4 Marks Each

Question 14 Marks

A toy is sold at $₹ 20 .$ Total cost of producing $x$ such toys is $C=1000+16.5 x+0.001 x^2 ₹$.How many toys should be produced for maximum profit? OR The daily cost of productionf or $x$ tons of a commodity is $10 x^2-1,000 x+50,000$. How many units should be produced for the minimum cost? Also find the minimum cost.

Answer

$1750$ toys or $25,000$

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Question 24 Marks

Find the value of $\lim _{x \rightarrow 0} \frac{\sqrt{3+x}-\sqrt{3}}{x}$

Answer

self practice

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Question 34 Marks

The weight of randomly selected $500$ adult persons from a region of a city follows normal distribution. The average weight of these persons is $55 \ kg$ and its standard deviation is $7 \ kg$.
$(1)$ Estimate the number of persons having weight between $41 \ kg$ to $62 \ kg$.
$(2)$ Estimate the number of persons having weight less than $41 \ kg$. OR The monthly bill amount of regular customers of a provision store follows normal distribution. If $7.78 \%$ customers have monthly bill amount less than $₹ 3,590$ and $94.52 \%$ customers have bill amount les than $₹ 5,100$ then determine the parameters of the normal distribution.

Answer

$(1)\ 409$ persons $(2)\ 11$ persons or $4300$

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Question 44 Marks

$(1)$ Tania can hit the target in $3$ out of $5$ attempts whereas Kathan can hit the target in $5$ out of $6$ attempts. If both of them attempt simultaneously, find the probability that the target is hit. $(2)$ Give the illustrations of impossible and certain events.

Answer

$(1)\ \frac{14}{15}$

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Statistics 4 Marks Each

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