Mathematics questions
18011 published questions with worked solutions.
- The value of 2+2 ( 15+ 13 1 5^3 + 15 1 5^5 + ) is
- If e^x 1-x =B_0+B_1x+B_2x^2+ +B_nx^n+ , then B_n-B_ n-1 equals
- If |x|<1, then the coefficient of x^3 in the expansion of (1+x+x^2 ) in ascending powers of x, is
- The coefficient of n^ -r in the expansion of _ 10 ( n n-1 ), is
- If (1-x+x^2 )=a_1x+a_2x^2+a_3x^3+ , and n is not a multiple of 3 then a_n is equal to
- The sum of the series 1^2 2 1! + 2^2 3 2! + 3^2 4 3! + 4^2 5 4! + , is
- If S= _ n=1 ^ ( ^nC_0+ ^nC_1+ ^nC_2+ + ^nC_n ^nP_n ), then S equals
- The sum of the series x-1 x+1 + 12 x^2-1 (x+1)^2 + 13 x^3-1 (x+1)^3 + , is equal to
- If S_n denotes the sum of the products of the first n numbers taken two at a time, then _ n=0 ^ S_n (n+1)! equals
- The value of (x+y)(x-y)+ 1 2! (x+y)(x-y) (x^2+y^2 )+ 1 3! (x+y)(x-y) (x^4+y^4+x^2y^2 )+ , is
- The sum of the series 12 2! + 28 3! + 50 4! + 78 5! + , is
- If a= _ n=0 ^ x^ 3n (3n)! , b= _ n=1 ^ x^ 3n-2 (3n-2)! and c= _ n=1 ^ x^ 3n-1 (3n-1)! , then the value of a^3+b^3+c^3-3abc is
- If S= _ n=2 ^ ^nC_2 (n+1)! , then S equals
- The sum of the series 1+ 1^2+2^2 2! + 1^2+2^2+3^2 3! + 1^2+2^2+3^2+4^2 4! + , is
- 2 x- (x+1)- (x-1) is equal to
- If S= _ n=0 ^ ( x)^ 2n (2n)! , then S equals
- If S= _ n=2 ^ ^nC_2 3^ n-2 n! , then S equals
- The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its...
- Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of the sum of the first seven terms to...
- The minimum value of the sum of real numbers a^ -5 ,a^ -4 ,3a^ -3 ,1,a^8 and a^ 10 with a>0 is