Sample QuestionsBoard Question Paper : August 2020 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 $f(x)=\frac{4}{x^2} ?$
- ✓
$\frac{4}{2 x}$
- B
$\frac{-8}{x^3}$
- C
$\frac{8}{x^3}$
- D
$0$
Answer: A.
View full solution →What is the value of $\lim _{x \rightarrow-2} 20$ ?
Answer: A.
View full solution →Which of the following is approximate value of mean deviation for normal variable?
- ✓
$\frac{4}{5} \sigma$
- B
$\frac{4}{5} \mu$
- C
$\frac{2}{3} \sigma$
- D
$\frac{2}{3} \mu$
Answer: A.
View full solution →What is the total area under the normal curve to the right hand side of perpendicular line at $X=\mu$ ?
Answer: B.
View full solution →What are the parameters of Binomial Probability distribution ?
- ✓
$n$ and $p$
- B
$n$ and $q$
- C
$p$ and $q$
- D
$n p q$
Answer: A.
View full solution →What is marginal revenue?
Express $0.001$ neighbourhood of $3$ in interval form.
View full solution →Give the values of the constants used in probability density function of normal variable.
What is the shape of normal curve ?
State the type of skewness for binomial distribution if the value of $p=\frac{1}{4}$ ?
View full solution →Find $\frac{d y}{d x}, y=\sqrt{x^2+3}$.
View full solution →Find $f^{\prime}(0)$ if $f(x)=x^4-4 x^3+3 x^2+x+1$.
View full solution →Find the value of $\lim _{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^2-2 x}\right]$.
View full solution →If $N(3, b )=(2.95, k)$ then find the values of $b$ and $k$. OR Express $3.8$
View full solution →A normal variable $X$ has the probability density function as :$f(x)=\frac{011}{10 \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-100}{10}\right)^2} ;-\propto$
View full solution →There are one dozen mangoes in a box of which $3$ mangoes are rotien. $3$ mangoes are randomly selected from the box with replacement. If $X$ denotes the number of rotten mangoes in the selected mangoes, obtain the probability distribution of $X$ and heance find the expected value of the rotten mangoes in the selected mangoes.
View full solution →The mean and variance of the binomial distribution are $2$ and $\frac{6}{5}$ respectively. Find $P(x \leq 1)$ for this binomial distribution.
View full solution →Two six faces balanced dice and thrown simultaneoulsy. If the sum of numbers on both the dice is more than $7$ then find the probability that both the dice show same numbers.
View full solution →The probability that a teenager comming to a restaurant for dinner orders pizza is $0.63 .$ The probability of ordering cold drink is $0.54.$ The probability that the teenager orders at least one out of pizza and cold drink is $0.88 .$ Find the probability that the teenager coming for dinner on a certain day orders only one of the two items from pizza and cold drink. OR From the following information of Krina Company, calculate cash flow from operating activities:If $5 P(A)=3 P(B)=2 P(A \cup B)=\frac{3}{2}$ for the events $A$ and $B$ then find $P\left(A^{\prime} \cup B^{\prime}\right)$.
View full solution →Obtain the linear equation for trend for a time series with $n=6, \sum y=501, \sum t y=1762$.
View full solution →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.
View full solution →Find the value of $\lim _{x \rightarrow 0} \frac{\sqrt{3+x}-\sqrt{3}}{x}$
View full solution →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.
View full solution →$(1)$ 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.
View full solution →The number of two wheelers reigstered $($in thousand$)$ in a city in different years is as follows. Use the method of fitting linear equation to these data to obtain the estimates for the number of vehicles registered in the year $2016$ and $2017 :$
| Year |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
$2015$ |
| No. of vehicles$(‘000)$ |
$69$ |
$75$ |
$82$ |
$91$ |
$101$ |
$115$ |
OR Find the trend using five yearly moving averages for the following data about yearly production $($in tons$)$ of a factory :
| Year |
$2006$ |
$2007$ |
$2008$ |
$2009$ |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
$2015$ |
$2016$ |
| Production $($tons$)$ |
$212$ |
$206$ |
$193$ |
$190$ |
$214$ |
$259$ |
$230$ |
$270$ |
$230$ |
$213$ |
$115$ |
View full solution →The following data gives the experience of machine operators and their performance ratings :
| Operator |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
| Experience $($years$) x$ |
$12$ |
$5$ |
$10$ |
$3$ |
$18$ |
$4$ |
$12$ |
$16$ |
| Performance rating $y$ |
$82$ |
$74$ |
$79$ |
$77$ |
$88$ |
$67$ |
$87$ |
$86$ |
View full solution →Find Karl Pearson's correlation coefficient between density of population $($per square $km)$ and death rate $($per thousand$)$ from the following data:
| City |
$A$ |
$B$ |
$C$ |
$D$ |
$E$ |
$F$ |
$G$ |
| Density $($per sq.km$.)$ |
$750$ |
$600$ |
$350$ |
$500$ |
$200$ |
$700$ |
$850$ |
| Death rate$($per thousand$)$ |
$30$ |
$20$ |
$15$ |
$20$ |
$10$ |
$25$ |
$50$ |
View full solution →The quantity consumed and total expenditure of four different items are as gien below. Find Paasche's, Laspeyre's and Fisher's index numbers for the year $2015$ with respect to the year $2013 .$
| items |
Base year $2013$ |
Current year $2015$ |
| |
Total Expenditure
$(r)$ |
Consumption
$($Quantity$)$ |
Total Expenditure
$(r)$ |
Consumption
$($Quantity$)$ |
| $A$ |
$420$ |
$60 \ kg.$ |
$375$ |
$25 \ kg.$ |
| $B$ |
$170$ |
$10\ litre$ |
$416$ |
$20\ litre$ |
| $C$ |
$525$ |
$15 \ kg.$ |
$613.2$ |
$6 \ kg.$ |
| $D$ |
$345$ |
$3 \ kg.$ |
$400$ |
$2.5.kg$ |
View full solution →