## Kerala Plus One Maths Chapter Wise Questions and Answers Chapter 8 Binomial Theorem

**Short Answer** **Type Questions **

**(Score 3)**

Question 1.

Compute (101)^{4} using binomial theorem.

Answer:

(101)^{4} = (100+1)^{4 }= (100)^{4}+4×( 100)^{3}+6×( 100)^{2}+4× 100+1

= 104060401

Question 2.

Term independent of x in the expansion of

a. ^{18}C_{6}

b. ^{18}C_{6} 3^{6} ^{ }c. ^{18}C_{12}

d. 3^{6 }Answer:

b. ^{18}C_{6} 3^{6}

Question 3.

If r^{th} term in the expansion of contains x^{20}, then r=………….

Answer:

Question 4.

a. Find the number of terms in the expansion of (a + b + c)^{10}.

b. Write the general term in the expansion of (x^{2} – yx)^{12}, x ≠0

Answer:

Question 5.

If coefficients of x^{-7} and x^{-8} in the expansion of terms are come in the 8^{th} & 9^{th} term only.

Answer:

Question 6.

Expand the expression (1 -x+x^{2})^{4 }Answer:

Question 7

a.Find the coefficient of x^{10} in the binomial expansion of

b. Prove that there is no term involving x^{6 }Answer:

b. Choose 22-3x=6

which is not possible since r is a positive integer.

∴ There is no term containing x^{6}.

Question 8.

Find the constant term in the expansion of

Answer:

**Short Answer** **Type Questions **

**(Score 4)**

Question 1.

Find the Coefficient of a^{2} b^{5} in the expansion of(a+b)^{3}(a-2b)^{4}.

Answer:

Question 2.

Find the remainder, when 5^{99} is divided by 13.

Answer:

We know that, 5^{4} = 625 = 13 × 48 + 1

5^{4} = 13 λ + 1 = where λ is a positive integer.

Question 3.

If a and b are distinct integers, prove that (a – b) is a factor of (a^{n} – b^{n}), whenever n is a positive integer.

Answer:

Question 4.

a. Find the term independent of x in the expansion of

b. If the middle term in the expansion of is independent of x, find the value of m.

Answer:

Question 5.

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

a. 2 and 9

b. 3 and 2

c. 2/3 and 9

d. 3/2 and 6

Answer:

Question 5.

a Find the coefficient of x^{6} x^{3} in the expansion of (x+2y)^{9} is

a. 670

b. 0

c. 672

d. 574

b. Find the constant term in the expansion of is …

Answer:

Question 6.

i. If p is a real number and the middle term in the expansion of

1120, then find the value of p.

ii. If the middle term of is equal to ,then find the value of x.

Answer:

**Long Answer** **Type Questions **

**(Score 6)**

Question 1.

i. Find the coefficient of x in the expansion of (1-3x + 7x^{2})(1 – x)^{16}.

ii. Find the term independent of x in the expression of

Answer:

Question 2.

a. Find the coefficient of xy^{3} in the expansion of (x+2y)^{9}.

b. In the binomial expansion of (x+y)°, the coefficients of 4th and 13th terms are equal.

Find the value of n.

Answer:

a.In the expansion of (x+2y)^{9}, the general term is

This will contain x^{6}y^{3}, if 9-r = 6 or r=3. On putting r = 3 in Eq(i), we get

Question 3.

If x^{p} occurs in the expansion of then prove that its coefficients is

Answer:

Question 4.

In a class test, Renu score (out of 50) marks, which is equal to the coefficient of x^{2} in the expansion of (1+x)^{7}. But she reported to her parents that she had scored 70% marks in the test.

i. What is the actual score of Renu in the test ?

ii. What value is shown here by Renu ?

Answer:

i. Actual score of Renu in the test

= Coefficient of x^{2} in the expansion of (1 +x)^{7 }Since, she got 21 marks out of 50. So, score in percentage

Hence, Renu score 42%. But she reported her parents that she got 70%.

ii. The value shown by Renu is dishonesty

Question 5.

Using binomial theorem, prove that 2^{3n}-7n-1 is divisible by 49 ,where n∈N.

Answer:

**NCERT Questions and Answers**

Question 1.

Which is larger (1.01)^{1040000} or 10,000?

Answer:

Question 2.

Expand

Answer:

Question 3.

Find (a + b)^{4} – (a – b)^{4}. Hence, evaluate

Answer:

Question 4.

Evaluate

Answer:

Question 5.

Expand the expression (2x – 3)^{6 }Answer:

Question 6.

Evaluate (99)^{5 }Answer:

Question 7.

Find the middle terms in the expansion of

Answer:

Question 8.

Find the 13^{th} term in the expansion of

Answer:

Question 9.

Find the value of ‘m’ for which the coefficient of x^{2} in the expansion (1 + x)^{m} is 6.

Answer:

Question 10.

Find the coefficient of a^{5}b^{7} in (a – 2b)^{12 }Answer:

Question 11.

The sum of the coefficients of the first 3 terms in the expansion of being a natural number is 559. Find the term of the expansion containing x^{3}.

Answer:

^{}

The term containing x^{3 }put 12 – 3r = 3, r = 3 Required term is ^{12}C_{r}(-3)^{3} x^{3}=-5940 x^{3}

Question 12.

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

Answer:

The coefficients of (r – 5)^{th} and (2r-1)^{th} terms of the expansion (1 + x)^{34 }