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Recent questions tagged isi2014-dcg
1
votes
2
answers
61
ISI2014-DCG-61
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
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...
Arjun
514
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
arithmetic-series
+
–
0
votes
1
answer
62
ISI2014-DCG-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 $\frac{n(4n^2-1)c^2}{6}$ $\frac{n(4n^2+1)c^2}{3}$ $\frac{n(4n^2-1)c^2}{3}$ $\frac{n(4n^2+1)c^2}{6}$
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...
Arjun
360
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
arithmetic-series
+
–
2
votes
1
answer
63
ISI2014-DCG-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
If $^nC_{r-1}=36$, $^nC_r=84$ an $^nC_{r+1}=126$ then $r$ is equal to$1$$2$$3$none of these
Arjun
400
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
+
–
1
votes
1
answer
64
ISI2014-DCG-64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $-3$
The value of $\lambda$ such that the system of equation$$\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = &...
Arjun
638
views
Arjun
asked
Sep 23, 2019
Linear Algebra
isi2014-dcg
linear-algebra
matrix
system-of-equations
+
–
1
votes
0
answers
65
ISI2014-DCG-65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is$\frac{\pi}{4}$$\frac{\pi}{8}$$\frac{\pi}{6}$$2 \pi$
Arjun
465
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
summation
non-gate
+
–
1
votes
1
answer
66
ISI2014-DCG-66
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionary. The fiftieth word in this arrangement is $\text{IAANG}$ $\text{NAAGI}$ $\text{NAAIG}$ $\text{IAAGN}$
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionar...
Arjun
424
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
arrangements
+
–
2
votes
1
answer
67
ISI2014-DCG-67
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
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$$y=3$
Arjun
478
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
logarithms
+
–
1
votes
2
answers
68
ISI2014-DCG-68
The number of integer solutions for the equation $x^2+y^2=2011$ is $0$ $1$ $2$ $3$
The number of integer solutions for the equation $x^2+y^2=2011$ is$0$$1$$2$$3$
Arjun
516
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
integer-solutions
+
–
3
votes
2
answers
69
ISI2014-DCG-69
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to$18$$720$$360$$36$
Arjun
698
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
number-system
factors
+
–
0
votes
0
answers
70
ISI2014-DCG-70
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$, $(B^{-1}AB)^3$ is equal to $\begin{pmatrix} a^3 & a^3 \\ 0 & a^3 \end{pmatrix}$ ... $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$ $\begin{pmatrix} a^3 & 0 \\ -3a^3 & a^3 \end{pmatrix}$
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$, $(B^{-1}AB)^3$ is equal to$\begin{pmatrix} a^...
Arjun
374
views
Arjun
asked
Sep 23, 2019
Linear Algebra
isi2014-dcg
linear-algebra
matrix
inverse
+
–
1
votes
2
answers
71
ISI2014-DCG-71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of such arrangements is $24$ $16$ $12$ $32$
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of...
Arjun
626
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
arrangements
circular-permutation
+
–
1
votes
1
answer
72
ISI2014-DCG-72
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$ $0$ $1$ $2^n$
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$$0$$1$$2^n$
Arjun
623
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
summation
+
–
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