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Recent questions tagged isi2018-dcg

2 votes
2 answers
1
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$
asked Sep 18, 2019 in Numerical Ability gatecse 153 views
2 votes
1 answer
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
asked Sep 18, 2019 in Probability gatecse 130 views
0 votes
1 answer
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? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
asked Sep 18, 2019 in Numerical Ability gatecse 149 views
2 votes
1 answer
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 $99$ $100$ $101$ $102$
asked Sep 18, 2019 in Combinatory gatecse 147 views
1 vote
1 answer
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: $A=B\cup C$. $B$ ... the above 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 gatecse 135 views
1 vote
1 answer
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
asked Sep 18, 2019 in Probability gatecse 110 views
1 vote
2 answers
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 $8$ $14$ $15$ $22$
asked Sep 18, 2019 in Set Theory & Algebra gatecse 128 views
1 vote
2 answers
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? $20$ $35$ $41$ $21$
asked Sep 18, 2019 in Combinatory gatecse 112 views
1 vote
1 answer
9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
asked Sep 18, 2019 in Calculus gatecse 201 views
0 votes
1 answer
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
asked Sep 18, 2019 in Calculus gatecse 67 views
1 vote
0 answers
11
The sum of $99^{th}$ power of all the roots of $x^7-1=0$ is equal to $1$ $2$ $-1$ $0$
asked Sep 18, 2019 in Numerical Ability gatecse 68 views
1 vote
1 answer
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 $A$? $2405$ $2455$ $1200$ $1230$
asked Sep 18, 2019 in Combinatory gatecse 142 views
0 votes
1 answer
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. $95 \%$ families own either a ... (i) & (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 gatecse 112 views
1 vote
1 answer
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 $2$ ... total number 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 gatecse 135 views
1 vote
1 answer
15
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is $6$ $9$ $12$ $18$
asked Sep 18, 2019 in Numerical Ability gatecse 65 views
1 vote
1 answer
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 $(1,-1)$ $(1,0)$ $(-1,-1)$ $(0,1)$
asked Sep 18, 2019 in Linear Algebra gatecse 106 views
2 votes
1 answer
17
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is $4096$ $4083$ $2^{13}-1$ $2^{12}-1$
asked Sep 18, 2019 in Combinatory gatecse 132 views
1 vote
1 answer
18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
asked Sep 18, 2019 in Geometry gatecse 50 views
0 votes
1 answer
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 $16$ $9$ $3$ $12$
asked Sep 18, 2019 in Numerical Ability gatecse 71 views
2 votes
1 answer
20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
asked Sep 18, 2019 in Geometry gatecse 69 views
0 votes
0 answers
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.
asked Sep 18, 2019 in Geometry gatecse 46 views
0 votes
1 answer
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 $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2\pi}{3}$
asked Sep 18, 2019 in Geometry gatecse 49 views
0 votes
1 answer
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 $3x-3y=2$ $2x+3=0$ $3x+2=0$ $3y-2=0$
asked Sep 18, 2019 in Geometry gatecse 54 views
0 votes
1 answer
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 $0$ $3$ $5$ $7$
asked Sep 18, 2019 in Calculus gatecse 63 views
0 votes
1 answer
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 $C$ and cuts the second circle at the points $A$ and $B$ 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 gatecse 75 views
0 votes
1 answer
26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
asked Sep 18, 2019 in Geometry gatecse 101 views
0 votes
1 answer
27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
asked Sep 18, 2019 in Numerical Ability gatecse 52 views
0 votes
0 answers
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 $a=\infty, \: b=0$ $a=0, \: b=\infty$ $a=0, \: b=0$ $a=\infty, \: b=\infty$
asked Sep 18, 2019 in Calculus gatecse 55 views
0 votes
0 answers
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.
asked Sep 18, 2019 in Calculus gatecse 102 views
1 vote
1 answer
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.
asked Sep 18, 2019 in Numerical Ability gatecse 113 views
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