(D) Using the Binomial Theorem,$(a+b)^n = \sum_{k=0}^{n} {^nC_k} a^{n-k} b^k$.$(102)^4 = (100+2)^4$$= {^4C_0}(100)^4(2)^0 + {^4C_1}(100)^3(2)^1 + {^4C

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Using the Binomial Theorem,$(a+b)^n = \sum_{k=0}^{n} {^nC_k} a^{n-k} b^k$.$(102)^4 = (100+2)^4$$= {^4C_0}(100)^4(2)^0 + {^4C_1}(100)^3(2)^1 + {^4C_2}(100)^2(2)^2 + {^4C_3}(100)^1(2)^3 + {^4C_4}(100)^0(2)^4$$= 1 \cdot 100000000 + 4 \cdot 1000000 \cdot 2 + 6 \cdot 10000 \cdot 4 + 4 \cdot 100 \cdot 8 + 1 \cdot 1 \cdot 16$$= 100000000 + 8000000 + 240000 + 3200 + 16$$= 108243216$Thus,the correct option is $D$.

Class 11 Mathematics Binomial Theorem Expansion of binomial theorem

Medium

$(102)^4 = ?$

AP EAMCET 2020 All AP EAMCET

A
$108242316$
B
$108423216$
C
$102843216$
D
$108243216$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Binomial Theorem

Subtopic

Expansion of binomial theorem

Previous Year

AP EAMCET 2020 Paper All AP EAMCET years →

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

MediumAP EAMCET 2008

View Solution

Given $(1 - 2x + 5x^2 - 10x^3) (1 + x)^n = 1 + a_1x + a_2x^2 + \dots$ and that $a_1^2 = 2a_2$,then the value of $n$ is:

View Solution

The first $3$ terms in the expansion of $(1 + ax)^n$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively

Medium

View Solution

Find the coefficient of $x^{5}$ in the product $(1+2x)^{6}(1-x)^{7}$ using the binomial theorem.

Difficult

View Solution

Let $(a + bx + cx^2)^{10} = \sum_{i=0}^{20} p_i x^i$,where $a, b, c \in N$. If $p_1 = 20$ and $p_2 = 210$,then $2(a + b + c)$ is equal to

DifficultJEE MAIN 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$(102)^4 = ?$

Similar Questions

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

Given $(1 - 2x + 5x^2 - 10x^3) (1 + x)^n = 1 + a_1x + a_2x^2 + \dots$ and that $a_1^2 = 2a_2$,then the value of $n$ is:

The first $3$ terms in the expansion of $(1 + ax)^n$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively

Find the coefficient of $x^{5}$ in the product $(1+2x)^{6}(1-x)^{7}$ using the binomial theorem.

Let $(a + bx + cx^2)^{10} = \sum_{i=0}^{20} p_i x^i$,where $a, b, c \in N$. If $p_1 = 20$ and $p_2 = 210$,then $2(a + b + c)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module