Related InterviewSolutions

• In an H.P., pth term is qr and qth term is pr, show that rth term is pq.
• If H be the harmonic mean between x and y, then prove that \(\frac{H+x}{H-x}\) + \(\frac{H+y}{H-y}\) = 2.
• Insert three harmonic means between 5 and 6.
• Find the harmonic mean of the roots of the equation (5+√2)\(x\)2 - (4 + √5)\(x\) + (8+2√5) = 0.
• If A.M. between two numbers is to their G.M. as 5 : 4 and the difference of their G.M. and H.M. is \(\frac{16}{5}\), find the numbers.
• Let the positive numbers a, b, c, d be in A.P. Then, abc, abd, acd, bcd are(a) NOT in A.P./G.P./H.P (b) In A.P. (c) In G.P. (d) In H.P
• If a1, a2, a3, ....., an are in H.P. then what will (a1a2 + a2a3 + ..... + an – 1 an) equal to?
• If a and b are two real numbers such that 0 < a < b and the arithmetic mean between a and b is \(\frac{4}{3}\) times the harmonic mean between them, then \(\frac{b}{a}\) is equal to(a) \(\frac{2}{\sqrt3}\)(b) \(\frac{3}{2}\)(c) 3 (d) \(\frac{8}{3}\)
• If \(\frac{a-x}{px}\) = \(\frac{a-y}{qy}\) = \(\frac{a-z}{rz}\) and p, q, r are in A.P., show that x, y, z are in H.P.
• If x > 1, y > 1, z > 1 are in G.P., then show that \(\frac{1}{1+\text{log}\,x}\), \(\frac{1}{1+\text{log}\,y}\), \(\frac{1}{1+\text{log}\,z}\) are in H.p.