Mathematics questions
18011 published questions with worked solutions.
- In the expansion of (x+ x^2-1 )^6+ (x- x^2-1 )^6, the number of terms, is
- If C_0,C_1,C_2, ,C_n are coefficients in the binomial expansion of (1+x)^n, then C_0C_2+C_1C_3+C_2C_4+ +C_ n-2 C_n is equal to
- The positive value of a so that the coefficients of x^5 and x^ 15 are equal in the expansion of (x^2+ a x^3 )^ 10 is
- If the second, third and fourth term in the expansion of (x+a)^n are 240, 720 and 1080 respectively, then the value of n is
- The value of 2 ,C_0+ 2^2 2C_1+ 2^3 3C_2+ 2^4 4C_3+ + 2^ 11 11 C_ 10 , is
- If (1+x+x^2)^n=C_0+C_1x+C_2x^2+ , then the value of C_0C_1-C_1C_2+C_2C_3- , is
- If the sum of the coefficients in the expansion of (1-3x+10x^2 )^n is a and if the sum of the coefficients in the expansion of...
- If n N, then the sum of the coefficients in the expansion of the binomial (5x-4y)^n, is
- The interval in which x must lie so that the numerically greatest term in the expansion of (1-x)^ 21 has the numerically greatest...
- If in the expansion of (x^3- 1 x^2 )^n, n N, sum of the coefficients of x^5 and x^ 10 is zero, then n=
- If (1+x)^ 2n =a_0+a_1x+a_2x^2+ +a_ 2n x^ 2n , then (a_0-a_2+a_4-a_6+ -a_ 2n )^2+ (a_1-a_3+a_5-a_7+ +a_ 2n-1 )^2 is equal to
- The coefficient of y in the expansion of (y^2+ cy )^5, is
- The number of terms with integral coefficients in the expansion of (7^ 1/3 +5^ 1/2 x )^ 600 , is
- If the coefficients of x^7 and x^8 in (2+ x3 )^n are equal, then n is equal to
- The coefficient of x^n in the expansion of (1-2x+3x^2-4x^3+ )^ -n , is
- If the ratio of the 7^ th term from the beginning to the seventh term from the end in the expansion of ( [3]2+ 1 [3]3 )^x is 16...
- The expansion of (8-3x)^ 3/2 in terms of powers of x is valid only if
- If the binomial coefficients of 2^ nd , 3^ rd and 4^ th terms in the expansion of 2^ _ 10 (10-3^x) + [5] 2^ (x-2) _ 10 3 ^m are...
- If in the expansion of (1+x)^ 20 , the coefficients of r^ th and (r+4)^ th terms are equal, then the value of r, is
- If n is a positive integer and C_k= ^nC_k, then _ k=1 ^nk^3 ( C_k C_ k-1 )^2 equals