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Recent questions tagged isi2015dcg
+1
vote
2
answers
1
ISI2015DCG1
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
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

70
views
isi2015dcg
numericalability
progression
logarithms
0
votes
1
answer
2
ISI2015DCG2
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x9)^2$ & $b = \underset{x \in S}{\Sigma} (x10)^2$. Then $a <b$ $a>b$ $a=b$ None of these
asked
Sep 18
in
Verbal Ability
by
gatecse
Boss
(
16.8k
points)

35
views
isi2015dcg
numericalability
numbersystem
summation
0
votes
2
answers
3
ISI2015DCG3
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
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

45
views
isi2015dcg
linearalgebra
determinant
0
votes
2
answers
4
ISI2015DCG4
If $\tan x=p+1$ and $\tan y=p1$, then the value of $2 \cot (xy)$ is $2p$ $p^2$ $(p+1)(p1)$ $\frac{2p}{p^21}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

41
views
isi2015dcg
numericalability
trigonometry
0
votes
1
answer
5
ISI2015DCG5
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
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

27
views
isi2015dcg
linearalgebra
matrices
+1
vote
1
answer
6
ISI2015DCG6
The coefficient of $x^2$ in the product $(1+x)(1+2x)(1+3x) \dots (1+10x)$ is $1320$ $1420$ $1120$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

31
views
isi2015dcg
numericalability
numbersystem
coefficients
0
votes
1
answer
7
ISI2015DCG7
Let $x^22(4k1)x+15k^22k7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

32
views
isi2015dcg
numericalability
quadraticequations
roots
+1
vote
2
answers
8
ISI2015DCG8
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 $16$ $17$ $18$ $10$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

38
views
isi2015dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
9
ISI2015DCG9
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

16
views
isi2015dcg
numericalability
numbersystem
remaindertheorem
0
votes
1
answer
10
ISI2015DCG10
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2015dcg
numericalability
progression
0
votes
1
answer
11
ISI2015DCG11
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
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
linearalgebra
systemofequations
+1
vote
1
answer
12
ISI2015DCG12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

19
views
isi2015dcg
numericalability
numbersystem
factors
0
votes
1
answer
13
ISI2015DCG13
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

15
views
isi2015dcg
numericalability
numbersystem
0
votes
1
answer
14
ISI2015DCG14
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
numericalability
numbersystem
0
votes
1
answer
15
ISI2015DCG15
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

20
views
isi2015dcg
numericalability
numbersystem
numberseries
summation
0
votes
2
answers
16
ISI2015DCG16
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
numericalability
geometry
area
0
votes
2
answers
17
ISI2015DCG17
The set $\{(x,y): \mid x \mid + \mid y \mid \leq 1\}$ is represented by the shaded region in
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
numericalability
geometry
area
0
votes
1
answer
18
ISI2015DCG18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

41
views
isi2015dcg
numericalability
numbersystem
binomialtheorem
0
votes
1
answer
19
ISI2015DCG19
The expression $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all positive integer values of $n$ all nonnegative integer values of $n$ only even integer values of $n$ only odd integer values of $n$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2015dcg
numericalability
numbersystem
+1
vote
2
answers
20
ISI2015DCG20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2015dcg
numericalability
numbersystem
factors
0
votes
1
answer
21
ISI2015DCG21
The value of the term independent of $x$ in the expansion of $(1x)^2(x+\frac{1}{x})^7$ is $70$ $70$ $35$ None of these
asked
Sep 18
in
Combinatory
by
gatecse
Boss
(
16.8k
points)

11
views
isi2015dcg
permutationandcombination
binomialtheorem
0
votes
1
answer
22
ISI2015DCG22
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
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
linearalgebra
determinant
0
votes
2
answers
23
ISI2015DCG23
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

16
views
isi2015dcg
numericalability
logarithms
+1
vote
1
answer
24
ISI2015DCG24
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
asked
Sep 18
in
Combinatory
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
permutationandcombination
arrangements
+1
vote
1
answer
25
ISI2015DCG25
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 $x^2+2x+63=0$ $x^263x+2=0$ $x^22x63=0$ None of the above
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
26
ISI2015DCG26
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

10
views
isi2015dcg
numericalability
quadraticequations
roots
0
votes
1
answer
27
ISI2015DCG27
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 oneone and into oneone and onto manyone and onto manyone and into
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

20
views
isi2015dcg
functions
triangles
0
votes
1
answer
28
ISI2015DCG28
If one root of a quadratic equation $ax^2+bx+c=0$ be equal to the $n^{th}$ power of the other, then $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
numericalability
quadraticequations
roots
+2
votes
1
answer
29
ISI2015DCG29
The condition that ensures that the roots of the equation $x^3px^2+qxr=0$ are in $H.P.$ is $r^29pqr+q^3=0$ $27r^29pqr+3q^3=0$ $3r^327pqr9q^3=0$ $27r^29pqr+2q^3=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

24
views
isi2015dcg
numericalability
quadraticequations
cubicequation
0
votes
1
answer
30
ISI2015DCG30
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

15
views
isi2015dcg
numericalability
quadraticequations
roots
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