Practice Test-I
Q:1. If x , |x + 1|, |x – 1| are the three terms of an A.P its sum upto 20 terms is
(A) 90 or 175
(B) 180 or 350
(C) 360 or 700
(D) 720 or 1400
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Q:2. If a, b and c are positive real numbers then $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} $ is greater than or equal to
(A) 3
(B) 6
(C) 27
(D) none of these
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Q:3. If a, b and c are positive real numbers, then least value of $(a + b + c)(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) $ is
(A) 9
(B) 3
(C) 10/3
(D) none of these
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Q:4.The sum of the integers from 1 to 100 that are divisible by 2 or 5 is
(A) 3000
(B) 3050
(C) 3600
(D) none of these
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Q:5. If the sides of a right-angled triangle form an A.P. then the sines of the acute angle is
(A) 3/5 , 4/5
(B) 3/4 , 3/5
(C) 2/5 , 3/5
(D) none of these
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Q:6. If a, b , c, d and p are distinct real numbers such that
(a2 + b2 + c2)p2 – 2(ab + bc + cd ) p + (b2 + c2 + d2) ≤ 0 , then a, b, c, d are in
(A) A.P.
(B) G.P.
(C) H. P.
(D) none of these
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Q:7. If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)n is equal to
(A) p2
(B) p3
(C) p
(D) none of these
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Q:8. If $\large t_r = \frac{r+2}{r(r+1)}.\frac{1}{2^{r+1}}$ , then $\large \Sigma_{r=1}^{n} t_r $ is equal to
(A) $\large \frac{n 2^n – 1}{n + 1}$
(B) $\large \frac{n + 1}{2^{n + 1}(n+2)}$
(C) $\large \frac{n}{2^n} – 1$
(D) $\large \frac{(n+1) 2^n – 1}{2^{n + 1}(n+1)}$
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Q:9. $\large \Sigma_{j=1}^{n} $\large \Sigma_{i=1}^{n} i $ is equal to
(A) $\large \frac{n(n+1)}{2}$
(B) $\large \frac{n(n+1)^2}{2}$
(C) $\large \frac{n^2 (n+1)}{2}$
(D) none of these
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Q:10. If $\large \frac{1}{a} + \frac{1}{a-2b} + \frac{1}{c} + \frac{1}{c-2b} = 0 $ and a, b, c are not in A.P, then
(A) a, b, c are in G.P
(B) a , b/2 , c are in A.P
(C) a , b/2 , c are in H.P
(D) a, 2b, c are in H.P
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