Recent questions tagged isi2014-dcg

0 votes
1 answer
62
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^2-1)c^2}{6}$$\frac{n(4n^2+1)c^2}{3}$$\f...
2 votes
1 answer
63
If $^nC_{r-1}=36$, $^nC_r=84$ an $^nC_{r+1}=126$ then $r$ is equal to$1$$2$$3$none of these
1 votes
1 answer
64
The value of $\lambda$ such that the system of equation$$\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = &...
1 votes
0 answers
65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is$\frac{\pi}{4}$$\frac{\pi}{8}$$\frac{\pi}{6}$$2 \pi$
1 votes
1 answer
66
2 votes
1 answer
67
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$$y=3$
1 votes
2 answers
68
The number of integer solutions for the equation $x^2+y^2=2011$ is$0$$1$$2$$3$
3 votes
2 answers
69
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to$18$$720$$360$$36$
1 votes
2 answers
71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of...
1 votes
1 answer
72
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$$0$$1$$2^n$