Advertisements
Advertisements
Question
The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.
Options
102
25
26
None of these
Solution
The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is 26.
Explanation:
Since the total number of terms are 52 of which 26 terms get cancelled.
APPEARS IN
RELATED QUESTIONS
Expand the expression: (1– 2x)5
Expand the expression: `(2/x - x/2)^5`
Expand the expression: `(x/3 + 1/x)^5`
Expand the expression: `(x + 1/x)^6`
Using binomial theorem, evaluate f the following:
(101)4
Using binomial theorem, evaluate the following:
(99)5
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`
Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.
Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.
Find an approximation of (0.99)5 using the first three terms of its expansion.
Show that \[2^{4n + 4} - 15n - 16\] , where n ∈ \[\mathbb{N}\] is divisible by 225.
Expand the following (1 – x + x2)4
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that 4OE = (x + a)2n – (x – a)2n
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.
Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.