4 Marks Each

Question 14 Marks

The daily cost of production for $x$ tons of a commodity is $10 x^2-1000 x+50000$. How many units should be produced for the minimum cost? Also find the minimum cost. OR A toy is sold at $₹ 20$. Total cost of producing $x$ such toys is $C =1000+16.5 x +0.001 x ^2$ rupees. How many toys should be produced for maximum profit?

Answer

$25,000$ OR $1750$ toys $;-0.002<0$

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Question 24 Marks

Find the value of following using tabular method $: \lim _{x \rightarrow 2} \frac{2 x^2+3 x-14}{x-2}$

Answer

$x \rightarrow 2 \frac{\lim _2+3 x-14}{x-2}$

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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 $3000$ litre respectively.
$(1)$ Obtain the percentage of days of a month during which the daily sales of petrol is less than $30,000$ litre.
$(2)$ During the month of May, how many days are expected so that the sale of petrol is between $32,000$ litre to $35,000$ litre? OR A normal distribution has mean $52$ and variance $64.$ Obtain estimated limits which include exactly middle $25 \%$ of the observations.

Answer

$12$ days $($approximately$) 32,000$ litre and $35,000$ litre OR $49.48$ and $54.52$

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Question 44 Marks

$(A)$ Seven speakers $A, B, C, D, E, F, G$ are invited in a programme to deliver speech in random order. Find the probability-that speaker $B$ delivers speech immediately after speaker $A$.
$(B)$ If $P \left( A ^{\prime}\right)=\frac{7}{25}, P \frac{ B }{ A }=\frac{5}{12}$ and $P \frac{ A }{ B }=\frac{1}{2}$ for two events $A$ and $B$ in the sample space of a random experiment, then find $P ( A \cap B )$ and $P ( B )$.

Answer

$(A)\ \frac{1}{7}\ (B)\ \frac{3}{5}$

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Statistics 4 Marks Each

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