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Test: Binomial Theorem For Positive Index - JEE MCQ


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15 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Binomial Theorem For Positive Index

Test: Binomial Theorem For Positive Index for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Binomial Theorem For Positive Index questions and answers have been prepared according to the JEE exam syllabus.The Test: Binomial Theorem For Positive Index MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binomial Theorem For Positive Index below.
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Test: Binomial Theorem For Positive Index - Question 1

The number of terms in the expansion of (2x - 3y)8 is

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 1

Since this binomial is to the power 8, there will be nine terms in the expansion.

Test: Binomial Theorem For Positive Index - Question 2

The middle term in the expansion of 

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 2

n = 10

Middle term = (n/2) + 1
= (10/2) + 1
= 6th term

T(6) = T(5+1)
= 10C5[(2x2)/3]5 [(3/2x2)]5
= 10C5
= 252

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Test: Binomial Theorem For Positive Index - Question 3

In the expansion of (a+b)n, N the number of terms is:

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 3

The total number of terms in the binomial expansion of (a + b)n is n + 1, i.e. one more than the exponent n.

Test: Binomial Theorem For Positive Index - Question 4

Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal.

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Test: Binomial Theorem For Positive Index - Question 5

The sixth term in the expansion of  is

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Test: Binomial Theorem For Positive Index - Question 6

If the coefficients of 7th and 13th terms in the expansion of (1 + x)n are equal, then n is equal to

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 6

Test: Binomial Theorem For Positive Index - Question 7

The 6th term in the expansion of   is

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 7

Test: Binomial Theorem For Positive Index - Question 8

What is the coefficient of x5 in the expansion of (1-x)-6 ?

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 8

(1-x)-6 
=> (1-x)(-6/1)
It is in the form of (1-x)(-p/q), p =6, q=1

(1-x)(-p/q) = 1+p/1!(x/q)1 + p(p+q)/2!(x/q)2 + p(p+q)(p+2q)/3!(x/q)3 + p(p+q)(p+2q)(p+3q)/4!(x/q)4........

= 1+6/1!(x/1)1 + 6(7)/2!(x/1)2 + 6(7)(8)/3!(x/1)3 + 6(7)(8)(9)/4!(x/1)4 +.......................

So, coefficient of x5 is (6*7*8*9*10)/120
= 252

Test: Binomial Theorem For Positive Index - Question 9

In the expansion of the binomial expansion (a + b)n, which of the following is incorrect ?

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 9

Correct Answer: d

Explanation:- The coefficient of terms (x+a)n equidistant from the beginning and the end are equal. These coefficients are known as the binomial coefficients.

nCr = nCn – r, r = 0,1,2,…,n.

Test: Binomial Theorem For Positive Index - Question 10

The middle term in the expansion of (x + y)10 is the

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 10

Number of terms(n) = 10 
Middle term = (n/2) + 1

= (10/2) + 1
= 5 + 1
= 6th term

Test: Binomial Theorem For Positive Index - Question 11

In a binomial expansion with power 13

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 11

Test: Binomial Theorem For Positive Index - Question 12

If in the expansion of (1+x)20, the coefficients of rth and (r+4)th terms are equal, then the value of r is equal to:

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 12

Coefficients of the rth and (r+4)th terms in the given expansion are Cr−120  and 20Cr+3.
Here,Cr−120  = 20Cr+3
⇒ r−1+r+3 = 20 
[∵ if nCnCy  ⇒ x = y or x+y = n]

⇒ r = 2 or 2r = 18
⇒ r = 9  

Test: Binomial Theorem For Positive Index - Question 13

The number of terms in the expansion of (x – y + 2z)7 are:

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 13

Here the number of terms can be calculated by:
= ((n+ 1) * (n+2)) /2
where, n =7

∴ Number of terms = 36

Test: Binomial Theorem For Positive Index - Question 14

The number of terms in the expansion of (a + b + c)n are:

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 14

No. of terms is n+2C2

Test: Binomial Theorem For Positive Index - Question 15

The general term in the expansion of (a - b)n is

Detailed Solution for Test: Binomial Theorem For Positive Index - Question 15

If a and b are real numbers and n is a positive integer, then:
(a - b)n = nC0 an + nC1 a(n – 1) b1 + nC2 a(n – 2) b2+ ...... + nCr a(n – r) br+ ... + nCnbn,

The general term or (r + 1)th term in the expansion is given by:
Tr + 1 = (-1)Cr a(n–r) br

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