4 Marks Each

Question 14 Marks

The demand function of a watch is $p=6000-2 x$. Find the demand which maximizes the revenue and also find the corresponding price. OR Find the values of $x$ which maximize or minimize $f(x)=2 x^3+3 x^2-36 x+10$. Also find the maximum and minimum values of $f(x)$.

Answer

$P=3000 \text { OR } 42 . x=2 ; f(x)=-34$

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Question 24 Marks

Find the value of $\lim _{x \rightarrow 2} \frac{\sqrt{x+7}-3}{x-2}$

Answer

$\frac{1}{3+3}=\frac{1}{6} $

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Question 34 Marks

In a city, daily sale of petrol at a petrol pump follows normal distribution and its mean and standard deviation are $33,000$ litre and $3,000$ litre respectively.
$(1)$ Obtain the percentage of days of a month during which the daily sale of petrol is less than $30,000$ litre.
$(2)$ During the month of May, how many days are exepected so that the sale of petrol is between $32,000$ litre to $35,000$ litre? OR For a group of $1,000$ persons, the average height is $165\ cms$ and variance is $100 ( cms )^2$. The distribution of hieght of these persons follows normal distribution. From this information, determine the third decile and the $60^{\text {th }}$ percentile.

Answer

$(1)\ 15.87 \% ; 30000$ litre $(2)\ 12$ day; $32000$ litre $\& \ 35000$ litre OR $6 \%$ and $167.55\ cms$

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Question 44 Marks

$(A)$ Find the proabability of getting vowels in the first, third and sixth place when all the letters of the word $\text{ORANGE}$ are arranged in all possible ways.
$(B)$ Draw the Venn diagram for' events $A-B$ and $A \cap B$.

Answer

$(A)\ P ( A )=0.05$

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Statistics 4 Marks Each

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