Sample QuestionsBoard Question Paper : July 2022 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 $f(x)=\frac{4}{x^2}$ ?
- A
$\frac{4}{2 x}$
- ✓
$-\frac{8}{x^3}$
- C
$\frac{8}{x^3}$
- D
$0$
Answer: B.
View full solution →What is the formula for elasticity of demand?
- ✓
$-\frac{p}{x} \cdot \frac{d x}{d p}$
- B
$\frac{p}{x} \cdot \frac{d x}{d p}$
- C
$-\frac{x}{p} \cdot \frac{d p}{d x}$
- D
$-\frac{p}{x} \cdot \frac{d p}{d x}$
Answer: A.
View full solution →What is the modulus form of $N (5,0.02)$ ?
- A
$|x+5|<0.02$
- B
$|x-0.02|<5$
- C
$|x-5|>0.02$
- ✓
$|x-5|<0.02$
Answer: D.
View full solution →What is the value of $\lim _{x \rightarrow 3} 3 x+1\ ?$
- A
$9$
- ✓
$10$
- C
$\frac{4}{3}$
- D
$8$
Answer: B.
View full solution →If the mean of a normal distribution is $13.25$ and its standard deviation is $10$ then, which of the following is the value of third quartile?
Answer: D.
View full solution →What is marginal revenue?
If $\lim _{x \rightarrow-1} 4 x+k=6$ then find the value of $K$.
View full solution →Write the probability density function of normal random variable.
"Standard score is independent of unit of measurement". Is this statement true or false?
State the relation between the probability of success and failure in Bernoulli trials.
Find $f^{\prime \prime}(0)$, if $f(x)=x^4-4 x^3+3 x^2+x+1$.
View full solution →Find the value of $\lim _{x \rightarrow 2} \frac{x^5-32}{x-2}$.
View full solution →If $N\left(k_1, 0.5\right)=\left(19.5, k_2\right)$ then find the value of $k_1$ and $k_2$.
View full solution →Find parameters of the binomial distribution where mean $=4$ and variance $=2$.
View full solution →Define :$(i)$ Favourable outcomes $(ii)$ Union of events
View full solution →If the daily cost of production for $x$ tons of a commodity is $10 x^2-1000 x+50,000$ then how many units should be produced for the minimum cost? Also, find the minimum cost.
View full solution →Normally, $40 \%$ students fail in one examination. Find the probability that at least $4$ students in a group of $6$ students pass in this examination.
View full solution →Fit a linear equation from the following data for variable $(y)$ of a time series. $n=6, \Sigma y=501, \Sigma t y=1762$
View full solution →The following information is obtained to study the relationship between average rainfall $($in $cm.)$ and the yield of maize $($in quintal per hectare$)$ in different talukaa of Gujarat.
| Particulars |
Rainfall (cm) x |
Yield of maize (quintal per hectare) y |
| mean |
$82$ |
$180$ |
| variance |
$64$ |
$225$ |
| Correlation coefficient $0.82$ |
Estimate the yield of maize when the rainfall is $60 \ cm$. View full solution →Obtain the regression line of Yon $X$ from the following data
$n =6, \Sigma x=1020, \Sigma y =990, \Sigma(x-170)^2=60$
$\Sigma( y -165)^2=105, \Sigma(x-170)(y-165)=45 .$
View full solution →Find the values of $x$ which maximize or minimize $y=2 x^3-15 x^2+36 x+12$. Also, find the maximum and minimum values of $y$.
View full solution →Find the value of $\lim _{x \rightarrow 0} \frac{\sqrt{3 x+x}-\sqrt{3}}{x}$
View full solution →The maximum temperature of a city during summer follows normal distribution. On a particular day, the probability that the maximum temperature of the city is more than $31^{\circ}$ celsius is $0.3085 ,$ whereas the probability that during some other day, the maximum temperature is less than $27^{\circ}$ is $0.0668 .$ Find mean and standard deviation of the maximum temperature of the city.
View full solution →The average monthly expense of students residing in university hostel is $₹ 2,000$ and its standard deviation is $₹ 500 .$ If the monthly expense of students follow normal distribution then $(1)$ Find percentage of students having expense between $₹ 750$ and $₹ 1,250.\ (2)$ Find percentage of students having expense less than $₹ 2,400$.
View full solution →The average monthly closing price of shares of a company in the year $2019$ are given in the following table. Find the trend using four monthly moving averages.
| Month |
January |
February |
march |
April |
| Share price |
$253$ |
$231$ |
$350$ |
$261$ |
| Month |
May |
June |
July |
August |
| Share price |
$262$ |
$266$ |
$263$ |
$261$ |
| Month |
Sept. |
Oct. |
Nov. |
Dec. |
| Share price |
$281$ |
$278$ |
$278$ |
$272$ |
View full solution →The following data are available for the number of passengers who travelled in the last $5$ years by the aircrafts of an airline company. Estimate the trend for the year $2019$ by fitting linear trend.
| years |
$2014$ |
$2015$ |
$2016$ |
$2017$ |
$2018$ |
| No. of Passengers $($thousands$)$ |
$45$ |
$47$ |
$44$ |
$40$ |
$38$ |
View full solution →The information regarding the experience $($in years$)$ of eight workers on a machine and their performance ratings based on the nondefective units they manufactured in every $100$ units is as follows.
| Experience of workers $($years$)$ |
$5$ |
$12$ |
$15$ |
$8$ |
$20$ |
$18$ |
$22$ |
$25$ |
| Performance rating |
$80$ |
$82$ |
$85$ |
$81$ |
$90$ |
$90$ |
$95$ |
$97$ |
Obtain the regression line of the performance rating on the experience and estimate the performance rating if a worker has an experience of $17$ years. View full solution →From the following information of a sample of ten students of a school regarding their marks in two subjects Accountancy and Statistics, find the coefficient of correlation between the marks of two subjects.
| Marks in Accountancy |
$60$ |
$80$ |
$50$ |
$80$ |
$95$ |
$40$ |
$70$ |
$40$ |
$35$ |
$90$ |
| Marks in Statistics |
$50$ |
$75$ |
$60$ |
$85$ |
$90$ |
$40$ |
$65$ |
$30$ |
$45$ |
$70$ |
View full solution →The details of monthly sale of Laptop $($in thousand units$)$ and its profit $($in lakh$)$ for the last six months for a company making laptops are given below.
| No. of laptops sold $($thousand units $x )$ |
$3$ |
$8$ |
$12$ |
$5$ |
$7$ |
$5$ |
| Profit $($lakh $₹) y$ |
$6$ |
$10$ |
$15$ |
$10$ |
$9$ |
$8$ |
Find the correlation coefficient between "number of laptops sold' and its 'profit". View full solution →