Mathematics questions
18011 published questions with worked solutions.
- If m is a root of the given equation (1-ab)x^2- (a^2+b^2 )x-(1+ab)=0 and m harmonic means are inserted between a and b, then the...
- The number which should be added to the numbers 2,14,62, so that the resulting numbers may be in GP, is
- If 9 AM's and HM's are inserted between 2 and 3 and if the harmonic mean H is corresponding to arithmetic mean A, then A+ 6H is...
- Statement 1: Let F_1(n)=1+ 12+ 13+ + 1n, then _ r=1 ^nF_1(r)=(n+1)F_1(n)-n. Statement 2: 1^ -1 +2^ -1 +3^ -1 + +n^ -1 n> ( 1+2+3+...
- Statement 1: If 3x+4y=5, then the greatest value of x^2y^3 is 3 16 . Statement 2: Greatest value occurs when 9x=8y.
- If m^ th term of HP is n and n^ th term is m, then the r^ th term will be
- If a^ n+1 +b^ n+1 a^n+b^n be the harmonic mean between a and b, then the value of n is
- If 1 b-c , 1 c-a , 1 a-b be consecutive terms of an AP, then (b-c)^2,(c-a)^2,(a-b)^2 will be in
- If a_1=a_2=2, a_n=a_ n-1 -1 (n>2), then a_5 is
- If a_1,a_2, ,a_ n+1 are in AP, then 1 a_1a_2 + 1 a_2a_3 + + 1 a_na_ n+1 is
- If A_1,A_2 are two A.M.'s between a and b and G_1,G_2 are two GM's between a and b then A_1+A_2 G_1G_2 is
- The sum to n terms of the series 2^2+4^2+6^2+ is
- Consider the following statements: 1. If a_n denotes the n^ th term of an AP, then a_n= a_ n+k +a_ n-k 2. 2. In an AP, if the sum...
- x+y+z=15, if 9,x,y,z,a are in AP, while 1x+ 1y+ 1z= 53, if 9,x,y,z,a are in HP, then value of a will be
- If a,b,c are in AP, then the straight line ax+by+c=0 will always pass through the point
- If the AM and GM of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be
- If the p^ th , q^ th and r^ th term of a GP and HP are a,b,c, then a(b-c) a+b(c-a) b+c(a-b) c is equal to
- If a,b,c,d,e,f are in AP, then the value of e-c will be
- The sum of the infinite terms of the series 5 3^2+7^2 + 9 7^2+11^2 + 13 11^2+15^2 + is
- The AM, HM and GM between two numbers are 144 15 , 15 and 12, but not necessarily in this order. Then, HM, GM and AM respectively...