Mathematics questions
18011 published questions with worked solutions.
- The sum of the series 1^2+1+2^2+2+3^2+3+ +n^2+n is
- The set of all possible values of x for which 13 is the A.M. of 5^ 1+x and 5^ 1-x , is
- x^ 1/2 x^ 1/4 x^ 1/8 x^ 1/16 to is equal to
- If a,b,c,d are in HP, then ab+bc+cd is equal to
- If the sum of first p terms, first q terms and first r terms of an A.P. be x,y and z respectively. Then, xp(q-r)+ yq(r-p)+...
- If a,b,c are in A.P.; a,x,b are in G.P. and b,y,c are in G.P., then x^2,b^2,y^2 are in
- In a G.P. if the (m+n)^ th term is p and (m-n)^ th term is q, then its m^ th term is
- The sum of the series 1+2.2+3.2^2+4.2^3+5.2^4+ +100.2^ 99 , is
- If a,b,c,d,e,f are A.M.'s between 2 and 12, then a+b+c+d+e+f is equal to
- If a,b,c are in G.P., then _a , _b , _c are in
- Let a and b be roots of x^2-3x+p=0 and let c and d be the roots of x^2-12x+q=0, where a,b,c,d form an increasing GP. Then the...
- If 1+ 1+2 2+ 1+2+3 3+ to n terms is S, then S is equal to
- The following consecutive terms 1 1+ x , 1 1-x , 1 1- x of a series are in
- The sum to n terms of the series (n^2-1^2 )+2 (n^2-2^2 )+3 (n^2-3^2 )+ , is
- If x,|x+1|,|x-1| are first three terms of an A.P., then the sum of its first 20 terms is
- Two sequences a_n and b_n are defined by a_n= ( 5^ n+1 3^ n-1 ), b_n= ( 53 ) ^n, then
- Let H_n=1+ 12+ 13+ + 1n, then the sum to n terms of the series 1^2 1^3 + 1^2+2^2 1^3+2^3 + 1^2+2^2+3^2 1^3+2^3+3^3 + , is
- If _xa, a^ x/2 and _bx are in G.P., then x is equal to
- If the sum of n terms of the series 704+ 12(704)+ 14(704)+ and 1984- 12(1984)+ 14(1984)- are equal, then n=
- If a,b,c are in A.P. and a^2,b^2,c^2 are in H.P., then