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Recent questions tagged isi2016-dcg

2 votes
1 answer
1
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is in Arithmetic progression (AP) Geometric progression (GP) Harmonic progression (HP) None of these
asked Sep 18, 2019 in Numerical Ability gatecse 85 views
1 vote
2 answers
2
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then $a<b$ $a>b$ $a=b$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 104 views
0 votes
1 answer
3
The value of $\begin{vmatrix} 1+a& 1& 1& 1\\ 1&1+b &1 &1 \\ 1&1 &1+c &1 \\ 1&1 &1 &1+d \end{vmatrix}$ is $abcd(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d})$ $abcd(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d})$ $1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}$ None of these
asked Sep 18, 2019 in Linear Algebra gatecse 60 views
0 votes
1 answer
4
If $f(x)=\begin{bmatrix}\cos\:x & -\sin\:x & 0 \\ \sin\:x & \cos\:x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
asked Sep 18, 2019 in Linear Algebra gatecse 81 views
0 votes
2 answers
5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
asked Sep 18, 2019 in Geometry gatecse 70 views
1 vote
1 answer
6
The coefficient of $x^{2}$ in the product $(1+x)(1+2x)(1+3x)\cdots (1+10x)$ is $1320$ $1420$ $1120$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 53 views
0 votes
1 answer
7
Let $x^{2}-2(4k-1)x+15k^{2}-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
asked Sep 18, 2019 in Numerical Ability gatecse 44 views
1 vote
1 answer
8
Let $S=\{0,1,2,\cdots,25\}$ and $T=\{n\in S\: : \: n^{2}+3n+2\: \text{is divisible by}\: 6\}$. Then the number of elements in the set $T$ is $16$ $17$ $18$ $10$
asked Sep 18, 2019 in Numerical Ability gatecse 53 views
1 vote
1 answer
9
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$
asked Sep 18, 2019 in Numerical Ability gatecse 69 views
0 votes
1 answer
10
Let $a$ be the $81$-digit number of which all the digits are equal to $1.$ Then the number $a$ is , divisible by $9$ but not divisible by $27$ divisible by $27$ but not divisible by $81$ divisible by $81$ None of the above
asked Sep 18, 2019 in Numerical Ability gatecse 44 views
0 votes
1 answer
11
Let two systems of linear equations be defined as follows: $\begin{array}{lll} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ and $\begin{array}{lll} & x+y & =3 \\ Q: & 2x+2y & =4 \\ & 5x+5y & =12 \end{array}$. Then, $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above
asked Sep 18, 2019 in Linear Algebra gatecse 55 views
1 vote
1 answer
12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
asked Sep 18, 2019 in Numerical Ability gatecse 47 views
0 votes
1 answer
13
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 68 views
0 votes
1 answer
14
For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when $n\geq 3$ $n<3$ $n=3$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 45 views
0 votes
0 answers
15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
asked Sep 18, 2019 in Geometry gatecse 43 views
0 votes
1 answer
16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
asked Sep 18, 2019 in Geometry gatecse 48 views
0 votes
1 answer
17
The smallest integer $n$ for which $1+2+2^{2}+2^{3}+2^{4}+\cdots+2^{n}$ exceeds $9999$, given that $\log_{10}2=0.30103$, is $12$ $13$ $14$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 44 views
0 votes
0 answers
18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
asked Sep 18, 2019 in Numerical Ability gatecse 43 views
1 vote
2 answers
19
The expression $3^{2n+1}+2^{n+2}$ is divisible by $7$ for all positive integer values of $n$ all non-negative integer values of $n$ only even integer values of $n$ only odd integer values of $n$
asked Sep 18, 2019 in Numerical Ability gatecse 67 views
1 vote
1 answer
20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 45 views
2 votes
1 answer
21
The value of the term independent of $x$ in the expansion of $(1-x)^{2}(x+\frac{1}{x})^{7}$ is $-70$ $70$ $35$ None of these
asked Sep 18, 2019 in Combinatory gatecse 113 views
1 vote
1 answer
22
The value of $\:\:\begin{vmatrix} 1&\log_{x}y &\log_{x}z \\ \log_{y}x &1 &\log_{y}z \\\log_{z}x & \log_{z}y&1 \end{vmatrix}\:\:$ is $0$ $1$ $-1$ None of these
asked Sep 18, 2019 in Linear Algebra gatecse 73 views
0 votes
1 answer
23
The value of $\log_{2}e-\log_{4}e+\log_{8}e-\log_{16}e+\log_{32}e-\cdots\:\:$ is $-1$ $0$ $1$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 58 views
2 votes
1 answer
24
If the letters of the word $\text{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is $8!$ $6!$ $3!6!$ None of these
asked Sep 18, 2019 in Combinatory gatecse 71 views
1 vote
1 answer
25
If $\alpha$ and $\beta$ be the roots of the equation $x^{2}+3x+4=0,$ then the equation with roots $(\alpha+\beta)^{2}$ and $(\alpha-\beta)^{2}$ is $x^{2}+2x+63=0$ $x^{2}-63x+2=0$ $x^{2}-2x-63=0$ None of these
asked Sep 18, 2019 in Numerical Ability gatecse 48 views
1 vote
2 answers
26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
asked Sep 18, 2019 in Numerical Ability gatecse 77 views
0 votes
1 answer
27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is one-one and into one-one and onto many-one and onto many-one and into
asked Sep 18, 2019 in Set Theory & Algebra gatecse 62 views
1 vote
1 answer
28
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$
asked Sep 18, 2019 in Numerical Ability gatecse 72 views
1 vote
0 answers
29
The condition that ensures that the roots of the equation $x^{3}-px^{2}+qx-r=0$ are in H.P. is $r^{2}-9pqr+q^{3}=0$ $27r^{2}-9pqr+3q^{3}=0$ $3r^{3}-27pqr-9q^{3}=0$ $27r^{2}-9pqr+2q^{3}=0$
asked Sep 18, 2019 in Numerical Ability gatecse 54 views
0 votes
1 answer
30
Let $p,q,r,s$ be real numbers such that $pr=2(q+s).$ Consider the equations $x^{2}+px+q=0$ and $x^{2}+rx+s=0.$ Then at least one of the equations has real roots. both these equations have real roots. neither of these equations have real roots. given data is not sufficient to arrive at any conclusion.
asked Sep 18, 2019 in Numerical Ability gatecse 56 views
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