Mathematics
If a = 3, n = 8 and Sn = 192, then the common difference of the A.P. is:
4
5
6
7
AP
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Answer
a = 3
n = 8
Sn = 192
Sn = [2a + (n - 1)d]
⇒ 192 = [2(3) + (8 - 1)d]
⇒ 192 = 4[6 + 7d]
⇒ = [6 + 7d]
⇒ 48 = [6 + 7d]
⇒ 48 - 6 = 7d
⇒ 42 = 7d
⇒ d =
⇒ d = 6.
Hence, option 3 is the correct option.
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Case Study I
A spiral is made up of successive semicircles, with centers alternately at A and B, starting with center at A, of radii 0.5 cm, 1 cm, 1.5 cm, 2 cm, …… as shown in the given figure.
Based on this information, answer the following questions:
(Take π = )
What is the radius of the 9th semicircle?
(a) 4 cm
(b) 4.5 cm
(c) 3.5 cm
(d) 5 cmThe length of the 15th semicircle is :
(a) 8π cm
(b) 7π cm
(c) 7.5π cm
(d) 6.5π cmThe difference of lengths of the 19th and 12th semicircles is :
(a) 3.5π cm
(b) 3 cm
(c) 4π cm
(d) 4.5π cmThe total length of the spiral made up of first 7 consecutive semicircles is:
(a) 38 cm
(b) 42 cm
(c) 44 cm
(d) 46 cmThe lengths of the semicircles form an A.P. What is the common difference of this A.P.?
(a) 0.5π cm
(b) π cm
(c) 0.25π cm
(d) 1.25π cm
Case Study II
The production of TV sets in a factory increases uniformly by a fixed number every year.
It produced 16000 sets in the 6th year and 22600 in the 9th year.Based on this information, answer the following questions:
The production of the TV sets during the first year was :
(a) 4000
(b) 4500
(c) 5000
(d) 5500What was the uniform increase in the production of TV sets every year?
(a) 1800
(b) 2400
(c) 1600
(d) 2200The production of the TV sets during the 8th year was:
(a) 20000
(b) 20400
(c) 21200
(d) 22800The total production of the TV sets during first 6 years was:
(a) 56000
(b) 72000
(c) 66000
(d) 63000The average production of the TV sets during first 6 years was:
(a) 10500
(b) 11000
(c) 11500
(d) 12000