Advertisements
Advertisements
प्रश्न
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
विकल्प
Equal
Equal with opposite signs
Reciprocal of each other
None of these
उत्तर
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are equal.
Explanation:
Coefficient of x p and x q in the expansion of (1 + x)p + q are p + qCp and p + qCq
And p + qCp and p + qCq = `("p" + "q")/(("p")("q"))`
APPEARS IN
संबंधित प्रश्न
Expand the expression: (2x – 3)6
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 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.
If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.
[Hint: write an = (a – b + b)n and expand]
Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`
Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Expand the following (1 – x + x2)4
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
If n is a positive integer, find the coefficient of x–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`
Which of the following is larger? 9950 + 10050 or 10150
The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.
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 ______.
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.
If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.
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 O2 – E2 = (x2 – a2)n
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
The number of terms in the expansion of (x + y + z)n ______.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.
The positive integer just greater than (1 + 0.0001)10000 is ______.
