Sample QuestionsBoard Question Paper : March 2018 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is the derivative of $f(x)=5 x^2+2$ ?
- A
$5 x$
- B
$7 x$
- ✓
$10 x$
- D
$12 x$
Answer: C.
View full solution →What is the modulus form of $N (-5,0,02)$ ?
- ✓
$|x+5|<0.02$
- B
$|x-0.02|<5$
- C
$|x-5|>0.02$
- D
$|x-5|<0.02$
Answer: A.
View full solution →What is the area under the normal curve to the right-hand side of the perpendicular line at $x=\mu$ ?
Answer: B.
View full solution →In normal distribution, usually what percentage of the observations are included in the limits $\mu \pm 2.575 \sigma$ ?
- A
$68.26 \%$
- B
$95 \%$
- ✓
$99 \%$
- D
$99.73 \%$
Answer: C.
View full solution →For a positively skewed binomial distribution with $n=20$, which of the following values might be the value of mean?
Answer: A.
View full solution →Find $f^{\prime}(x)$ for the function $f(x)=21$.
View full solution →Find the value of $\lim _{x \rightarrow 4} \frac{x^4-81}{x-3}$
View full solution →Mean of a normal distribution is $13.25$ and its standard deviation is $10.$ Estimate the value of its third quartile.
View full solution →Standard score is independent of unit of measurement. Is this statement true or false?
State the relation between mean and variance of binomial distribution.
Find $f^{\prime}(x)$, if $f(x)=\sqrt{x^2+5}$
View full solution →If $f(x)=x^2-x+3$ then for which value of $x \cdot f(x)=0$ ?
View full solution →Find the value of $\lim _{x \rightarrow 4} \frac{x^2-2 x-3}{x^2-1}$
View full solution →Express $|x+1|<0.5$ in neighbourhood and interval form. OR If $|x-10|$
View full solution →A normal variable $X$ has the probability density function as$f(x)=$ constant $x e^{\frac{ L }{50}(x-10)^2} ;-\infty$
View full solution →A person has kept $4$ cars to run on rent. The probability that any car is rented during the day is $0.6 .$ Find the probability that more than one but less than $4$ cars are rented during a day.
View full solution →State the properties of Bernoulli Trials.
The events $A$ and $B$ in the sample space of a random experiment are mutually exclusive. If $3 P(A)=4 P(B)=1$, then find $P(A \cup B)$
View full solution →Define the following terms $:(1)$ Sample Space $(2)$ Mutually Exclusive Events $(3)$ Complimentary Event $OR$ The events $A_1$ and $A_2$ of a random experiment are as follows. Find the sets showing the union events $A_1 \cup A_2$ and intersection events $A_1 \cap A_2 :$
View full solution →Fit a linear equation of trend from the following data for variable $(y)$ of a time series: $n =4, \Sigma y =270, \Sigma ty =734$
View full solution →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 $f(x)$. OR If the production cost function for a producer is $C =100+0.015 x ^2$ and revenuc function is $R=3 x$, then find the profit function. How many units should be prdouced by the producer for maximum profit?
View full solution →Find the value of $\lim _{x \rightarrow 2} \frac{x^3-8}{\sqrt{x}-\sqrt{2}}$
View full solution →An amount of purchase of a customer in a mall of a city follows normal distribution with mean $₹ 8$ and standard deviation $₹ 200$. If a customer is selected at random, then find the probabilitics for the following events:
$(1)$ Amount of purchase made by him is in between $₹ 850$ to $₹ 1,200$.
$(2)$ Amount of purchase made by him is in betwecn $₹ 600$ to $₹ 750$. OR A normal variable $X$ has mean $400$ and variance $900.$ Find the fourth decile and $90^{th}$ percentile for this distribution.
View full solution →$(A)$ If $P \left( A ^{\prime}\right)=\frac{7}{25}$ and $P ( B \mid A )=\frac{5}{12}$ for two events $A$ and $B$ in the sample space of a random cxperiment, the find $P ( A \cap B )$.
$(B)$ There are two children in a family. If the first child is a girl, then find the probability that both the children in the family are girls
View full solution →Find the trend using four monthly moving average for the following data showing monthly sales $($in lakh $8:)$ of a shop :
| Month |
march |
april |
may |
june |
july |
Aug. |
Sept. |
Oct. |
Nov. |
Dec. |
| Sales $($lakh $₹)$ |
$5$ |
$3$ |
$7$ |
$6$ |
$4$ |
$8$ |
$9$ |
$10$ |
$8$ |
$9$ |
OR
The birth rates of a state in different years are given in the following table. Fit :$1 “ 5$'linear trend for these data. Also find the estimate for birth rate in the year $2017:$
| Year |
$2009$ |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
$2015$ |
| Birth rate |
$22.2$ |
$21.8$ |
$21.3$ |
$20.9$ |
$20.6$ |
$20.2$ |
$19.9$ |
View full solution →Obtain the regression line of the demand on the price using the following information collected for the demand and the price of a Commodity. Estiamte the demand of the commodity it price is $₹40.$
| Price $₹$ |
$38$ |
$36$ |
$37$ |
$37$ |
$36$ |
$38$ |
$39$ |
| Demand $($hundred units$)$ |
$12$ |
$18$ |
$15$ |
$12$ |
$17$ |
$13$ |
$13$ |
View full solution →An Engineer Association wants to know the relation betwene the production$($thousand units$)$ and the unit production cost of different factories. The informationcollected from six factories regarding their production and unit production cost is given below:
| Production $($thousand units$)$ |
$15$ |
$20$ |
$35$ |
$24$ |
$18$ |
$21$ |
| Cost per unit of Production $(R)$ |
$95$ |
$90$ |
$75$ |
$80$ |
$87$ |
$70$ |
Find the correlation co—efficient between production and cost per unit of production. View full solution →Find the Laspeyre’s, Paasche’s and Fisher’s index numbers for the year $2015$ with the base year $2014$ using the following information :
| Item |
unit |
Price $(₹)$ |
Quantity $($Consumption$)$ |
| Year $2014$ |
Year $2015$ |
Year $2014$ |
Year $2015$ |
| $A$ |
$20 \ kg$ |
$80$ |
$120$ |
$5 \ kg.$ |
$7 \ kg.$ |
| $B$ |
$kg$ |
$20$ |
$24$ |
$2400\ gm$ |
$4000\ gm$ |
| $C$ |
Quintal |
$2000$ |
$2800$ |
$10 \ kg.$ |
$15 \ kg.$ |
| $D$ |
Dozen |
$40$ |
$70$ |
$30$ Pieces |
$36$ Pieces |
View full solution →