Question types

‘Board Question Paper : March 2022 question types

60 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.

60
Questions
6
Question groups
5
Question types
Sample Questions

‘Board Question Paper : March 2022 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If $y=a x+b, a$ and $b$ are constant then what will be $\frac{d y}{d x}$ ?
  • $a$
  • B
    $b$
  • C
    $b$
  • D
    0

Answer: A.

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Q 2MCQ1 Mark
What is the value of $\lim _{x \rightarrow 3} \frac{x^4-81}{x-3}$.
  • A
    $192$
  • B
    $324$
  • C
    $36$
  • $108$

Answer: D.

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Q 3MCQ1 Mark
What is the value of $\lim _{x \rightarrow-2} 10$ ?
  • $10$
  • B
    $-2$
  • C
    $8$
  • D
    Indeterminate

Answer: A.

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Q 4MCQ1 Mark
If the distribution of normal variable is shown as $N(20,4)$ then which of the following intervals includes $99.73 \%$ of observations?
  • A
    $(18,22)$
  • B
    $(16,24)$
  • $(14,26)$
  • D
    $(12,28)$

Answer: C.

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Q 5MCQ1 Mark
What is the area under the normal curve to the left hand side of perpendicular line $\mu$ ?
  • A
    $0$
  • $0.5$
  • C
    $1$
  • D
    $-0.5$

Answer: B.

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Q 142 Marks Each2 Marks
The mean and variance of a binomial distribution are $3.9$ and $2.73$ respectively. Find the number of Bernouli trials conducted in this distribution.
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Q 152 Marks Each2 Marks
Find the probability of getting $D$ in the first place in all possible arrangements of cach and every letter of the word DHYAN.
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Q 163 Marks Each3 Marks
The following information is obtained for monthly advertisement cost and the sales of the last year for a company providing online shopping.
particulars Advertisement cost $($Ten thousand$)$ Sales $($Lakh $₹)$
mean $10$ $90$
Standard deviation $3$ $12$
$r = 0.8$
Obtain the regression line of the sales on the advertisement cost.
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Q 173 Marks Each3 Marks
The details of expenditure on clothing for the worker class of a region are as follows. Find the index number for clothing by Family Budget Method.
Item Saree Dhoti shirting other
Unit Piece piece meter Meter
Quantity in year $2020$ $5$ $8$ $20$ $15$
Price in year $2020 (₹)$ $300$ $70$ $32.40$ $20.90$
Price in year $2021 (₹)$ $400$ $100$ $38$ $23.80$
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Q 183 Marks Each3 Marks
The probability that a bomb dropped from a plane over a bridge will hit the bridge is $\frac{1}{5}$. Two bombs are enough to destroy the bridge. If $6$ bombs are dropped on the bridge, find the probability that the bridge will be destroyed.
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Q 193 Marks Each3 Marks
For three mutually exclusive and exhaustive events $A , B$ and $C$ in the sample space of a random experiment $2 P ( A )=3 P ( B )=4 P ( C )$. Find $P ( B \cup C )$.
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Q 203 Marks Each3 Marks
If two balanced coins are tossed, then find the probability of $(1)$ getting one head and one tail $(2)$ getting at least one head.
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Q 214 Marks Each4 Marks
A producer produces $x$ units at cost $200 x+15 x^2$. The demand function is $P =$ $1200-10 x$. Find the profit function and how many units should be produced for maximum profit.
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Q 234 Marks Each4 Marks
The weight of randomly selected $500$ adult persons from a region of a city follows normal distribution. The average weight of these persons in $55 \ kg$ and its standard deviation is $7\ kg :(i)$ Estimate the number persons having weight between $41 \ kg$ to $62 \ kg. (ii)$ Estimate the percentage of persons having weight less than $41 \ kg$.
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Q 244 Marks Each4 Marks
$(A)$ For a normal distribution, the first quartile and the mean deviation are $20$ and $24$ respectively. Obtain an estimate of the value of mode.
$(B)$ The monthly production of units in a factory is normally distributed with mean $u$ and standard deviation $\sigma$. The $Z$ scores corresponding to the production of $2400$ units and $1800$ units are $1$ and $-0.5$ respectively. Find its mean and standard deviation.
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Q 255 Mark Each5 Marks
Find the trend using four monthly moving averages for the following data showing monthly sales $($in lakhs $₹)$ of a shop.
month Sales $($lakh $₹)$
march $5$
April $3$
May $7$
June $6$
July $4$
August $8$
September $9$
October $10$
November $8$
December $9$
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Q 265 Mark Each5 Marks
The information about death rate of a state in different years is given in the following table. Fit a linear equation to find trend and hence estimate the death rate for the year $2023.$
year $2015$ $2016$ $2017$ $2018$ $2019$ $2020$ $2021$
Death rate $7.6$ $6.9$ $7.1$ $7.3$ $7.2$ $6.9$ $6.9$

 
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Q 275 Mark Each5 Marks
The monthly sale of different types of laptops $($in hundred units$)$ and its profit $($in lakh $₹)$ for the last six months for a company is given below :
month $1$ $2$ $3$ $4$ $5$ $6$
Number of laptops sold $($hundred units $x)$ $5$ $7$ $5$ $12$ $8$ $3$
Profit $($lakh $₹ y)$ $8$ $9$ $10$ $15$ $10$ $6$
Obtain the regression line of $Y$ on $X$. Also, estimate $Y$ for $X =7$.
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Q 285 Mark Each5 Marks
From the following information of heights of husband and wife, Calculate the rank correlation coefficient between their heights.
Height of husband $(cms)$ $156$ $153$ $185$ $157$ $163$ $191$ $162$
Weight of wife $( cms )$ $154$ $148$ $162$ $157$ $162$ $170$ $154$
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Q 295 Mark Each5 Marks
From the following information, find correlation coefficient between heights and weights.
Height $(cm) x$ $155$ $165$ $158$ $162$ $153$ $160$
Weight $(cm) y$ $53$ $63$ $56$ $60$ $52$ $60$
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