Case Study Questions for Class 12 Maths Chapter 9 Differential Equations

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Case Study Questions for Class 12 Maths Chapter 9 Differential Equations

Read the following text and answer the following questions on the basis of the same:

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in 5 hours.

(i) The value of

$$
\int \frac{1}{K x} d x=
$$
(A) \log |x|+C
(B) \log |K x|+C
(C) \frac{1}{K} \log |x|+C
(D) \frac{-1}{K x^2}+C

(ii) If ‘N’ is the number of bacteria, the corresponding differential equation is ___________.

(A) \frac{d N}{d t}=K t
(B) \frac{d N}{d t}=K N
(C) \frac{d K}{d t}=N
(D) \frac{d K}{d N}=t

(iii) The general solution is ____________.

(A) \log |N|=K t+C
(B) \log |N t|=K+C
(C) \log |N|=t
(D) \log |K t|=N+C

(iv) If N0 is the initial count of bacteria, after 10 hours the count is ________.

(A) \frac{1}{5} \log 3
(B) 3 \log N_0
(C) 9 N_0
(D) 2 N_0

(v) The bacteria become 10 times in _____________ hours.

(A) 5 \log 7
(B) \frac{5 \log 10}{\log 3}
(C) \frac{5}{\log 3}
(D) \log \left(\frac{10^5}{3}\right)

Show Answer Answers:
(i) C
(ii) B
(iii) A
(iv) C
(v) B

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