In Online Math Quiz on Progressions we will complete 10 multiple choice questions on Progressions.
1. If x\(_{1}\), x\(_{2}\), x\(_{3}\), .... are in AP then x\(_{a}\), x\(_{b}\), x\(_{c}\) are in AP if a, b, c are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
2. Let t\(_{r}\) denote the rth term of an AP. If t\(_{m}\) = \(\frac{1}{n}\) and t\(_{n}\) = \(\frac{1}{m}\) then t\(_{mn}\) equals
(i) \(\frac{1}{mn}\)
(ii) \(\frac{1}{m}\) + \(\frac{1}{n}\)
(iii) 1
(iv) 0
3. If a, b, c, d ∈ N and they are four consecutive terms of an AP then the ath, bth, cth, dth terms of a GP are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
4. If in a progression x\(_{1}\), x\(_{2}\), x\(_{3}\), ...., etc., (x\(_{r}\) - x\(_{r + 1}\)) bears a constant ratio with x\(_{r}\) ∙ x\(_{r + 1}\) then the terms of the progression are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
5. If \(\frac{x_{2}x_{3}}{x_{1}x_{2}}\) = \(\frac{x_{2} + x_{3}}{x_{1} + x_{2}}\) = 3 \(\left ( \frac{x_{2} - x_{3}}{x_{1} - x_{4}} \right )\) then x\(_{1}\), x\(_{2}\), x\(_{3}\), x\(_{r}\) are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
6. Let p, r, r be three positive prime numbers. The progression in which \(\sqrt{p}\), \(\sqrt{q}\), \(\sqrt{r}\) can be three terms (not necessarily consecutive) is
(i) AP
(ii) GP
(iii) HP
(iv) None of these
7. Let a function f(z) = 2z + 1. Then the number of real values of z for which the three unequal numbers f(z), f(2z), f(4z) are in GP is
(i) 1
(ii) 2
(iii) 0
(iv) None of these.
8. Let x\(_{1}\), x\(_{2}\), x\(_{3}\), .... are in AP then x\(_{a}\), x\(_{b}\), x\(_{c}\) are in GP. Then x\(_{b}\) : x\(_{a}\) is equal to
(i) \(\frac{c - a}{b - a}\)
(ii) \(\frac{b - a}{c - b}\)
(iii) \(\frac{c - b}{b - a}\)
(iv) None of these
9. If x, y, z are in GP then x + y, 2y, y + z are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
10. If p, q, r, s are nonzero real numbers such that
(p^{2} + q^{2} + r^{2})(q^{2} + r^{2} + s^{2}) ≤ (pq + qr + rs)^{2} then p, q, r, s are in
(i) AP
(ii) GP
(iii) HP
(iv) None of these
Answers for the Online Math Quiz on Progressions are given below to check the exact answers of the above 10 multiple choice questions.
Answers:
1. (i)
2. (iii)
3. (ii)
4. (iii)
5. (iii)
6. (iv)
7. (iii)
8. (iii)
9. (iii)
10. (ii)
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