JEE  >  Maths 35 Years JEE Main & Advanced Past year Papers  >  Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Document Description: Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The notes and questions for Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced have been prepared according to the JEE exam syllabus. Information about Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced covers topics like and Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced.

Introduction of Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced in English is available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced in Hindi for Maths 35 Years JEE Main & Advanced Past year Papers course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
1 Crore+ students have signed up on EduRev. Have you?

Q.1. The larger of 9950 + 10050 and 10150 is ................ (1982 - 2 Marks) 

Ans.  (101)50

Sol.  Consider (101)50 – {(99)50 + (100)50} = (100 + 1)50  –  (100 – 1)50 – (100)50
= (100)50 [(1+ 0.0 1)50 – (1– 0.01)50 – 1]
= (100)50 [2 (50C1(0.01) + 50C3(0.01)3  + ....) – 1]
= (100)50 [2 (50C3(0.01)3  + ....)] >  0
∴ (101)50 > (99)50 + (100)50 
 ∴  (101)50   is greater.

 

Q.2. The sum of the coefficients of the plynomial (1 + x – 3x2)2163 is ................ (1982 - 2 Marks) 

Ans. -1

Sol.  If we put  x = 1 in the expansion of (1+ x – 3x2)2163 = A0 + A1x + A2x2 + ...
we will get the sum of coefficients of given polynomial, which clearly comes to be – 1.

 

Q.3. If (1 + ax )n = 1 + 8x + 24x2 + ....  then a = ...... and n = ............... (1983 - 2 Marks) 

Ans. a = 2, n = 4

Sol.  (1 + ax)n = 1 + 8x + 24x+ ...
⇒ (1 + ax)n = 1 + nxa +Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

= 1 + 8 x + 24x 2+ ...
Comparing like powers of  x we get

nax = 8x ⇒ na = 8 ....(1)

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE ....(2)

Solving (1) and (2),  n = 4,  a = 2
 

Q.4. Let n be positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of (1 + x)n are in A.P., then the value of n is .............. (1994 -  2 Marks) 

Ans. 7

 Sol.  We know that for a +ve integer n (1 + x)n = nC0 + nCx + nCx2 + ......+ nCxn
ATQ coefficients of 2nd, 3nd, and 4th terms are in A.P. i.e.nC1, nC2, nC3 are in A.P.
⇒ 2.nC2 =  nC1 +  nC3

 

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE⇒ n2 – 9n + 14 = 0

⇒ (n – 7) (n – 2) = 0 ⇒  n = 7  or  2
But for the existance of 4th term, n = 7.

 

 

Q.5. The sum of the rational terms in th e expansion of  Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE   is ................ (1997 - 2 Marks)

Ans. 41

Sol.  Let Tr +1 be the general term in the expansion of

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Let Tr +1will be rational if 25–r/2 and 3r/5 are rational numbers.

⇒ Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are integers.

⇒ r = 0 and r = 10   ⇒  T1 and T11 are rational terms.
⇒ Sum of T1  and T11 = 10C025 – 0.30 + 10C1025–5.32
= 1.32.1 + 1.1.9 = 32 + 9 = 41

The document Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.
All you need of JEE at this link: JEE

Related Searches

mock tests for examination

,

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

Semester Notes

,

Free

,

practice quizzes

,

Previous Year Questions with Solutions

,

Summary

,

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

ppt

,

Objective type Questions

,

shortcuts and tricks

,

Important questions

,

MCQs

,

past year papers

,

Viva Questions

,

study material

,

Sample Paper

,

video lectures

,

pdf

,

Fill in the Blanks: Mathematical Induction and Binomial Theorem | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

Exam

,

Extra Questions

;