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Recent questions tagged isi2016-dcg

3 votes

1 answer

1

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

226 views

1 vote

2 answers

2

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

339 views

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3

ISI2016-DCG-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

gatecse asked in Linear Algebra Sep 18, 2019

249 views

0 votes

1 answer

4

ISI2016-DCG-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

gatecse asked in Linear Algebra Sep 18, 2019

261 views

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2 answers

5

ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$

gatecse asked in Geometry Sep 18, 2019

234 views

1 vote

1 answer

6

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

234 views

0 votes

1 answer

7

ISI2016-DCG-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 $2$ $4$ $3$ $1$

gatecse asked in Quantitative Aptitude Sep 18, 2019

166 views

1 vote

1 answer

8

ISI2016-DCG-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 $16$ $17$ $18$ $10$

gatecse asked in Quantitative Aptitude Sep 18, 2019

172 views

1 vote

1 answer

9

ISI2016-DCG-9
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$

gatecse asked in Quantitative Aptitude Sep 18, 2019

228 views

0 votes

1 answer

10

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

179 views

1 vote

1 answer

11

ISI2016-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array}{lll} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above

gatecse asked in Linear Algebra Sep 18, 2019

280 views

1 vote

1 answer

12

ISI2016-DCG-12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$

gatecse asked in Quantitative Aptitude Sep 18, 2019

181 views

0 votes

1 answer

13

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

219 views

0 votes

1 answer

14

ISI2016-DCG-14
For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when $n\geq 3$ $n<3$ $n=3$ None of these

gatecse asked in Quantitative Aptitude Sep 18, 2019

236 views

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0 answers

15

ISI2016-DCG-15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$

gatecse asked in Geometry Sep 18, 2019

179 views

0 votes

1 answer

16

ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in

gatecse asked in Geometry Sep 18, 2019

198 views

0 votes

1 answer

17

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

182 views

0 votes

0 answers

18

ISI2016-DCG-18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$

gatecse asked in Quantitative Aptitude Sep 18, 2019

166 views

1 vote

2 answers

19

ISI2016-DCG-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 $n$

gatecse asked in Quantitative Aptitude Sep 18, 2019

271 views

1 vote

1 answer

20

ISI2016-DCG-20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these

gatecse asked in Quantitative Aptitude Sep 18, 2019

167 views

2 votes

1 answer

21

ISI2016-DCG-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

gatecse asked in Combinatory Sep 18, 2019

309 views

1 vote

1 answer

22

ISI2016-DCG-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

gatecse asked in Linear Algebra Sep 18, 2019

227 views

0 votes

1 answer

23

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

230 views

2 votes

1 answer

24

ISI2016-DCG-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

gatecse asked in Combinatory Sep 18, 2019

272 views

1 vote

1 answer

25

ISI2016-DCG-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

gatecse asked in Quantitative Aptitude Sep 18, 2019

192 views

1 vote

2 answers

26

ISI2016-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$

gatecse asked in Quantitative Aptitude Sep 18, 2019

267 views

0 votes

1 answer

27

ISI2016-DCG-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

gatecse asked in Set Theory & Algebra Sep 18, 2019

222 views

1 vote

1 answer

28

ISI2016-DCG-28
If one root of a quadratic equation $ax^{2}+bx+c=0$ be equal to the n th power of the other, then $(ac)^{\frac{n}{n+1}}+b=0$ $(ac)^{\frac{n+1}{n}}+b=0$ $(ac^{n})^{\frac{1}{n+1}}+(a^{n}c)^{\frac{1}{n+1}}+b=0$ $(ac^\frac{1}{n+1})^{n}+(a^\frac{1}{n+1}c)^{n+1}+b=0$

gatecse asked in Quantitative Aptitude Sep 18, 2019

301 views

1 vote

0 answers

29

ISI2016-DCG-29
The condition that ensures that the roots of the equation $x^{3}-px^{2}+qx-r=0$ are in H.P. is $r^{2}-9pqr+q^{3}=0$ $27r^{2}-9pqr+3q^{3}=0$ $3r^{3}-27pqr-9q^{3}=0$ $27r^{2}-9pqr+2q^{3}=0$

gatecse asked in Quantitative Aptitude Sep 18, 2019

168 views

0 votes

1 answer

30

ISI2016-DCG-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.

gatecse asked in Quantitative Aptitude Sep 18, 2019

205 views

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