Sample QuestionsBoard Question Paper : March 2019 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is $\frac{d y}{d x}$ if $y=a x^n$, $a$ is a constant ?
- A
$n x^{ n -1}$
- ✓
an $x^{n-1}$
- C
$0$
- D
an $x^{n+1}$
Answer: B.
View full solution →What is the modulus form of $0.3$ neighbourhood of $3 ?$
- A
$|x-0.3|<3$
- ✓
$|x-3|<0.3$
- C
$|x+3|<0.3$
- D
$|x-3|>0.3$
Answer: B.
View full solution →Which of the following is approximate value of quartile deviation for standard normal variate?
- A
$\frac{2}{3} \sigma$
- ✓
$\frac{2}{3}$
- C
$\frac{4}{5} \sigma$
- D
$\frac{4}{5}$
Answer: B.
View full solution →Which of the following are mean and variance of standard normal variable ?
Answer: A.
View full solution →Which of the following variable will be an illustration of discrete variable?
- A
- B
- C
Blood pressure of a student
- ✓
Answer: D.
View full solution →Find $f^{\prime}(x)$ if $ (x)=7 x^2-6 x+5$
View full solution →Find the value of $\lim _{x \rightarrow 5}(3 x+5)$
View full solution →What percentage of area is covered under the normal curve within the range $\mu-2 \sigma$ to $\mu+2 \sigma$.
View full solution →'STandard score is independent of unit of measurement'. Is this statement true or false?
Mean of a symmetrical binomial distribution is $9.$ Find the value of its parameter $n$.
View full solution →Find the derivative of $y=\left(3 x^2+4 x-2\right)(3 x+2)$ with respect to $x$.
View full solution →Differentiate $y=(3 x+7)^8$ with respect to $x$.
View full solution →Find the value of $\lim _{x \rightarrow 2} \frac{x^5-32}{x-2}$
View full solution →Find the value of $\lim _{x \rightarrow 1} \frac{2 x^2+x-3}{x^2-1}$ OR Defien the $\delta$ neighbourhood of $a.$
View full solution →The extreme quartiles of a normal variable are $10$ are $30,$ Find its mean deviation.
View full solution →The probability that a person living in a city is a non-vegetarian is $0.20 $. Find the probability of at the most two persons out of $6$ persons randomly selected from the city is non-vegetarian.
View full solution →The probability distribution of the monthly demand of laptop in a store is as follows:
| Demand of laptop |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
| Probability |
$0.10$ |
$0.15$ |
$0.20$ |
$0.25$ |
$0.18$ |
$0.12$ |
View full solution →If $P ( A )=\frac{2}{3}, P ( B )=\frac{3}{5}, P ( B / A )=\frac{3}{4}$ for two events in the sample space of a random experiment, then find $P ( A / B )$.
View full solution →One number is randomly selected from the natural number $1$ to $100 . $ Find the probability that the number selected is either a single digit number or a perfect square.OR Two cities $A$ and $B$ of different states have rains on $60 \%$ and $75 \%$ days respectively during the monsoon. For the cities $A$ and $B$, find the probability on a certain monsoon day $:(1)$ both the cities have rains,$(2)$ at least one city has rains.Note : The events of rains on a day in these two cities are independent.
View full solution →Fit a linear equation from the following data for variable $(y)$ of a time series: $n =5, \Sigma y =190, \Sigma$ ty $=602$.
View full solution →The demand function of a watch is $p=6000-2 x$. Find the demand which maximizes the revenue and also find the corresponding price. OR 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 $f(x)$.
View full solution →Find the value of $\lim _{x \rightarrow 2} \frac{\sqrt{x+7}-3}{x-2}$
View full solution →In a city, daily sale of petrol at a petrol pump follows normal distribution and its mean and standard deviation are $33,000$ litre and $3,000$ litre respectively.
$(1)$ Obtain the percentage of days of a month during which the daily sale of petrol is less than $30,000$ litre.
$(2)$ During the month of May, how many days are exepected so that the sale of petrol is between $32,000$ litre to $35,000$ litre? OR For a group of $1,000$ persons, the average height is $165\ cms$ and variance is $100 ( cms )^2$. The distribution of hieght of these persons follows normal distribution. From this information, determine the third decile and the $60^{\text {th }}$ percentile.
View full solution →$(A)$ Find the proabability of getting vowels in the first, third and sixth place when all the letters of the word $\text{ORANGE}$ are arranged in all possible ways.
$(B)$ Draw the Venn diagram for' events $A-B$ and $A \cap B$.
View full solution →The data about goods transported in different years by a division of railway are given below. Fitting a linear equation find the estiamte for the year $2017:$
| Year |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
$2015$ |
| Good transported |
$180$ |
$192$ |
$195$ |
$204$ |
$202$ |
OR
The quantity index numbers consumption of édible oil in a state are given in the following table. Find the trend using five yearly moving averages :
| Year |
$2005$ |
$2006$ |
$2007$ |
$2008$ |
$2000$ |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
$2015$ |
| Index No. |
$115$ |
$121$ |
$119$ |
$120$ |
$117$ |
$119$ |
$120$ |
$118$ |
$116$ |
$124$ |
$125$ |
View full solution →In order to study the relationship between the repairing time of accident damaged cars and the cost of repair, the fullowing information is collected:
| Repairing time of a car $($man hours$)$ |
$32$ |
$40$ |
$25$ |
$29$ |
$35$ |
$43$ |
| Repairing cost $($thousand $₹)$ |
$25$ |
$35$ |
$18$ |
$22$ |
$28$ |
$46$ |
Obtain the regression line of $Y ($repairing cost$)$ and $X ($repairing time$).$ If the time taken to repair a car is $50$ hours, find an estimate of the repairing cost. View full solution →Find the correlation co-efficient between the density of population and death rate from the following information
$($Use Karl Pearson's method$) :$
| Density $($Per Sq.Km.$) x$ |
$200$ |
$500$ |
$400$ |
$700$ |
$600$ |
$300$ |
| Death rate $($per thousand$) y$ |
$10$ |
$12$ |
$10$ |
$15$ |
$9$ |
$12$ |
View full solution →Compute the Laspayre's, Paasche's and Fisher's index numbers for the year $2016$ from the data given below :
| Item |
Quantity |
price |
| Year $2015$ |
Year $2016$ |
Year $2015$ |
Year $2016$ |
| $A$ |
$25 \ kg$ |
$32 \ kg$ |
$42$ |
$45$ |
| $B$ |
$15$ litre |
$20$ litre |
$28$ |
$30$ |
| $C$ |
$10$ pieces |
$20$ pieces |
$30$ |
$36$ |
| $D$ |
$8$ meter |
$15$ meter |
$20$ |
$25$ |
| $E$ |
$30$ litre |
$36$ litre |
$60$ |
$65$ |
View full solution →