Mathematics questions
18011 published questions with worked solutions.
- If 1 1^2 + 1 2^2 + 1 3^2 + to = ^2 6, then 1 1^2 + 1 3^2 + 1 5^2 + equals
- Sum to n terms of the series 1 1.2.3.4 + 1 2.3.4.5 + 1 3.4.5.6 + , is
- If _ r=1 ^ 1 (2r-1)^2 = ^2 8, then _ r=1 ^ 1 r^2 is equal to
- If S_n denotes the sum of n terms of an AP with common difference d, then
- If a,b,c,d are in GP, then (a^3+b^3 )^ -1 , (b^3+c^3 )^ -1 , (c^3+d^3 )^ -1 are in
- The determinant = vmatrix a&b&a +b &c&b +c +b&b +c&0 vmatrix is equal to zero, if
- The sum of the series 1^2-2^2+3^2-4^2+5^2-6^2+ -2008^2+2009^2 is
- The sum of first two terms of an infinite G.P. is 1 and every term is twice the sum of the successive terms. Its first term is
- Let _ r=1 ^nr^4=f(n), then _ r=1 ^n(2r-1)^4 is equal to
- If x,y,z be three positive prime numbers. The progression in which x, y, z can be three terms (not necessarily consecutive) is
- If |x|<1 and |y|<1, the sum to infinity of the sequence x+y, (x^2+xy+y^2 ), (x^3+x^2y+xy^2+y^3 ), is
- If x^a=x^ b/2 z^ b/2 =z^c, then a,b,c are in
- If 2(y-a) is the H.M. between y-x and y-z, then x-a,y-a,z-a are in
- If the sum of the first n terms of a series be 5n^2+2n, then its second term is
- The sum upto (2n+1) terms of the series a^2-(a+d)^2+(a+2d)^2-(a+3d)^2+ , is
- If x^ 18 =y^ 21 =z^ 28 , then 3,3 _yx,3 _zy,7 _xz are in
- If three numbers are in H.P., then the numbers obtained by subtracting half of the middle number from each of them are in
- The sum of first 10 terms of the series (x+ 1x )^2+ (x^2+ 1 x^2 )^2+ (x^3+ 1 x^3 )^2+ is
- 1^3-2^3+3^3-4^3+ +9^3=
- If _ r=1 ^na_r= 16n(n+1)(n+2) for all n 1, then _ n _ r=1 ^n 1 a_r is