Advertisements
Advertisements
प्रश्न
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
विकल्प
50
202
51
None of these
उत्तर
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is 51.
Explanation:
Number of terms in the expansion of (x + a)100 = 101
Number of terms in the expansion of (x – a)100 = 101
Now 50 terms of expansion will cancel out with negative 50 terms of (x – a)100
So, the remaining 51 terms of first expansion will be added to 51 terms of other
Therefore, the number of terms = 51
APPEARS IN
संबंधित प्रश्न
Using binomial theorem, evaluate the following:
(99)5
Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.
Evaluate `(sqrt3 + sqrt2)^6 - (sqrt3 - sqrt2)^6`
Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`
Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`
Find the rth term in the expansion of `(x + 1/x)^(2r)`
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`
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`
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
Find the coefficient of x50 after simplifying and collecting the like terms in the expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ... + x1000 .
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.
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
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 number of terms in the expansion of (x + y + z)n ______.
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 ______.
The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.
Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______.
