Q.1 If three successive coeff. In the expansion of ( 1+ x )ⁿ are 220,495 and 792 then find N.
Q.2 If P be the sum of odd terms and Q that of even terms in the expansion of ( x+a )ⁿ prove that
(i) P² - Q² = ( X² - A² )²ⁿ
(ii) 4PQ = ( X+A)²ⁿ -( X-A )²ⁿ
(iii) 2(P² + Q²) = [Xx+A)²ⁿ + ( X-A )²ⁿ ]
Q.3 If the coeff. Of 5th 6th and 7th terms in the expansion of ( 1+ x )ⁿ are in A.P, then find the value of N.
Q.4 In the expansion of 
the ratio of 7th term from the beginning to the 7th term the end is 1:6 find N.
Q.5 Show that the middle term in the expansion of ( 1+ x )²ⁿ is 
Q.6 If a and b are distinct integers, prove that a-b is a factor of 
whenever N is positive.
Q.7 The second, third and fourth terms in the binomial expansion ( x+ a )ⁿ are 240, 720 and 1080 respectively. Find x, a and n.
Q.8 The coefficients of three consecutive terms in the expansion of ( 1+ a )ⁿ are in the ratio 1:7:42. Find n.
Q.9 Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of 
is 
Q.10 Find the sixth term of the expansion (y1/2 + x1/3)n, if the binomial coefficient of the third term from the end is 45.
Q.11 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.
Q.12 If the coefficient of second, third and fourth terms in the expansion of (1 + x)2” are in A.P., then show that 2n2 – 9n + 7 = 0.
Q.13 If the coeff of 
and 
terms in the expansion of 
are equal find 
.
Q.14 Find the term independent of 
in the expansion of 
Q.15 Expand 
.
Q.16 In the expansion of 
prove that coefficients of 
and 
are equal.
Q.17 Find 
Hence evaluate 
Q.18 Show that the coefficient of the middle term in the expansion of
is equal to the sum of the coefficients of two middle terms in the expansion of 
Q.19 In the expansion of (1 + x2 )⁸⁴ , find the difference between the coefficients of x⁶ and x⁴ .
Q.20 Find a positive value of m for which the coefficient of 
in the expansion 
is 6.
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