4 Marks Each

Question 14 Marks

Find the maximum and ininimum values of $y=x^3-2 x^2-4 x-1$ OR $\Lambda$ 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

$\frac{13}{27}$ OR $1750$

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Question 24 Marks

Find the value of $\lim _{x \rightarrow 0} \frac{f(2+h)-f(2)}{h}$ where $f(x)=2 x^2+3$

Answer

$8$

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Question 34 Marks

The monthly income of $1000$ employees of a group follows normal distribution. The mean of the distribution is $₹ 15,000$ and its standard deviation is $₹ 4000$. From this information :

$(1)$ Obtain range of monthly income for middle $60 \%$ of the employes.

$(2)$ If monthly income of $250$ employees is between $₹ 15,000$ and certain fixed income $₹ x_1$ then find the value of $x_1$.

Answer

$(1)\ X_1=11,640, X_2=18,360$
$(2)\ X_1=17,700 $ OR $(1)\ 250$ children $(2)\ 50$ is $96$ marks

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Question 44 Marks

$(A)$ Find the probability of getting $R$ in the first place in all possible arrangements of each and every letter of the word $\text{RUTVA}.$
$(B)$ If $P ( B )=2 P ( A / B )=0.4$ then find $P ( A \cap B )$

Answer

$(1)\ \frac{1}{5}\ (2)\ 0.08$

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Statistics 4 Marks Each

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