case study questions on binomial theorem class 11

CBSE Question Bank for Class 11 Maths Chapter 8 Binomial Theorem Free PDF

LEVEL UP CBSE Question Bank for Class 11 Maths  Chapter 8 Binomial Theorem  will provide you with  detailed, latest, comprehensive  &  confidence inspiring   solutions  to the maximum number of Questions covering all the  topics from  your  NCERT Text Books !

Given below are the  Important Questions for Class 11 Maths  (with Solutions) from the exam point of view. To download the “ CBSE Question Bank for Class 11 Maths”,  just click on the “ Download PDF ” and “ Download Solutions ” buttons

CBSE Question Bank for Class 11 Maths Chapter 8 Binomial Theorem PDF

Checkout our cbse question banks for other chapters.

• Chapter 6 Linear Inequalities CBSE Question Bank
• Chapter 7 Permutations and Combinations CBSE Question Bank
• Chapter 9 Sequences and Series CBSE Question Bank
• Chapter 10 Straight Lines CBSE Question Bank

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

Comments are closed.

Contact Form

Privacy Policy

• Class 11 Maths
• Chapter 8: Binomial Theorem

Important Questions for Class 11 Maths Chapter 8 - Binomial Theorem

Important questions for class 11 Maths Chapter 8 Binomial Theorem are provided here. While calculating the higher powers, the multiplication process becomes complex. To avoid the difficulty of repeated multiplication, the binomial theorem was introduced. In class 11 Maths Chapter 8, students can learn about the binomial theorem for positive integral indices. Also, it covers the concept of middle terms. Here, all the important questions from chapter 8 are provided with solutions. These questions are referred from the previous year questions papers and NCERT textbooks. Access, all the chapters important questions for class 11 Maths at BYJU’S.

Class 11 Maths Chapter 8 – Binomial Theorem describe the following important concepts:

• Introduction to binomials
• For Positive integers “n” and special cases
• General and middle terms

Also, Check:

• Important 1 Mark Questions for CBSE Class 11 Maths
• Important 4 Marks Questions for CBSE Class 11 Maths
• Important 6 Marks Questions for CBSE Class 11 Maths

Important Questions for Class 11 Maths Chapter 8 Binomial Theorem with Solutions

Practice the given below important questions for class 11 Maths Chapter 8  Binomial Theorem. Solving the binomial theorem problem is a little bit time-consuming task. But, the repeated practise of these problems helps you to manage the time in the examination and allows you to solve the problems without any mistake.

Question 1:

Expand the expression (2x-3) 6 using the binomial theorem.

Given Expression: (2x-3) 6

By using the binomial theorem, the expression (2x-3) 6 can be expanded as follows:

(2x-3) 6 = 6 C 0 (2x) 6 – 6 C 1 (2x) 5 (3) + 6 C 2 (2x) 4 (3) 2 – 6 C 3 (2x) 3 (3) 3 + 6 C 4 (2x) 2 (3) 4 – 6 C 5 (2x)(3) 5 + 6 C 6 (3) 6

(2x-3) 6 = 64x 6 – 6(32x 5 )(3) +15(16x 4 )(9) – 20(8x 3 )(27) +15(4x 2 )(81) – 6(2x)(243) + 729

(2x-3) 6 = 64x 6 -576x 5 + 2160x 4 – 4320x 3 + 4860x 2 – 2916x + 729

Thus, the binomial expansion for the given expression (2x-3) 6 is 64x 6 -576x 5 + 2160x 4 – 4320x 3 + 4860x 2 – 2916x + 729.

Question 2:

Evaluate (101) 4 using the binomial theorem

Given: (101) 4.

Here, 101 can be written as the sum or the difference of two numbers, such that the binomial theorem can be applied.

Therefore, 101 = 100+1

Hence, (101) 4 = (100+1) 4

Now, by applying the binomial theorem, we get:

(101) 4 = (100+1) 4 = 4 C 0 (100) 4 + 4 C 1 (100) 3 (1) + 4 C 2 (100) 2 (1) 2 + 4 C 3 (100)(1) 3 + 4 C 4 (1) 4

(101) 4 = (100) 4 +4(100) 3 +6(100) 2 +4(100) + (1) 4

(101) 4 = 100000000+ 4000000+ 60000+ 400+1

(101) 4 = 104060401

Hence, the value of (101) 4 is 104060401.

Question 3:

Using the binomial theorem, show that 6 n –5n always leaves remainder 1 when divided by 25

Assume that, for any two numbers, say x and y, we can find numbers q and r such that x = yq + r, then we say that b divides x with q as quotient and r as remainder. Thus, in order to show that 6 n – 5n leaves remainder 1 when divided by 25, we should prove that 6 n – 5n = 25k + 1, where k is some natural number.

We know that,

(1 + a) n = n C 0 + n C 1 a + n C 2 a 2 + … + n C n a n

Now for a=5, we get:

(1 + 5) n = n C 0 + n C 1 5 + n C 2 (5) 2 + … + n C n 5 n

Now the above form can be weitten as:

6 n = 1 + 5n + 5 2 n C 2 + 5 3 n C 3 + ….+ 5 n

Now, bring 5n to the L.H.S, we get

6 n – 5n = 1 + 5 2 n C 2 + 5 3 n C 3 + ….+ 5 n

6 n – 5n = 1 + 5 2 ( n C 2 + 5 n C 3 + ….+ 5 n-2 )

6 n – 5n = 1 + 25 ( n C 2 + 5 n C 3 + ….+ 5 n-2 )

6 n – 5n = 1 + 25 k (where k = n C 2 + 5 n C 3 + ….+ 5 n-2 )

The above form proves that, when 6 n –5n is divided by 25, it leaves the remainder 1.

Hence, the given statement is proved.

Question 4:

Find the value of r, If the coefficients of (r – 5) th and (2r – 1) th terms in the expansion of (1 + x) 34 are equal.

For the given condition, the coefficients of (r – 5) th and (2r – 1) th terms of the expansion (1 + x) 34 are 34 C r-6 and 34 C 2r-2 respectively.

Since the given terms in the expansion are equal,

34 C r-6 = 34 C 2r-2

From this, we can write it as either

So, we get either r = – 4 or r = 14.

We know that r being a natural number, the value of r = – 4 is not possible.

Hence, the value of r is14.

Important Questions for Class 11 Maths Chapter 8 Binomial Theorem for Practice

Practising the important questions for class 11 Maths Chapter 8 Binomial Theorem help you score good marks in the final examination.

• Expand (2a – 3b) 4 by binomial theorem.
• Using Binomial theorem, expand (a + 1/b) 11 .
• Write the general term in the expansion of (a 2 – b ) 6 .
• Find x, if T 11 and T 12 in the expansion of (2+ x) 50 are equal.
• The coefficients of three consecutive terms in the expansion of (1 + a) n are in the ratio 1:7:42. Find n.
• Find the coefficient of x in the expansion of (1 – 3x + 1x 2 )( 1 -x) 16 .
• 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.
• If the integers r > 1, n > 2 and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x) 2n are equal, then; (i) n=2r (ii) n=3r (iii) n=2r+1 (iv) none of these
• The ratios of the coefficient of x p and x q in the expansion of (1+x) p+q is                               .

To get all chapter-wise important questions for class 11 Maths, stay tuned with BYJU’S – The Learning App and download the app to learn all Maths-related concepts easily by exploring more videos.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.