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Previous GATE
+3
votes
3
answers
1
ISI2014DCG10
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is $40$ $50$ $60$ $30$
asked
Sep 23
in
Numerical Ability
by
Arjun
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425k
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60
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isi2014dcg
numericalability
numbersystem
divisors
+1
vote
1
answer
2
ISI2014DCG11
Let $x_1$ and $x_2$ be the roots of the quadratic equation $x^23x+a=0$, and $x_3$ and $x_4$ be the roots of the quadratic equation $x^212x+b=0$. If $x_1, x_2, x_3$ and $x_4 \: (0 < x_1 < x_2 < x_3 < x_4)$ are in $G.P.,$ then $ab$ equals $64$ $5184$ $64$ $5184$
asked
Sep 23
in
Numerical Ability
by
Arjun
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(
425k
points)

25
views
isi2014dcg
quadraticequations
roots
geometricprogression
+1
vote
2
answers
3
ISI2014DCG16
The sum of the series $\dfrac{1}{1.2} + \dfrac{1}{2.3}+ \cdots + \dfrac{1}{n(n+1)} + \cdots $ is $1$ $1/2$ $0$ nonexistent
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

46
views
isi2014dcg
numericalability
summation
series
+1
vote
2
answers
4
ISI2014DCG22
The conditions on $a$, $b$ and $c$ under which the roots of the quadratic equation $ax^2+bx+c=0 \: ,a \neq 0, \: b \neq 0 $ and $c \neq 0$, are unequal magnitude but of the opposite signs, are the following: $a$ and $c$ have the same sign while $b$ has the ... $c$ has the opposite sign. $a$ and $c$ have the same sign. $a$, $b$ and $c$ have the same sign.
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

27
views
isi2014dcg
numericalability
quadraticequations
+1
vote
1
answer
5
ISI2014DCG23
The sum of the series $\:3+11+\dots +(8n5)\:$ is $4n^2n$ $8n^2+3n$ $4n^2+4n5$ $4n^2+2$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

30
views
isi2014dcg
numericalability
summation
series
+1
vote
1
answer
6
ISI2014DCG26
Let $x_1 > x_2>0$. Then which of the following is true? $\log \big(\frac{x_1+x_2}{2}\big) > \frac{\log x_1+ \log x_2}{2}$ $\log \big(\frac{x_1+x_2}{2}\big) < \frac{\log x_1+ \log x_2}{2}$ There exist $x_1$ and $x_2$ such that $x_1 > x_2 >0$ and $\log \big(\frac{x_1+x_2}{2}\big) = \frac{\log x_1+ \log x_2}{2}$ None of these
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

32
views
isi2014dcg
numericalability
logarithms
+1
vote
1
answer
7
ISI2014DCG30
Consider the equation $P(x) =x^3+px^2+qx+r=0$ where $p,q$ and $r$ are all real and positive. State which of the following statements is always correct. All roots of $P(x) = 0$ are real The equation $P(x)=0$ has at least one real root The equation $P(x)=0$ has no negative real root The equation $P(x)=0$ must have one positive and one negative real root
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

20
views
isi2014dcg
numericalability
quadraticequations
roots
+1
vote
1
answer
8
ISI2014DCG36
Consider any integer $I=m^2+n^2$, where $m$ and $n$ are odd integers. Then $I$ is never divisible by $2$ $I$ is never divisible by $4$ $I$ is never divisible by $6$ None of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

18
views
isi2014dcg
numericalability
numbersystem
remaindertheorem
0
votes
0
answers
9
ISI2014DCG54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

25
views
isi2014dcg
numericalability
trigonometry
roots
0
votes
1
answer
10
ISI2014DCG55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^22(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

18
views
isi2014dcg
numericalability
geometry
quadraticequations
0
votes
1
answer
11
ISI2014DCG56
Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is $4$ $3$ $4$ $3$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

11
views
isi2014dcg
numericalability
geometry
rectangle
straightline
0
votes
1
answer
12
ISI2014DCG58
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of one of the vertices of this square are $(2, 2)$ $(2\sqrt{2},2)$ $(2, 2\sqrt{2})$ $(2\sqrt{2}, 2\sqrt{2})$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

18
views
isi2014dcg
numericalability
geometry
circle
square
0
votes
1
answer
13
ISI2014DCG60
The equation of any circle passing through the origin and with its centre on the $X$axis is given by $x^2+y^22ax=0$ where $a$ must be positive $x^2+y^22ax=0$ for any given $a \in \mathbb{R}$ $x^2+y^22by=0$ where $b$ must be positive $x^2+y^22by=0$ for any given $b \in \mathbb{R}$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

15
views
isi2014dcg
numericalability
geometry
circle
0
votes
0
answers
14
ISI2014DCG61
If $l=1+a+a^2+ \dots$, $m=1+b+b^2+ \dots$, and $n=1+c+c^2+ \dots$, where $\mid a \mid <1, \: \mid b \mid < 1, \: \mid c \mid <1$ and $a,b,c$ are in arithmetic progression, then $l, m, n$ are in arithmetic progression geometric progression harmonic progression none of these
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

14
views
isi2014dcg
numericalability
progression
0
votes
1
answer
15
ISI2014DCG62
If the sum of the first $n$ terms of an arithmetic progression is $cn^2$, then the sum of squares of these $n$ terms is $\frac{n(4n^21)c^2}{6}$ $\frac{n(4n^2+1)c^2}{3}$ $\frac{n(4n^21)c^2}{3}$ $\frac{n(4n^2+1)c^2}{6}$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

15
views
isi2014dcg
numericalability
arithmetic
progression
+1
vote
0
answers
16
ISI2014DCG65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

39
views
isi2014dcg
numericalability
summation
series
0
votes
1
answer
17
ISI2014DCG67
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

13
views
isi2014dcg
numericalability
logarithms
0
votes
1
answer
18
ISI2014DCG68
The number of integer solutions for the equation $x^2+y^2=2011$ is $0$ $1$ $2$ $3$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

17
views
isi2014dcg
numericalability
integersolutions
+1
vote
1
answer
19
ISI2014DCG69
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

16
views
isi2014dcg
numericalability
numbersystem
factors
0
votes
1
answer
20
ISI2015MMA2
If $a,b$ are positive real variables whose sum is a constant $\lambda$, then the minimum value of $\sqrt{(1+1/a)(1+1/b)}$ is $\lambda \: – 1/\lambda$ $\lambda + 2/\lambda$ $\lambda+1/\lambda$ None of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

40
views
isi2015mma
numericalability
numbersystem
minimumvalue
nongate
+1
vote
1
answer
21
ISI2015MMA3
Let $x$ be a positive real number. Then $x^2+\pi ^2 + x^{2 \pi} > x \pi+ (\pi + x) x^{\pi}$ $x^{\pi}+\pi^x > x^{2 \pi} + \pi ^{2x}$ $\pi x +(\pi+x)x^{\pi} > x^2+\pi ^2 + x^{2 \pi}$ none of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

31
views
isi2015mma
numbersystem
nongate
+1
vote
1
answer
22
ISI2015MMA11
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals $854$ $153$ $160$ none of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

14
views
isi2015mma
numericalability
numbersystem
remaindertheorem
0
votes
1
answer
23
ISI2015MMA12
Consider the polynomial $x^5+ax^4+bx^3+cx^2+dx+4$ where $a,b,c,d$ are real numbers. If $(1+2i)$ and $(32i)$ are two two roots of this polynomial then the value of $a$ is $524/65$ $524/65$ $1/65$ $1/65$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

18
views
isi2015mma
numericalability
numbersystem
polynomial
roots
nongate
0
votes
1
answer
24
ISI2015MMA13
The number of real roots of the equation $2 \cos \bigg( \frac{x^2+x}{6} \bigg) = 2^x +2^{x} \text{ is }$ $0$ $1$ $2$ infinitely many
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

12
views
isi2015mma
numericalability
quadraticequations
trigonometry
0
votes
1
answer
25
ISI2015MMA14
Consider the following system of equivalences of integers, $x \equiv 2 \text{ mod } 15$ $x \equiv 4 \text{ mod } 21$ The number of solutions in $x$, where $1 \leq x \leq 315$, to the above system of equivalences is $0$ $1$ $2$ $3$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

11
views
isi2015mma
numericalability
numbersystem
congruentmodulo
nongate
0
votes
1
answer
26
ISI2015MMA15
The number of real solutions of the equations $(9/10)^x = 3+xx^2$ is $2$ $0$ $1$ none of the above
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

15
views
isi2015mma
numericalability
numbersystem
quadraticequations
nongate
+1
vote
2
answers
27
ISI2015MMA16
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

42
views
isi2015mma
numericalability
quadraticequations
functions
nongate
+1
vote
1
answer
28
ISI2015MMA17
Let $X=\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \cdots + \frac{1}{3001}$. Then, $X \lt1$ $X\gt3/2$ $1\lt X\lt 3/2$ none of the above holds
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

16
views
isi2015mma
numericalability
summation
series
nongate
+1
vote
1
answer
29
ISI2015MMA18
The set of complex numbers $z$ satisfying the equation $(3+7i)z+(102i)\overline{z}+100=0$ represents, in the complex plane, a straight line a pair of intersecting straight lines a point a pair of distinct parallel straight lines
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

22
views
isi2015mma
numericalability
geometry
straightlines
complexnumber
nongate
0
votes
1
answer
30
ISI2015MMA24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k1)}$ converges to $1$ $1$ $0$ does not converge
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

14
views
isi2015mma
numbersystem
converges
summation
nongate
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