A computer purchased for ₹72900 loses two-third of its value every year. Its value is evaluated at the end of every year.

(1) Which of the following expressions gives the value of the computer (in ₹) after n years?

1. $\dfrac{72900}{\Big(\dfrac{2}{3}\Big)^{n}}$

2. $\dfrac{2^{n} \times 27900}{3^{n}}$

3. $\dfrac{72900}{3^{n}}$

4. $\dfrac{72900}{2^{n} \times 3^{n}}$

(2) Find the value of the computer after 3 years.

1. ₹8100
2. ₹2430
3. ₹5600
4. ₹2700

(3) In how many years will the value of the computer be less than ₹200 ?

1. 6 years
2. 7 years
3. 8 years
4. 10 years

(4) By how much will the value of the computer reduce in 4 years ?

1. ₹24300
2. ₹1800
3. ₹8100
4. ₹72000

In a bacteria culture under observation in a laboratory, the population of 50 bacteria doubles itself every hour.

(1) Which of the following expressions gives the bacterial population after n hours ?

1. $\dfrac{50}{2^{n}}$

2. 25ⁿ

3. 50 x 2ⁿ

4. $\dfrac{50^{n}}{2}$

(2) The population size of the bacteria after 3 hours will be

1. 200
2. 300
3. 400
4. 500

(3) How many bacteria will be there in the culture after 1 day ?

1. $\dfrac{50}{2^{12}}$

2. 50 x 2²⁴

3. 50 x 2¹²

4. $\dfrac{50}{2^{24}}$

(4) If the culture is observed after every one hour, find the number of hours after which the population size of the bacteria will be larger than 1000.

1. 5
2. 6
3. 8
4. 10

Assertion: x^m ÷ y^m = (x ÷ y)^m

Reason: a^m x b^m = (ab)^m

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Assertion: 2⁰ + 3⁰ + 4⁰ = (2 + 3 + 4)⁰

Reason: x⁰ = 1.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.