Advertisements
Advertisements
प्रश्न
Compute 1024
उत्तर
1024 = (100 + 2)4
= 4C0 (100)4(2)0 + 4C1 (100)4–1 (2)1 + 4C2 (100)4–2 (2)2 + 4C3 (100)4–3 (2)2 + 4C4 (100)4–4 (2)4
= `100^4 + 4 xx 100^3 xx 2 + (4 xx 3)/(1 xx 2) xx 100^2 xx 4 + 4 xx 100 xx 8 + 1 xx 1 xx 2^4`
= 100000000 + 8 × 1000000 + 24 × 10000 + 3200 + 16
= 100000000 + 8000000 + 240000 + 3216
= 108243216
APPEARS IN
संबंधित प्रश्न
Expand the following by using binomial theorem.
(2a – 3b)4
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Expand the following by using binomial theorem.
`(x + 1/x^2)^6`
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the middle terms in the expansion of
`(3x + x^2/2)^8`
The constant term in the expansion of `(x + 2/x)^6` is
The last term in the expansion of (3 + √2 )8 is:
Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:
Expand `(2x^2 - 3/x)^3`
Compute 97
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Find the last two digits of the number 3600
If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x + y)n are equal
If n is a positive integer and r is a non-negative integer, prove that the coefficients of xr and xn−r in the expansion of (1 + x)n are equal
In the binomial expansion of (a + b)n, if the coefficients of the 4th and 13th terms are equal then, find n
If the binomial coefficients of three consecutive terms in the expansion of (a + x)n are in the ratio 1 : 7 : 42, then find n
Prove that `"C"_0^2 + "C"_1^2 + "C"_2^2 + ... + "C"_"n"^2 = (2"n"!)/("n"!)^2`
Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is
