2 Marks Each

Question 12 Marks

Find $f^{\prime}(x)$, if $f(x)=\sqrt{x^2+5}$

Answer

$f^{\prime}(x)=\frac{d y}{d x}=\frac{x}{\sqrt{x^2+5}}$

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Question 22 Marks

If $f(x)=x^2-x+3$ then for which value of $x \cdot f(x)=0$ ?

Answer

$x=\frac{1}{2}$

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Question 32 Marks

Find the value of $\lim _{x \rightarrow 4} \frac{x^2-2 x-3}{x^2-1}$

Answer

$\frac{4-3}{4-1}=\frac{1}{3}$

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Question 42 Marks

Express $|x+1|<0.5$ in neighbourhood and interval form. OR If $|x-10|$

Answer

$(-1.5-0.5)$ OR $k_2=9.99$

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Question 52 Marks

A normal variable $X$ has the probability density function as$f(x)=$ constant $x e^{\frac{ L }{50}(x-10)^2} ;-\infty$

Answer

$6.625=6.63$

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Question 62 Marks

A die is randomly tossed two times. Determine the probability distribution of the sum of the numbers appearing both the times on the die. OR The probability distribution of a random variable is as follows :$p(x)=\frac{x+3}{10}, x=-2,1,2$. Hence, calculate $E(X)$.

Answer

$7$ OR $E \left( x ^2\right) 2.8$

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Question 72 Marks

State the limitations of graphical method for determining Trend.

Answer

self practice

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Question 82 Marks

If $=30$, and $=20$, and $b=0.6$, find the intercept of the regressino line of $Y$ on $X$ and write the equation of the line.

Answer

$\therefore \hat{ y }=2+0.6 x$

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Question 92 Marks

Finf the value of the correlatino coefficient if $\operatorname{Cov}(x, y): S_x^2=2: 5$ and $S_x: S_y=3: 2$

Answer

$r =0.6$

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Question 102 Marks

The Laspeyre's index number is $\frac{8}{9}$ times the Fisher's index number. If the Fisher's index number is $180 ,$ find the Paasche's index number.

Answer

$\therefore I_r=\frac{180 \times 180}{160}=202.5$

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Statistics 2 Marks Each

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