Progression - Online Quiz


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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.

Questions and Answers

Q 1 - What number of term arrives in the A.P. 7, 11, 15..... 139?

A - 33

B - 34

C - 32

D - 31

Answer : B

Explanation

Here a = 7 and d = (11-7) = 4
Let there be n terms in the given A.P. then,
Tn = 139 ⇒a+ (n-1) d =139
⇒ 7+ (n-1)*4 = 139 ⇒ (n-1) *4 = 132 ⇒ (n-1) = 33
⇒ n = 34

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:

A - - 10

B - -7

C - 7

D - 10

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 - On the off chance that the tenth term of the succession, a - b, a-2b, a-3b ...is 20 and its twentieth term is 10, then its xth term is:

A - 10-x

B - 20-x

C - 29-x

D - 30-x

Answer : D

Explanation

This is an A.P. in which A = a and d = (a-b) -a = -b
T₁₀ = 20 ⇒ a+9d = 20 ⇒ a+9*)-b) =20⇒a-9b=20 ... (i)
T₂₀ =10⇒ a+19d = 10 ⇒ a+19*(-b) =10⇒a-19b=10 ... (ii)
On subtracting (ii) from (i) we get 10b = 10 ⇒ b=1
Putting b= 1 in (i) we get a-9*1=20 ⇒ a =29.
∴ xth term = a + (x-1) *d=29+ (x-1) * (-b)
= 29 + (x-1) * (-1) = (30-x).

Q 4 - The total 5+6+7+8+.....+19=?

A - 150

B - 170

C - 180

D - 190

Answer : C

Explanation

This is an A.P. in which a = 5, d =1 and L=19.
Let the number of its term be n. Then,
Tṇ = 19 ⇒ a + (n-1) d =19
⇒ 5 + (n-1) * 1 = 19 ⇒ (n-1) =14 ⇒ n= 15.
∴ Sṇ = n/2 * (a+L) = 15/2 *(5+19) = 180.

Q 5 - In the event that a, a-2,3a are in A.P., Then a=?

A - -3

B - -2

C - 3

D - 2

Answer : B

Explanation

Since a, (a-2), 3a are in A.P. , we have
(a-2) - a = 3a - (a-2) ⇒ 2a +2 = -2 ⇒ 2a = -4 ⇒ a = -2.

Q 6 - What number of term of the series 3,9,27 ... will mean 363?

A - 5

B - 6

C - 7

D - 8

Answer : A

Explanation

Given series is a G.P. in which a =3, r= 3 and Sn =363
∴ Sn = a (rⁿ-1)/(r-1) ⇒ 3*(3ⁿ-1)/ (3-1) = 363 ⇒ 3ⁿ-1 = 363*2/3 = 242
3ⁿ= 243 = 3⁵⇒ n =5

Q 7 - A man needs to pay Rs 975 in yearly portion every portion being not exactly the prior one by Rs 5. The measure of first portions is Rs 100. In what time, the whole sum will be paid?

A - 10 years

B - 12 years

C - 15 years

D - 25 years

Answer : C

Explanation

Let the requisite time be n years.
Then, a =100 and d=-5
Let the number of terms be n. Then,
n/2 *[2a+ (n-1)d]  = 975
⇒ n/2 [200+ (n-1)*(-5) = 975   ⇒ n (205-5n) = 1950
⇒ 5n2 -205n +1950= 0 ⇒ n2- 41n+ 390 =0
⇒ n2 -26n-15n+ 390 = 0 ⇒ n (n-26) -15(n-26) = 0
⇒ (n-15) (n-26) = 0 ⇒ n= 15.   [∵n ≠ 26]

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:

A - 105

B - 120

C - 210

D - 225

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?

A - 10

B - 12

C - 14

D - 18

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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