JEE Main 2024 — Binomial Theorem Questions with Solutions

Let a=1+ ² C₂3 !+ ³ C₂4 !+ ⁴ C₂5 !+…, b=1+ ¹ C₀+ ¹ C₁1 !+ ² C₀+ ² C₁+ ² C₂2 !+ ³ C₀+ ³ C₁+ ³ C₂+ ³ C₃3 !+… Then (2 b)/(…

Let the coefficient of x r in the expansion of x + 3 n − 1 + x + 3 n − 2 x + 2 + x + 3 n − 3 x + 2 2 + . ... + x + 2 n…

C r n - 1 = k 2 - 8 C r + 1 n if and only if :

If C 1 11 2 + C 2 11 3 + … . . + C 9 11 10 = n m with gcd ( n , m ) = 1 , then n + m is equal to

The coefficient of x⁷⁰ in x²(1+x)⁹⁸+x³(1+x)⁹⁷+x⁴(1+x)⁹⁶+…+x⁵⁴(1+x)⁴⁶ is ⁹⁹ Cp- ⁴⁶ Cq. Then a possible value of p+q is :

Let α=₌₀ⁿ (4 r²+2 r+1 ) ⁿ Cr and β= (₌₀ⁿ ⁿ Crr+1 )+(1)/(n+1). If 140 < (2 α)/(β) < 281, then the value of n is _______

If the coefficient of x 30 in the expansion of 1 + 1 x 6 1 + x 2 7 1 − x 3 8 ; x ≠ 0 is α , then α equals _________.

Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of 1 3 x 1 3 + 1 2 x 2 3…

If for some m , n ; 6 C m + 2 6 C m + 1 + 6 C m + 2 > 8 C 3 and n − 1 P 3 : n P 4 = 1 : 8 , then n P m + 1 + n + 1 C m…

In the expansion of 1 + x 1 − x 2 1 + 3 x + 3 x 2 + 1 x 3 5 , x ≠ 0 , the sum of the coefficient of x 3 and x - 13 is e…