nongate
0
votes
1
answer
26
ISI2018DCG26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
(
17.5k
points)

56
views
isi2018dcg
curves
area
nongate
0
votes
1
answer
27
ISI2018DCG27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

15
views
isi2018dcg
numericalability
sequenceseries
summation
0
votes
0
answers
28
ISI2018DCG28
Let $f(x)=e^{\big( \frac{1}{x^23x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^}{\lim} f(x)$. Then $a=\infty, \: b=0$ $a=0, \: b=\infty$ $a=0, \: b=0$ $a=\infty, \: b=\infty$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

20
views
isi2018dcg
calculus
limits
functions
0
votes
0
answers
29
ISI2018DCG29
Let $f(x)=(x1)(x2)(x3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Then there exists $y\in(1,3)$ such that $f’’(y)=0.$ there exists $y\in(1,2)$ such that $f’’(y)=0.$ there exists $y\in(2,3)$ such that $f’’(y)=0.$ none of the above is true.
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

17
views
isi2018dcg
calculus
differentiation
+1
vote
1
answer
30
ISI2018DCG30
Let $0.01^x+0.25^x=0.7$ . Then $x\geq1$ $0\lt x\lt1$ $x\leq0$ no such real number $x$ is possible.
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

50
views
isi2018dcg
numericalability
numbersystem
inequality
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