Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 8 Binomial Theorem.

## Kerala Plus One Maths Chapter Wise Previous Questions Chapter 8 Binomial Theorem

### Plus One Maths Binomial Theorem 3 Marks Important Questions

Question 1.

i) The number of terms in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\) is _____.(IMP-2013)

ii) Find the middle term in the above expansion.

Answer:

i) 11

Question 2.

i) Find the general term in the expansion of (x + y)^{n}

ii) Find the middle term in the expansion of \(\left(2 x+\frac{1}{3 y}\right)^{18}\) (MARCH-2014)

Answer:

Question 3.

i) Write the general term in the expansion of (a + b)^{n }

ii) Find the 9th term in the expansion of \(\left(\frac{x}{2}+\frac{6}{x^{2}}\right)^{12}\) (IMP-2014)

Answer:

### Plus One Maths Binomial Theorem 4 Marks Important Questions

Question 1.

i) Find the general term in the expansion of \(\left(3 x^{2}-\frac{1}{3 x}\right)^{9}\) (MARCH-2010)

ii) Find the term independent of x in the above expansion.

Answer:

Question 2.

Consider the expansion of \(\left(x^{2}-\frac{1}{3 x}\right)^{9}\) (IMP-2010)

i) Find the coefficient of x^{9}

ii) Find the term which is independent of x.

Answer:

Question 3.

Consider the expansion of \(\left(\frac{x}{9}+9 y\right)^{2 n}\) (MARCH-2011)

i) The number of terms in the expansion is _____

(a) 2n

(b) n+1

(c) 2n+1

(d) 2/7-1

ii) What is its (n+1)^{th} term?

iii) If n = 5, find its middle term.

Answer:

Question 4.

i) Write the general term in the expansion (1 + x)^{44 }

Write 21st and ,22nd terms in the expansion of (1 + x)^{44}

iii) If 21^{st} and 22^{nd} terms in the expansion of (1 + x)^{44} are equal then find the value of x. (IMP-2011)

Answer:

Question 5.

8. Find(x + y)^{4} – (x – y)^{4}. (IMP-2012)

Hence evaluate: (√5 + √6)^{4} – (√5 – √6)^{4
}Answer:

Question 6.

i) How many terms are there in the expansion of (1 + x)^{2n} (n is a positive integer)? (IMP-2012)

ii) Show that the middle term in the (1 + x)^{2n}

expansion of is \(\frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n} x^{n}\)

Answer:

Question 7.

i) Find the general term in the expansion of \(\left(\frac{x}{2}-\frac{2}{x}\right)^{10}\) (MARCH-2012)

ii) Find the terms independent of x in the above expansion.

Answer:

Question 8.

i) Find the number of terms in the expansion of \(\left(x-\frac{1}{x}\right)^{14}\) (MARCH-2013)

ii) Find the general term in the expansion of \(\left(x-\frac{1}{x}\right)^{14}\)

iii) Find the term independent of x in the above expansion.

Answer:

i) 15

Question 9.

i)Write the number of terms in the expansion of (a -b)^{2n}

ii) Find the general term in the expansion of \(\left(x^{2}-y x\right)^{12}, x \neq 0\) (MARCH-2014)

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

Answer:

Question 10.

i) Write the expansion of (a + n)^{n}, where n is any positive integer. (IMP-2014)

ii) Find the value of ‘a’ if the 17^{th} term and 18^{th} term in the expansion of (2 +a)^{50} are equal.

Answer:

Question 11.

i) The number of term in the expansion of \(\left(x-\frac{1}{x}\right)^{2 n}\) is ______. (MARCH-2015)

(a) n+1

(b) n

(c) 2n+1

(d) 2n+2

ii) Find a, if the 17^{th} term and 18^{th} term of the expansion of (2 +a)^{50} are equal.

Answer:

Question 12.

i) Number of terms in the expansion of \(\left(x+\frac{1}{x}\right)^{20}\) (IMP-2016)

(a) 19

(b) 20

(c) 21

(d) 22

Consider the expansion of \(\left(3 x^{2}-\frac{1}{3 x}\right)^{9}\)

find the coefficient of x^{6} and the term independent of x.

Answer:

Question 13.

The 8th term in the expression (MARCH-2016)

of(√2 + √3)^{7} is

a) 27√2

b) 27√3

c) 72√2

d) 72√3

ii) Find the term independent of x in the expansion of \(\left(x+\frac{1}{2 x}\right)^{18} ; x>0\)

Answer:

Question 14.

Write the expansion of (a + b)^{4 (MAY-2017)}

Evaluate: (√5 + √6)4+ (√5 – √6)^{4}

Answer:

Question 15.

Consider the expansion of \(\left(x+\frac{1}{x}\right)^{10}\) (MARCH-2017)

i) The number of terms in the expansion is _____.

(a) 10

(b) 9

(c)11

(d) 12

ii) Find the term which is independent of x in the above expansion.

Answer:

### Plus One Maths Binomial Theorem 6 Marks Important Questions

Question 1.

i) Write the number of terms in the expansion of (a + b)^{n}

ii) Expand \(\left(\frac{x}{3}+\frac{1}{x}\right)^{5}\) (MARCH-2013)

iii) Find the general term in the expansion of \(\left(x^{2}-y\right)^{6}\)

Answer: