Mathematics questions
18011 published questions with worked solutions.
- The sum of n terms of three AP's whose first term is 1 and common differences are 1,2,3 respectively are S_1,S_2,S_3...
- Let a,p,q,r,s R 0 . If 3a^2+2 ( 1p- 1s )a+ 1 p^2 + 1 q^2 + 1 r^2 -2 ( 1 pq + 1 qr + 1 rs ) 0 for some real a, then p,q,r,s are in
- If the angles of a quadrilateral are in AP, whose common difference is 10^ , then the angles of the quadrilateral are
- For any odd integer n 1, n^3-(n-1)^3+ +(-1)^ n-1 1^3 is equal to
- Let S= 85+ 16 15 + + 128 2^ 18 +1 , then
- If n geometric means be inserted between a and b, then the n^ th geometric mean will be
- If the p^ th term of an AP be q and q^ th term be p, then its r^ th term will be
- Let the positive numbers a,b,c,d be in AP, then abc,abd,acd,bcd are
- _ n=1 ^ 10 _ i=1 ^ n-1 1 is equal to
- Statement 1: 3,6,12 are in GP, then 9,12,18 are in HP. Statement 2: If middle term is added in three consecutive terms of a GP,...
- If three unequal numbers p,q,r are in HP and their squares are in AP, then the ratio p:q:r is
- If 2p+3q+4r=15, then the maximum value of p^3q^5r^7 is
- The sum of the series 1 1+1^2+1^4 + 2 1+2^2+2^4 + 3 1+3^2+3^4 + to n terms is
- Statement 1: If |x-1|,|x-3| are first three terms of an AP, then its sixth term is 7< third terms. Statement 2: a,a+d,a+2d, are...
- If the number of terms in an AP is 2n+1, then the ratio of the sum of the odd terms to the sum of even terms is
- a_n and b_n be two sequences given by a_n=(x)^ 1 2^n +(y)^ 1 2^n and b_n=(x)^ 1 2^n -(y)^ 1 2^n for all n N, then a_1a_2a_3 a_n...
- The interior angles of a polygon are in AP. If the smallest angle be 120^ and the common difference be 5, then the number of side...
- Let a,b,c be three positive real numbers which are in HP. Statement 1: a+b 2a-b + c+b 2c-b 4. Statement 2: If x>0, then x+ 1x 4.
- Given that n AM's are inserted between two sets of numbers a,2b and 2a,b where a,b R. Suppose further that m^ th mean between...
- If x_1,x_2,x_3 as well as y_1,y_2,y_3 are in GP with the same common ratio, then the points (x_1,y_1),(x_2,y_2) and (x_3,y_3)