Binomial Theorem And Its Simple Applications — practice questions
45 curated practice questions from Binomial Theorem And Its Simple Applications (Mathematics JEE Advanced, NTA Exams) — 32 hard, 13 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.
- If 1 1-2 x+x^ 2 =1 + a 1 x + a 2 x 2 + ..., then the value of a r is
- If 0 ≤ r ≤ n, then the coefficient of x r in the expansion of P = 1 + (1 + x) + (1 + x) 2 + ..... + (1 + x) n is
- For r = 0, 1, ..., 10, let A r , B r and C r denote respectively, the coefficient of x r in the expansions of (1 + x )…
- For non-negative integers s and r , let s r = array ll s! r!(s-r)! & if r s, 0 & if r>s . array . For positive integers…
- If the fourth term in the expansion of ( px + 1 x )^ n is independent of x, then the value of term is
- The number 5 25 – 3 25 is divisible by :
- The sum 1 . 20 C 1 –2 . 20 C 2 + 3 . 20 C 3 – .....– 20 C 20 is equal to
- The coefficient of x 20 in the expansion of (1+x^ 2 )^ 40 (x^ 2 +2+ 1 x^ 2 )^ -5 is
- The greatest term (numerically) in the expansion of (3 – 5x) 11 , when x= 1 5 is
- The number of terms in the expansion of (x^ 2 +1+ 1 x^ 2 )^ n , n ∈ N is.
- If the ratio of 7th term from the beginning to the seventh term from the end in the expansion of ( [3] 2 + 1 [3] 3 )^ x…
- If x 1 , x 2 , ..... x n are any real numbers and n is any positive integer, then
- If rth and (r + 1)th term in the expansion of (1 + x) n are equal, then n =
- The greatest value of the term independent of x in the expansion of (x sin α + x –1 cos α) 10 , α ∈ R, is
- The number of distinct terms in the expansion of (x + y – z) 16 is
- The sum , is maximum when m is
- The greatest term (numerically) in the expansion of (2 + 3x) 9 , when x= 3 2 , is
- If s_ n = _ r=0 ^ n 1 ^ n C_ r and t_ n = _ r=0 ^ n r ^ n C_ r then t_ n s_ n is equal to
- Let for n = 1, 2, 3, ... . Then,
- If in the expression of (1 + x ) m (1 – x ) n , the coefficient of x and x 2 are 3 and –6 respectively then m is
- The sum of coefficients of the two middle terms in the expansions of (1 + x) 2n – 1 is equal to :
- Match the entries in Column-I representing in n with their values given in Column-II.
- Element in set of values of r for which, ^ 18 C _ r -2 +2 . ^ 18 C _ r -1 + ^ 18 C _ r ^ 20 C _ 13 is :
- If A = 2n C 0 . 2n C 1 + 2n C 1 2n–1 C 1 + 2n C 2 2n–2 C 1 + .....then A is
- The expression (x+ (x^ 3 -1 )^ 1 2 )^ 5 + (x- (x^ 3 -1 )^ 1 2 )^ 5 is a polynomial of degree
- If C r stands for n C r , then the sum of the series 2 ( n 2 )! ( n 2 )! n! [C_ 0 ^ 2 -2 C_ 1 ^ 2 + +(-1)^ n (n+1) C_ n…
- The coefficient of x 7 in the expansion of (1 – x – x 2 + x 3 ) 6 is
- Coefficient of t 24 in (1 + t 2 ) 12 (1 + t 12 ) (1 + t 24 ) is
- The total number of terms in the expansion of (a + b + c + d) n , n N is
- 1 . n C 1 + 2, n C 2 + 3 . n C 3 + ....+ n. n C n is equal to
- The value of ^ 50 C _ 4 + _ r =1 ^ 6 ^ 56- r C _ 3 is
- 30 0 30 10 - 30 1 30 11 + .+ 30 20 30 30 =
- The coefficient of x 50 in the expansion : (1 + x) 1000 + 2x (1 + x) 999 + 3x 2 (1 + x) 998 +...+1001 terms
- The greatest coefficent in the expansion of (1 + x) 2n is
- Integral part of (7+4 3 )^ n is ( n ~N )
- In the binomial expansion of (a – b) n , n ≥ 5, the sum of the 5 th and 6 th terms is zero. Then, a/b equals
- The expansion of (3x + 2) -1/2 is valid in ascending powers of x, if x lies in the interval
- If (1 +x) 15 = C 0 + C 1 x+C 2 x 2 +....+ C 15 x 15 , then ^ 15 C _ 0 ^ 2 - ^ 15 C _ 1 ^ 2 + ^ 15 C _ 2 ^ 2 - ^ 15 C _…
- If a_ n = _ r=0 ^ n 1 ^ n C_ r , then equals
- Match the following with their no. of terms. The correct matching is
- The ratio of the coefficient of x 10 in (1-x 2 ) 10 and the term independent of x in (x- 2 x )^ 10 , is
- The coefficient of x 4 in ( x 2 - 3 x^ 2 )^ 10 is
- The term independent of x in the expansion of (1 + x) n (1+ 1 x )^ n is :
- If n is a positive integer greater than 1, then a – n C 1 (a – 1) + n C 2 (a – 2) – ....+ (–1) n (a – n) is equal to
- If C r stands for n C r , then the sum of the series 2 ( n 2 )! ( n 2 )! n ! [ C _ 0 ^ 2 -2 C _ 1 ^ 2 +3 C _ 2 ^ 2 …