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Recent questions tagged isi2018-dcg
3
votes
2
answers
1
ISI2018-DCG-1
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$
The digit in the unit place of the number $7^{78}$ is$1$$3$$7$$9$
gatecse
715
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
number-system
unit-digit
+
–
4
votes
1
answer
2
ISI2018-DCG-2
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$? $0.25$ $0.50$ $0.48$ none of these
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$?$0.25$$0.50$$0.48$none of these
gatecse
781
views
gatecse
asked
Sep 18, 2019
Probability
isi2018-dcg
probability
number-system
+
–
0
votes
1
answer
3
ISI2018-DCG-3
If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is true? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is ...
gatecse
507
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
sequence-series
arithmetic-series
+
–
2
votes
1
answer
4
ISI2018-DCG-4
The number of terms with integral coefficients in the expansion of $\left(17^\frac{1}{3}+19^\frac{1}{2}x\right)^{600}$ is $99$ $100$ $101$ $102$
The number of terms with integral coefficients in the expansion of $\left(17^\frac{1}{3}+19^\frac{1}{2}x\right)^{600}$ is$99$$100$$101$$102$
gatecse
663
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2018-dcg
combinatory
binomial-theorem
+
–
1
votes
1
answer
5
ISI2018-DCG-5
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.
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...
gatecse
1.2k
views
gatecse
asked
Sep 18, 2019
Set Theory & Algebra
isi2018-dcg
set-theory
+
–
2
votes
1
answer
6
ISI2018-DCG-6
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
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 th...
gatecse
527
views
gatecse
asked
Sep 18, 2019
Probability
isi2018-dcg
probability
+
–
1
votes
2
answers
7
ISI2018-DCG-7
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 $8$ $14$ $15$ $22$
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, andthe set $C\cap A$ consists ...
gatecse
686
views
gatecse
asked
Sep 18, 2019
Set Theory & Algebra
isi2018-dcg
set-theory
+
–
1
votes
2
answers
8
ISI2018-DCG-8
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? $20$ $35$ $41$ $21$
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 ...
gatecse
511
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2018-dcg
combinatory
+
–
2
votes
1
answer
9
ISI2018-DCG-9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
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$$2019$
gatecse
656
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
functions
differentiation
+
–
1
votes
1
answer
10
ISI2018-DCG-10
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^4-3x^3+2x^2+x+1$ $x^4-x^3+x^2+2x+1$ $x^4-x^3+x^2+2(x+1)$ none of these
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to$4x^4-3x^3+2x^2+x+1$$x^4-x^3+x^2+2x+1$$x^4-x^3+x^2+2(x+1)$none of these
gatecse
385
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
polynomials
+
–
1
votes
0
answers
11
ISI2018-DCG-11
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to $1$ $2$ $-1$ $0$
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to$1$$2$$-1$$0$
gatecse
408
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
polynomials
roots
+
–
1
votes
1
answer
12
ISI2018-DCG-12
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 $A$? $2405$ $2455$ $1200$ $1230$
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$$1230$
gatecse
651
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2018-dcg
combinatory
+
–
0
votes
1
answer
13
ISI2018-DCG-13
In a certain town, $20\%$ families own a car, $90\%$ own a phone, $5 \%$ own neither a car nor a phone and $30, 000$ families own both a car and a phone. Consider the following statements in this regard: $10 \%$ families own both a car and a phone. $95 \%$ ... (iii) are correct and (ii) is wrong. (ii) & (iii) are correct and (i) is wrong. (i), (ii) & (iii) are correct.
In a certain town, $20\%$ families own a car, $90\%$ own a phone, $5 \%$ own neither a car nor a phone and $30, 000$ families own both a car and a phone. Consider the fol...
gatecse
593
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
percentage
+
–
1
votes
1
answer
14
ISI2018-DCG-14
In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way that every team has exactly $2$ ... of such $4$-team combinations is $\frac{8!}{2^4}$ $\frac{8!}{2^4(4!)}$ $\frac{8!}{4!}$ $\frac{8!}{(4!)^2}$
In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way thatevery team has exactly $2$ members, andthere are no ...
gatecse
469
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2018-dcg
combinatory
+
–
1
votes
1
answer
15
ISI2018-DCG-15
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is $6$ $9$ $12$ $18$
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is$6$$9$$12$$18$
gatecse
480
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
number-system
geometry
parallelograms
+
–
2
votes
2
answers
16
ISI2018-DCG-16
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 $(1,-1)$ $(1,0)$ $(-1,-1)$ $(0,1)$
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)$$(0,1)$
gatecse
514
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2018-dcg
linear-algebra
matrix
inverse
+
–
2
votes
1
answer
17
ISI2018-DCG-17
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is $4096$ $4083$ $2^{13}-1$ $2^{12}-1$
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is$4096$$4083$$2^{13}-1$$2^{12}-1$
gatecse
431
views
gatecse
asked
Sep 18, 2019
Combinatory
isi2018-dcg
combinatory
binomial-theorem
+
–
1
votes
1
answer
18
ISI2018-DCG-18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
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$$\sin x+\...
gatecse
302
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
trigonometry
non-gate
+
–
0
votes
1
answer
19
ISI2018-DCG-19
The area of the region formed by line segments joining the points of intersection of the circle $x^2+y^2-10x-6y+9=0$ with the two axes in succession in a definite order (clockwise or anticlockwise) is $16$ $9$ $3$ $12$
The area of the region formed by line segments joining the points of intersection of the circle $x^2+y^2-10x-6y+9=0$ with the two axes in succession in a definite order (...
gatecse
356
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
circle-intersection
non-gate
+
–
2
votes
1
answer
20
ISI2018-DCG-20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is$\frac{1}{18}$$\frac{11}{6}$$\frac{13}{6}$$\frac{17}{6}$
gatecse
279
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
trigonometry
inverse
non-gate
+
–
0
votes
0
answers
21
ISI2018-DCG-21
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.
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 $y$ th...
gatecse
254
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
cubes
non-gate
+
–
0
votes
1
answer
22
ISI2018-DCG-22
Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+b-c)=ab,$ then the angle $C$ is $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2\pi}{3}$
Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+b-c)=ab,$ then the angle $C$ is$\frac{\pi}{6}$$\fra...
gatecse
361
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
triangles
non-gate
+
–
0
votes
1
answer
23
ISI2018-DCG-23
Let $A$ be the point of intersection of the lines $3x-y=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 $3x-y=1$, is $3x-3y=2$ $2x+3=0$ $3x+2=0$ $3y-2=0$
Let $A$ be the point of intersection of the lines $3x-y=1$ and $y=1$. Let $B$ be the point of reflection of the point $A$ with respect to the $y$-axis. Then the equation ...
gatecse
300
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
lines
triangles
non-gate
+
–
0
votes
1
answer
24
ISI2018-DCG-24
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$
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 diff...
gatecse
410
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
+
–
0
votes
1
answer
25
ISI2018-DCG-25
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
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 ...
gatecse
458
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
circle
lines
non-gate
+
–
0
votes
1
answer
26
ISI2018-DCG-26
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$
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$
gatecse
552
views
gatecse
asked
Sep 18, 2019
Geometry
isi2018-dcg
curves
area
non-gate
+
–
0
votes
1
answer
27
ISI2018-DCG-27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is$2$$1$$\infty$not a convergent series
gatecse
385
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
sequence-series
summation
+
–
0
votes
1
answer
28
ISI2018-DCG-28
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$. Then $a=\infty, \: b=0$ $a=0, \: b=\infty$ $a=0, \: b=0$ $a=\infty, \: b=\infty$
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$....
gatecse
308
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
limits
functions
+
–
0
votes
0
answers
29
ISI2018-DCG-29
Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ 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.
Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Thenthere exists $y\in(1,3)$ such that $f’’(y)=0.$there exists $y\in(1,...
gatecse
350
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
+
–
2
votes
1
answer
30
ISI2018-DCG-30
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.
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.
gatecse
525
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
number-system
inequality
+
–
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