Mathematics questions
18011 published questions with worked solutions.
- If (1+x)^ 15 =a_0+a_1x+ +a_ 15 x^ 15 , then _ r=1 ^ 15 r a_r a_ r-1 is equal to
- 7^9+9^7 is divisible by
- If the second term in the expansion [ [13]a + a a^ -1 ]^n is 14a^ 5/2 , then the value of ^nC_3 ^nC_2 is
- 1+ 24+ 2 5 4 8 + 2 5 8 4 8 12 + 2 5 8 11 4 8 12 16 + is
- If x^ 2r occurs in (x+ 2 x^2 )^n, then n-2r must be of the form
- If the coefficient of x^7 in (ax^2+ 1 bx )^ 11 equal the coefficient of x^ -7 in (ax- 1 bx^2 )^ 11 , then a and b satisfy the...
- If the coefficient of r^ th and (r+1)^ th terms in the expansion of (3+7x)^ 29 are equal, then r equals
- If in the expansion of (a-2b)^n, the sum of the 5^ th and 6^ th term is zero, then the value of ab is
- If |x|< 12, then the coefficient of x^r in the expansion of 1+2x (1-2x)^2 is
- The coefficient of x^5 in the expansion of (1+x^2 )^5(1+x)^4 is
- If the fourth term in the expansion of (ax+ 1x )^n is 52, then
- The two consecutive terms in the expansion of (3+2x)^ 74 whose coefficient are equal, are
- If the coefficient of x^2 and x^3 in the expansion of (3+ax)^9 be same, then the value of a is
- The coefficient of x^ 100 in the expansion of _ j=0 ^ 200 (1+x)^j is
- In the expansion of (2-3x^3 )^ 20 , if the ratio of 10^ th term to 11^ th term is 45 22 , then x is equal to
- The total number of terms in the expansion of (x+y)^ 100 +(x-y)^ 100 after simplification is
- If the expansion of ( 3 x 7- 5 2x x )^ 13n contains a term independent of x in 14^ th term, then n should be
- The coefficient of x^4 in the expansion of ( x2- 3 x^2 )^ 10 is
- The coefficient of x in the expansion of (1+x)(1+2x)(1+3x) (1+100x) is
- The coefficient of x^n in the expansion of (1+2x+3x^2+ )^ 1/2 is