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Recent questions tagged isi2015-dcg

2 votes

4 answers

1

ISI2015-DCG-1
The sequence $\dfrac{1}{\log_3 2}, \: \dfrac{1}{\log_6 2}, \: \dfrac{1}{\log_{12} 2}, \: \dfrac{1}{\log_{24} 2} \dots $ is in Arithmetic progression (AP) Geometric progression ( GP) Harmonic progression (HP) None of these

gatecse asked in Quantitative Aptitude Sep 18, 2019

350 views

1 vote

4 answers

2

ISI2015-DCG-2
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then $a <b$ $a>b$ $a=b$ None of these

gatecse asked in Quantitative Aptitude Sep 18, 2019

358 views

0 votes

2 answers

3

ISI2015-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

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0 votes

2 answers

4

ISI2015-DCG-4
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 Quantitative Aptitude Sep 18, 2019

515 views

0 votes

1 answer

5

ISI2015-DCG-5
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

324 views

1 vote

1 answer

6

ISI2015-DCG-6
The coefficient of $x^2$ in the product $(1+x)(1+2x)(1+3x) \dots (1+10x)$ is $1320$ $1420$ $1120$ None of these

gatecse asked in Quantitative Aptitude Sep 18, 2019

244 views

0 votes

1 answer

7

ISI2015-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

269 views

1 vote

2 answers

8

ISI2015-DCG-8
Let $S=\{0, 1, 2, \cdots 25\}$ and $T=\{n \in S: n^2+3n+2$ 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

320 views

2 votes

1 answer

9

ISI2015-DCG-9
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

310 views

0 votes

1 answer

10

ISI2015-DCG-10
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

253 views

1 vote

1 answer

11

ISI2015-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array} {} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ 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

284 views

1 vote

1 answer

12

ISI2015-DCG-12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$

gatecse asked in Quantitative Aptitude Sep 18, 2019

330 views

0 votes

1 answer

13

ISI2015-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

203 views

0 votes

1 answer

14

ISI2015-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

208 views

0 votes

1 answer

15

ISI2015-DCG-15
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

189 views

0 votes

2 answers

16

ISI2015-DCG-16
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 Quantitative Aptitude Sep 18, 2019

243 views

0 votes

2 answers

17

ISI2015-DCG-17
The set $\{(x,y): \mid x \mid + \mid y \mid \leq 1\}$ is represented by the shaded region in

gatecse asked in Set Theory & Algebra Sep 18, 2019

233 views

0 votes

1 answer

18

ISI2015-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

315 views

0 votes

1 answer

19

ISI2015-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

263 views

2 votes

2 answers

20

ISI2015-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

326 views

0 votes

1 answer

21

ISI2015-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

276 views

0 votes

3 answers

22

ISI2015-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

347 views

0 votes

2 answers

23

ISI2015-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

259 views

2 votes

1 answer

24

ISI2015-DCG-24
If the letters of the word $\textbf{COMPUTER}$ 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

539 views

1 vote

1 answer

25

ISI2015-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 the above

gatecse asked in Quantitative Aptitude Sep 18, 2019

263 views

0 votes

1 answer

26

ISI2015-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

175 views

1 vote

1 answer

27

ISI2015-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

258 views

0 votes

1 answer

28

ISI2015-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 $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$

gatecse asked in Quantitative Aptitude Sep 18, 2019

154 views

3 votes

1 answer

29

ISI2015-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

244 views

0 votes

1 answer

30

ISI2015-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

185 views

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