1. In the binomial expansion of (7^1/2 + 5^1/3)³⁷, the number of integers are

2. In the binomial expansion of (a + b)ⁿ, the coefficient of fourth and thirteenth terms are equal to each other, then the value of n is

3. The coefficient of xⁿ in the expansion (1 + x + x² + …..)^-n is

4. The number of ordered triplets of positive integers which are solution of the equation x + y + z = 100 is

5. 5 [( √5 +1)⁵⁰ – (√5 –1)⁵⁰ ] is

6. The coefficient of xk in the expansion of A = 1 + (1 + x) + (1 + x)² + …. + (1 + x)n is :

7. The number of dissimilar terms in the expansion of  (a + b – c)^2n-1 – (a + b + c)²ⁿ⁺¹is

8. The total number of terms in the expansion of (x + a)¹⁰⁰ + (x – a) ¹⁰⁰ after simplification will be

9. The greatest coefficient in the expansion of (1 + x)¹⁰ is

10. If n is a positive integer, then (√5+1)²ⁿ + 1 − (√5−1)²ⁿ + 1 is

11. if n is a positive ineger then 2³ⁿn – 7n – 1 is divisible by

12. In the expansion of (a + b)ⁿ, if n is even then the middle term is

13. If the third term in the binomial expansion of (1 + x)^m is (-1/8)x² then the rational value of m is

14. In the expansion of (a + b)ⁿ, if n is odd then the number of middle term is/are

15. If A and B are coefficients of xⁿ in the expansion of (1+ x)²ⁿ and (1+ x)^{2n –1} then :