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Progression - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Progression. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - 105 th term of the A.P. 4, 9/2, 5, 11/2, 6 ....is

Answer : A

Explanation

 Here a = 4, d = (9/2-4) = 1/2
T₁0₅ = a+(105-1)*d=4+104*1/2=4+52=56.

Q 2 - In the event that the fourth term of a number juggling movement is 14 and its twelfth term is 70, then its first term is:

Answer : B

Explanation

  Let the first term of the A.P. be a and common difference be d. then,
a+ 3d = 14 ...(i)    a+11d = 70 ...(ii)
On subtracting (i) from (ii), we get 8d =56    d = 7
Putting d = 7 in (i), we get a+3*7=14 ⇒ a= (14-21) = -7   ∴ First term = -7

Q 3 - The main term of a number-crunching movement is 6 and its normal distinction is 5. The eleventh term is:

Answer : D

Explanation

Here a =6 and d = 5
T₁₁    = a + (11-1) d = a +10 d = (6+10*5) =56.

Q 4 - (1+2+3+4....+99+100+99+98+.....+3+2=1) =?

Answer : D

Explanation

Give series = 2 (1+2+3+4+?..+99) + 100
= 2 * 99/2 * (1+99) + 100=2* 4950 +100 = 9900 + 100 = 10000

Q 5 - The total of every single common number from 75 to 97 is:

Answer : D

Explanation

Sum = 75+76+77+...+97.
Here a =75, d = (76-75) =1
Let the number of terms be n. Then,
A+ (n-1) d =97⇒ 75 + (n-1)*1 =97 ⇒ (n-1) = 22 ⇒ n= 23.
∴ Sum = 23/2 (75 + 97) = (23/2 *172) = (23 *86 ) = 1978.

Q 6 - In the event that the fourth and ninth term of a G.P. is 54 and 13122 separately, there its second term is:

Answer : A

Explanation

Let its 1st term be a and common ratio r. Then,
ar³ = 54 and ar⁸ = 13122
∴ ar⁸/ ar³ = 13122/54 ⇒ r⁵ =243 = 3⁵ =r = 3
∴ a* 3³ = 54 ⇒ a*27 = 54 = > a =2
2nd term = ar = (2*3) =6

Q 7 - In the event that a ≠b, Then which of the accompanying proclamations is valid?

Answer : C

Explanation

For any two unequal numbers a and b, we have (A.M).> (g.m)
∴   (a+b)/2 > √ab

Q 8 - A man heaps logs of wood so that the top layer contains one log and every lower layer has one more than the layer above. In the event that there are 15 layers, the aggregate number of logs will be:

Answer : B

Explanation

Total number of logs = 1+2+3+...+15.
This is an A.P. in which a =1, d =1 and n= 15.
Sn = n/2(a+1) = 15/2 (1+15) =120

Q 9 - The number of inhabitants in microbes, society copies ever 2 minutes. How long will it take for the populace to develop from 1000 to 512000 microbes?

Answer : D

Explanation

Let the growth be 1000, 2000, 4000 ...512000.
This is a G.P. in which a = 1000, r = 2 and tn = 512000
Tn = ar&n-1 ⇒ 1000*2 &n-1 = 512000⇒ 2 &n-1 = 512= 2⁹ ⇒ (n-1) = 9.
∴ Time taken = (2*9) min = 18 min.

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