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Recent questions tagged binomialtheorem
+2
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2
answers
1
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \left( 1+\dfrac{C_{n1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $ \frac{(n+1)^n}{n!} $
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
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166
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isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
3
answers
2
ISI2014DCG18
$^nC_0+2^nC_1+3^nC_2+\cdots+(n+1)^nC_n$ equals $2^n+n2^{n1}$ $2^nn2^{n1}$ $2^n$ none of these
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

67
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
3
ISI2014DCG34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

49
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
0
votes
1
answer
4
ISI2015MMA9
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \ldots +C_nx^n, \: n$ being a positive integer. The value of $\left( 1+\frac{C_0}{C_1} \right) \left( 1+\frac{C_1}{C_2} \right) \cdots \left( 1+\frac{C_{n1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $\frac{(n+1)^n}{n!}$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

16
views
isi2015mma
permutationandcombination
binomialtheorem
0
votes
1
answer
5
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)

48
views
isi2015dcg
numericalability
numbersystem
binomialtheorem
0
votes
1
answer
6
ISI2015DCG21
The value of the term independent of $x$ in the expansion of $(1x)^2(x+\frac{1}{x})^7$ is $70$ $70$ $35$ None of these
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

21
views
isi2015dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
7
ISI2016DCG21
The value of the term independent of $x$ in the expansion of $(1x)^{2}(x+\frac{1}{x})^{7}$ is $70$ $70$ $35$ None of these
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

30
views
isi2016dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
8
ISI2017DCG11
The coefficient of $x^6y^3$ in the expression $(x+2y)^9$ is $84$ $672$ $8$ none of these
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

21
views
isi2017dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
9
ISI2018DCG4
The number of terms with integral coefficients in the expansion of $\left(17^\frac{1}{3}+19^\frac{1}{2}x\right)^{600}$ is $99$ $100$ $101$ $102$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

51
views
isi2018dcg
permutationandcombination
binomialtheorem
+2
votes
1
answer
10
ISI2018DCG17
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is $4096$ $4083$ $2^{13}1$ $2^{12}1$
asked
Sep 18, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

32
views
isi2018dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
11
ISI2016MMA14
The number of terms independent of $x$ in the binomial expansion of $\left(3x^2 + \dfrac{1}{x}\right)^{10}$ is $0$ $1$ $2$ $5$
asked
Sep 13, 2018
in
Combinatory
by
jothee
Veteran
(
105k
points)

31
views
isi2016mma
permutationandcombination
binomialtheorem
+4
votes
1
answer
12
BINOMIAL DISTRIBUTION
Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is I am getting 0.75 can anyone confirm this ?
asked
Oct 6, 2017
in
Probability
by
junaid ahmad
Loyal
(
8.6k
points)

334
views
probability
binomialtheorem
0
votes
1
answer
13
TestBook Live 2017
Which power of x has the greatest coefficient in the expansion of (1+1/2 x)^10 ?
asked
Jan 18, 2017
in
Mathematical Logic
by
Sarvottam Patel
Junior
(
987
points)

154
views
binomialtheorem
+3
votes
3
answers
14
TIFR2016A13
Let $n \geq 2$ be any integer. Which of the following statements is not necessarily true? $\begin{pmatrix} n \\ i \end{pmatrix} = \begin{pmatrix} n1 \\ i \end{pmatrix} + \begin{pmatrix} n1 \\ i1 \end{pmatrix}, \text{ where } 1 \leq i \leq n1$ $n!$ divides the product of any ... $ i \in \{1, 2, \dots , n1\}$ If $n$ is an odd prime, then $n$ divides $2^{n1} 1$
asked
Dec 28, 2016
in
Others
by
jothee
Veteran
(
105k
points)

171
views
tifr2016
binomialtheorem
+5
votes
4
answers
15
Time complexity and output
#include <stdio.h> #define N 3 int main() { int array[N] = {1,2,3}; int i,j; for ( i=1; i<(1<<N); i++) { for( j=0; j<N; j++) { if((1<<j)&i) { printf("%d", array[j]); } } printf("\n"); } return 0 ... $N = n \;\; , n \; \text{ is a positive integer }$ ? B. What is the output? C. What will be the complexity when $N$ is large.
asked
Dec 17, 2016
in
Programming
by
dd
Veteran
(
57.2k
points)

633
views
timecomplexity
bitwise
programminginc
permutationandcombination
summation
subset
binomialtheorem
+1
vote
1
answer
16
find the coffecient of x^198
asked
Nov 29, 2016
in
Combinatory
by
Akriti sood
Boss
(
12.2k
points)

241
views
binomialtheorem
engineeringmathematics
+2
votes
3
answers
17
Probability Binomial Distribution
Probability of getting a total of 7 atleast once in three toss of a fair die is 125/216 91/216 117/216 9/216
asked
Jan 3, 2016
in
Probability
by
pC
Boss
(
21.5k
points)

653
views
binomialtheorem
probability
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