Mathematics questions
18011 published questions with worked solutions.
- If a and d are two complex numbers, then the sum to (n+1) terms of the following series aC_0-(a+d)C_1+(a+2d)C_2- is
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n, then _ 0 r<s n (r+s)C_rC_s is equal to
- In the expansion of the following expression 1+(1+x)+(1+x)^2+ +(1+x)^n, the coefficient of x^k (0 k n) is
- Statement 1: If _ r=1 ^nr^3 ( ^nC_r ^nC_ r-1 )=196, then the sum of the coefficients of powers of x in the expansion of the...
- ^nC_0- 12 , ^nC_1+ 13 , ^nC_2- +(-1)^n ^nC_n n+1 is equal to
- If the coefficients of the (2r+4)^ th , (r-2)^ th terms in the expansion of (1+x)^ 18 are equal, then the value of r is
- The value of _ n _ r=1 ^n ( _ t=0 ^ r-1 1 5^n ^nC_r ^rC_t 3^t ) is equal to
- The largest value of x for which the fourth term in the expansion (5^ 25 _5 4^x+44 + 1 5^ _5 [3] 2^ x-1 +7 )^8 is 336 is
- If R is remainder when 6^ 83 +8^ 83 is divided by 49, then the value of R/5 is
- If the three consecutive coefficient in the expansion of (1+x)^n are 28, 56 and 70, then the value of n is
- Least positive integer just greater than (1+0.00002)^ 50000 is
- Let a=3^ 1 223 +1 and for all n 3, let f(n)= ^nC_0 a^ n-1 - ^nC_1 a^ n-2 + ^nC_2 a^ n-3 - +(-1)^ n-1 ^nC_ n-1 a^0. If the value...
- The largest real value of x such that _ k=0 ^4 ( 3^ 4-k (4-k)! ) ( x^k k! )= 32 3 is
- Let 1+ _ r=1 ^ 10 (3^r ^ 10 C_r+r ^ 10 C_r )=2^ 10 ( 4^5+ ) where , N and f(x)=x^2-2x-k^2+1. If , lies between the roots of...
- If the middle term in the expansion of ( x2+2 )^8 is 1120; then the sum of possible real values of x is
- If the constant term in the binomial expansion of (x^2- 1x )^n, n N is 15, then the value of n is equal to
- Degree of the polynomial [ x^2+1 + x^2-1 ]^8+ [ 1 x^2+1 + x^2-1 ]^8 is
- Let a and b be the coefficient of x^3 in (1+x+2x^2+3x^3 )^4 and (1+x+2x^2+3x^3+4x^4 )^4 respectively. Then the value of 4a/b is
- Given (1-2x+5x^2-10x^3 )(1+x)^n=1+a_1x+a_2x^2+ and that a_1^2=2a_2 then the value of n is
- The remainder, if 1+2+2^2+2^3+ +2^ 1999 is divided by 5 is