Simple Applications: JEE Questions & Solutions

The coefficient of x^48 in (1+x) + 2(1+x)^2 + 3(1+x)^3 + + 100(1+x)^100 is equal to

Let Cr denote the coefficient of x^r in the binomial expansion of (1+x)^n, n N, 0 r n. If Pn = C0 - C1 + 2^23C2 - 2^34C3 + + (-2)^nn+1Cn,…

The value of 100 C5051 + 100 C5152 + + 100 C100101 is:

The sum of the coefficients of x^499 and x^500 in (1+x)^1000+x(1+x)^999+x^2(1+x)^998+ +x^1000 is:

If r=0^5 ^11C2r+12r+2 = mn, gcd(m, n) = 1, then m - n is equal to:

The sum of all rational terms in the expansion of ( 1 + 2^1/3 + 3^1/2)^6 is equal to

The least value of n for which the number of integral terms in the Binomial expansion of ( 7 + 11)^n is 183, is:

The sum of all rational terms in the expansion of ( 2 + 3)^8 is

If r=1^9 ( r+32^r) ^9Cr = ( 32)^9 -,, N, then ( +)^2 is equal to

Let (1 + x + x^2)^10 = a0 + a1 x + a2 x^2 + + a20 x^20. If (a1 + a3 + a5 + + a19) - 11a2 = 121k, then k is equal to

For an integer n 2, if the arithmetic mean of all coefficients in the binomial expansion of (x + y)^2n-3 is 16, then the distance of the…

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The sum of the series 2 1 ^20C4 - 3 2 ^20C5 + 4 3 ^20C6 - 5 4 ^20C7 + + 18 17 ^20C20, is equal to

If A denotes the sum of all the coefficients in the expansion of (1 - 3x + 10x^2)^n and B denotes the sum of all the coefficients in the…

Remainder when 64^32^32 is divided by 9 is equal to:

Suppose 2^-p, p, 2^-, are the coefficients of four consecutive terms in the expansion of (1 + x)^n. Then the value of p^2 - ^2 + 6 + 2p…

Let = ^nCkk + 1 and = (^nCk ^nCk+1)k + 2. If 5 = 6, then n equals:

Let a be the sum of all coefficients in the expansion of (1-2x+2x^2)^2023 (3-4x^2+2x^3)^2024. If the equations cx^2+dx+e=0 and 2bx^2+ax+4=0…

The sum of all rational terms in the expansion of ( 12^5 + 15^3)^15 is equal to:

The coefficient of x^70 in: x^2(1 + x)^98 + x^3(1 + x)^97 +... + x^54(1 + x)^46 is (99Cp) - (46Cq). A possible value of p + q is:

If (^30C1)^2+ 2(^30C2)^2 + 3(^30C2)^2 + + 30(^30C30)^2 = 60!(30!)^2, then is equal to:

The constant term in the expansion of (2x + 1x^7 + 3x^2)^5 is.

The remainder when (2023)^2023 is divided by 35 is:

The coefficient of x^301 in (1 + x)^500 + x(1 + x)^499 + x^2(1 + x)^498 + + x^500 is:

If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ( 2+ 1 3)^n is 6:1, then the third…

Among the statements: (S1): 2023^2022 - 1999^2022 is divisible by 8 (S2): 13(13^n - 1) - 13 is divisible by 144 for infinitely many n N…

If the coefficients of three consecutive terms in the expansion of (1 + x)^n are in the ratio 1: 5: 20, then the coefficient of the fourth…

The coefficient of x^7 in (1 - x + 2x^3)^10 is:

The number of integral terms in the expansion of ( 3^ 12 + 5^ 14)^680 is equal to:

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)^n+2, which are in the ratio 1: 3: 5, is equal…

The sum of the coefficients of the first 50 terms in the binomial expansion of (1-x)^100, is equal to

If 1n+1 ^nCn+ 1n ^nCn-1 + + 12 ^nC1 + ^nC0 = 102310 then n is equal to:

The remainder, when 7^110 is divided by 17, is

Let (a+bx+cx^2)^10= i=0^20 pi x^i, a,b,c N. If p1=20 and p2=210, then 2(a+b+c) is equal to