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Recent questions tagged numbersystem
+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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

180
views
isi2014dcg
numericalability
numbersystem
factors
+1
vote
1
answer
2
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

40
views
isi2014dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
3
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

36
views
isi2014dcg
numericalability
numbersystem
factors
0
votes
1
answer
4
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

52
views
isi2015mma
numericalability
numbersystem
minimumvalue
nongate
+1
vote
1
answer
5
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

40
views
isi2015mma
numbersystem
nongate
+1
vote
1
answer
6
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

18
views
isi2015mma
numericalability
numbersystem
remaindertheorem
0
votes
1
answer
7
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

23
views
isi2015mma
numericalability
numbersystem
polynomial
roots
nongate
0
votes
1
answer
8
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

17
views
isi2015mma
numericalability
numbersystem
congruentmodulo
nongate
0
votes
1
answer
9
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

22
views
isi2015mma
numericalability
numbersystem
quadraticequations
nongate
0
votes
1
answer
10
ISI2015MMA24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k1)}$ converges to $1$ $1$ $0$ does not converge
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

21
views
isi2015mma
numbersystem
convergencedivergence
summation
nongate
0
votes
0
answers
11
ISI2015MMA29
The set $\{x \: : \begin{vmatrix} x+\frac{1}{x} \end{vmatrix} \gt6 \}$ equals the set $(0,32\sqrt{2}) \cup (3+2\sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2 \sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2\sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2 \sqrt{2},32\sqrt{2}) \cup (3+2 \sqrt{2}, \infty )$
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

15
views
isi2015mma
numbersystem
nongate
0
votes
1
answer
12
ISI2015MMA41
Let $k$ and $n$ be integers greater than $1$. Then $(kn)!$ is not necessarily divisible by $(n!)^k$ $(k!)^n$ $n! \cdot k! \cdot$ $2^{kn}$
asked
Sep 23, 2019
in
Numerical Ability
by
Arjun
Veteran
(
431k
points)

21
views
isi2015mma
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
13
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

45
views
isi2015dcg
numericalability
numbersystem
coefficients
+1
vote
2
answers
14
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

60
views
isi2015dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
15
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

26
views
isi2015dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
16
ISI2015DCG12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

33
views
isi2015dcg
numericalability
numbersystem
factors
0
votes
1
answer
17
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

20
views
isi2015dcg
numericalability
numbersystem
0
votes
1
answer
18
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

19
views
isi2015dcg
numericalability
numbersystem
0
votes
1
answer
19
ISI2015DCG18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

49
views
isi2015dcg
numericalability
numbersystem
binomialtheorem
0
votes
1
answer
20
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

25
views
isi2015dcg
numericalability
numbersystem
+1
vote
2
answers
21
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

28
views
isi2015dcg
numericalability
numbersystem
factors
+1
vote
1
answer
22
ISI2016DCG6
The coefficient of $x^{2}$ in the product $(1+x)(1+2x)(1+3x)\cdots (1+10x)$ is $1320$ $1420$ $1120$ None of these
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

18
views
isi2016dcg
numericalability
numbersystem
+1
vote
1
answer
23
ISI2016DCG8
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 $16$ $17$ $18$ $10$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

26
views
isi2016dcg
numericalability
numbersystem
remaindertheorem
0
votes
1
answer
24
ISI2016DCG10
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

17
views
isi2016dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
25
ISI2016DCG12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

17
views
isi2016dcg
numericalability
numbersystem
remaindertheorem
0
votes
0
answers
26
ISI2016DCG13
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
numericalability
numbersystem
remaindertheorem
0
votes
0
answers
27
ISI2016DCG18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

12
views
isi2016dcg
numericalability
numbersystem
+1
vote
2
answers
28
ISI2016DCG19
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, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

25
views
isi2016dcg
numericalability
numbersystem
remaindertheorem
+1
vote
1
answer
29
ISI2016DCG20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

18
views
isi2016dcg
numericalability
numbersystem
factors
+2
votes
2
answers
30
ISI2018DCG1
The digit in the unit place of the number $7^{78}$ is $1$ $3$ $7$ $9$
asked
Sep 18, 2019
in
Numerical Ability
by
gatecse
Boss
(
17.5k
points)

77
views
isi2018dcg
numericalability
numbersystem
unitdigit
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