Aspire Faculty ID #15285 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

The coefficient of $x^4$ in expansion of $(1 + x + x^2 + x^3)^{11}$ is …

Solution

We can write generating function $f(x) = (1 + x + x^2 + x^3)^{11}$. Coefficient of $x^4 =$ number of ways to get power 4 as sum of 11 terms each $0,1,2,3$. By multinomial expansion, coefficient of $x^4 = {}^{11}C_4 + 10{}^{11}C_3 + 6{}^{11}C_2 + {}^{11}C_1 = 990$.
← Previous Next →

Previous 10 Questions — JAMIA MCA 2016

Nearest first
1
The coefficient of $x^8 y^{10}$ in $(x + y)^{18}$ is …
Topic: JAMIA MCA 2016
 2
The number of numbers greater than 23000 that can be formed from the digits 1, 2, 3, 4, 5 is …
Topic: JAMIA MCA 2016
 3
The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is …
Topic: JAMIA MCA 2016
 4
If ${}^8C_r - {}^7C_3 = {}^7C_2$, then $r$ is equal to …
Topic: JAMIA MCA 2016
 5
If sum of $n$ terms of a series is $3n^2 + 4n$, then the series is …
Topic: JAMIA MCA 2016
 6
If $\log_{2}(5\cdot2^{x}+1),\ \log_{4}(2^{\,1-x}+1)$ and $1$ are in A.P., then $x$ equals …
Topic: JAMIA MCA 2016
 7
If the roots of $x^3-9x^2+23x-15=0$ are in A.P., then their common difference is …
Topic: JAMIA MCA 2016
 8
Let sum of $n$ terms of an A.P. be $S_n=3n^2+5$. If $T_n$ (the $n$th term) of this series is $159$, then $n$ is …
Topic: JAMIA MCA 2016
 9
If $m^{\text{th}}$ term of an A.P. is $n$ and $n^{\text{th}}$ term is $m$, then its $10^{\text{th}}$ term is …
Topic: JAMIA MCA 2016
 10
Let cube roots of unity be $1, \omega, \omega^{2}$. Which of the following is a cube root of the equation $(x - 1)^{3} …
Topic: JAMIA MCA 2016

Next 10 Questions — JAMIA MCA 2016

Ascending by ID
1
If $A$ be a set of cardinality $n$, then number of one-to-one onto functions from set $A$ to $A$ is …
Topic: JAMIA MCA 2016
 2
If $f$ is a function from a finite set $A$ having $10$ elements to a finite set $B$ having $5$ elements, then number of…
Topic: JAMIA MCA 2016
 3
If $A$ and $B$ are two sets, then $(A \cup B)' \cap B$ is equal to …
Topic: JAMIA MCA 2016
 4
If $A = \{a, b, c\}$ and $B = \{a, b, d, e, f\}$ are two sets, then number of elements in $(A - B) \times (A \cap B)$ i…
Topic: JAMIA MCA 2016
 5
If $A$ and $B$ are two disjoint sets having $3$ and $5$ elements respectively, then power-set of $A \times (B - A)$ con…
Topic: JAMIA MCA 2016
 6
If $y = \tan^{-1}\!\left(\dfrac{1 + \tan x}{1 - \tan x}\right)$, then $\dfrac{dy}{dx}$ is equal to …
Topic: JAMIA MCA 2016
 7
If $\sqrt{x + y} + \sqrt{y - x} = \sqrt{2}a$, then $\dfrac{d^2 y}{d x^2}$ is equal to …
Topic: JAMIA MCA 2016
 8
If $y = \log(\tan \theta)$, then $\dfrac{dy}{d\theta}$ is equal to …
Topic: JAMIA MCA 2016
 9
If $y = x + e^{x}$, then $\dfrac{dx}{dy}$ is …
Topic: JAMIA MCA 2016
 10
If $y=(x^{x})^{x}$, then $\dfrac{dy}{dx}$ is …
Topic: JAMIA MCA 2016
Ask Your Question or Put Your Review.

loading...