# 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 â€˜Nâ€™ 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) $\log \left(\frac{10^5}{3}\right)$

(i) C
(ii) B
(iii) A
(iv) C
(v) B

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