Recent questions tagged number-system

6 votes
3 answers
62
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is$40$$50$$60$$30$
2 votes
1 answer
63
Consider any integer $I=m^2+n^2$, where $m$ and $n$ are odd integers. Then$I$ is never divisible by $2$$I$ is never divisible by $4$$I$ is never divisible by $6$None of t...
3 votes
2 answers
64
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to$18$$720$$360$$36$
3 votes
2 answers
65
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$$\lambda + 2/\lambda...
3 votes
3 answers
66
Let $x$ be a positive real number. Then$x^2+\pi ^2 + x^{2 \pi} x \pi+ (\pi + x) x^{\pi}$$x^{\pi}+\pi^x x^{2 \pi} + \pi ^{2x}$$\pi x +(\pi+x)x^{\pi} x^2+\pi ^2 + x^{2 \...
2 votes
2 answers
67
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals$854$$153$$160$none of the above
1 votes
1 answer
68
Consider the polynomial $x^5+ax^4+bx^3+cx^2+dx+4$ where $a,b,c,d$ are real numbers. If $(1+2i)$ and $(3-2i)$ are two two roots of this polynomial then the value of $a$ i...
1 votes
1 answer
69
1 votes
1 answer
70
0 votes
2 answers
71
1 votes
1 answer
73
Let $k$ and $n$ be integers greater than $1$. Then $(kn)!$ is not necessarily divisible by$(n!)^k$$(k!)^n$$n! \cdot k! \cdot$$2^{kn}$
1 votes
1 answer
74
The coefficient of $x^2$ in the product $(1+x)(1+2x)(1+3x) \dots (1+10x)$ is$1320$$1420$$1120$None of these
1 votes
2 answers
75
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$$10$
2 votes
1 answer
76
1 votes
1 answer
77
0 votes
1 answer
78
For all the natural number $n \geq 3, \: n^2+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
0 votes
1 answer
79
For natural numbers $n$, the inequality $2^n >2n+1$ is valid when$n \geq 3$$n < 3$$n=3$None of these
0 votes
1 answer
80
0 votes
1 answer
81
The expression $3^{2n+1} + 2^{n+2}$ is divisible by $7$ forall positive integer values of $n$all non-negative integer values of $n$only even integer values of $n$only odd...
2 votes
2 answers
82
The total number of factors of $3528$ greater than $1$ but less than $3528$ is$35$$36$$34$None of these
1 votes
1 answer
83
The coefficient of $x^{2}$ in the product $(1+x)(1+2x)(1+3x)\cdots (1+10x)$ is$1320$$1420$$1120$None of these
1 votes
1 answer
84
Let $S=\{0,1,2,\cdots,25\}$ and $T=\{n\in S\: : \: n^{2}+3n+2\: \text{is divisible by}\: 6\}$. Then the number of elements in the set $T$ is$16$$17$$18$$10$
0 votes
1 answer
85
1 votes
1 answer
86
0 votes
1 answer
87
For all the natural number $n\geq 3,\: n^{2}+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
0 votes
0 answers
88
The value of $(1.1)^{10}$ correct to $4$ decimal places is$2.4512$$1.9547$$2.5937$$1.4512$
1 votes
2 answers
89
The expression $3^{2n+1}+2^{n+2}$ is divisible by $7$ forall positive integer values of $n$all non-negative integer values of $n$only even integer values of $n$only odd i...
1 votes
1 answer
90
The total number of factors of $3528$ greater than $1$ but less than $3528$ is$35$$36$$34$None of these