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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
by
gatecse
350
views
isi2015-dcg
quantitative-aptitude
arithmetic-series
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
by
gatecse
358
views
isi2015-dcg
quantitative-aptitude
summation
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
by
gatecse
394
views
isi2015-dcg
linear-algebra
determinant
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
by
gatecse
515
views
isi2015-dcg
quantitative-aptitude
trigonometry
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
by
gatecse
324
views
isi2015-dcg
linear-algebra
matrix
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
by
gatecse
244
views
isi2015-dcg
quantitative-aptitude
number-system
coefficients
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
by
gatecse
269
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
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
by
gatecse
320
views
isi2015-dcg
quantitative-aptitude
number-system
remainder-theorem
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
by
gatecse
310
views
isi2015-dcg
quantitative-aptitude
number-system
remainder-theorem
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
by
gatecse
253
views
isi2015-dcg
quantitative-aptitude
sequence-series
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
by
gatecse
284
views
isi2015-dcg
linear-algebra
system-of-equations
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
by
gatecse
330
views
isi2015-dcg
quantitative-aptitude
number-system
factors
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
by
gatecse
203
views
isi2015-dcg
quantitative-aptitude
number-system
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
by
gatecse
208
views
isi2015-dcg
quantitative-aptitude
number-system
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
by
gatecse
189
views
isi2015-dcg
quantitative-aptitude
summation
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
by
gatecse
243
views
isi2015-dcg
quantitative-aptitude
geometry
area
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
by
gatecse
233
views
isi2015-dcg
set-theory
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
by
gatecse
315
views
isi2015-dcg
quantitative-aptitude
number-system
binomial-theorem
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
by
gatecse
263
views
isi2015-dcg
quantitative-aptitude
number-system
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
by
gatecse
326
views
isi2015-dcg
quantitative-aptitude
number-system
factors
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
by
gatecse
276
views
isi2015-dcg
combinatory
binomial-theorem
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
by
gatecse
347
views
isi2015-dcg
linear-algebra
determinant
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
by
gatecse
259
views
isi2015-dcg
quantitative-aptitude
logarithms
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
by
gatecse
539
views
isi2015-dcg
combinatory
arrangements
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
by
gatecse
263
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
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
by
gatecse
175
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
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
by
gatecse
258
views
isi2015-dcg
functions
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
by
gatecse
154
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
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
by
gatecse
244
views
isi2015-dcg
quantitative-aptitude
cubic-equations
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
by
gatecse
185
views
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
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