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Board Question Paper : May 2021 Statistics - Board Question Paper : May 2021

Gujarat Board (GSEB) - STD 12 Commerce - Statistics (GSEB - English Medium). 63 questions in this chapter.

Question types

Board Question Paper : May 2021 question types

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

63
Questions
6
Question groups
5
Question types
Sample Questions

Board Question Paper : May 2021 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 $u$ and $v$ are functions of $x$, then what is the formula for derivative of $\frac{u}{v}$ ?
  • A
    $\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^2}$
  • B
    $\frac{v \frac{d u}{d x}+u \frac{d v}{d x}}{v^2}$
  • ✓
    $\frac{u \frac{d u}{d x}-v \frac{d v}{d x}}{u^2}$
  • D
    $\frac{u \frac{d u}{d x}+v \frac{d v}{d x}}{u^2}$

Answer: C.

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Q 2MCQ1 Mark
If $y=a x+b, a$ and $b$ are constant then what will be $\frac{d y}{d x}$ ?
  • ✓
    $a$
  • B
    $b$
  • C
    $a+b$
  • D
    $a+b$

Answer: A.

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Q 3MCQ1 Mark
What is the interval form of $0.02$ neighbourhood of $-2 ?$
  • A
    $(1.98,2.02)$
  • B
    $(-1.98,2.02)$
  • C
    $ (-2.02, -1.98)$
  • ✓
    $(-2.02,1.98)$

Answer: D.

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Q 5MCQ1 Mark
Which of the following is probability density function for standard normal variable$?$
  • A
    $f(z)=e^{-1 / 2 z^2} ;-\infty$
  • ✓
    $f(z)=\frac{1}{\sqrt{2 \pi}} e^{-1 / 2 z^2} ;-\infty$
  • C
    $f(z)=\frac{1}{\sqrt{2 \pi}} e^{-1 / 2 z^2} ; 0$
  • D
    $f(z)=\frac{1}{\sqrt{2 \pi}} e^{-z^2} ;-\infty$

Answer: B.

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Q 132 Marks Each2 Marks
Find parameters of the binomial distribution where mean $=4$ and variance $=2$. Express $|3 x+1|<2$ in neighbourhood and interval form.
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Q 163 Marks Each3 Marks
Following results are obtained for a bivariate data :
Particulars $x$ $y$
No. of observations $8$
Sum of squares of deviations taken from Mean $130$ $145$
Sum of product of deviations taken from Mean $115$
Mean $100$ $100$
Obtain the regression line of $y$ on $x$.
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Q 173 Marks Each3 Marks
The information of price $($in $₹)$ of a pen and the supply of pen $($in units$),$ at the end of each month of a year for a company is given below. Estimate the supply of pen when its price is $₹ 40$.
Detail Price $(x)$ Supply $(y)$
Average $30$ $500$
variance $25$ $10,000$
$r = 0.8$
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Q 183 Marks Each3 Marks
An official has ranked nine villages of a sample on the basis of the work done in the area of 'Swachchata Abhiyan' and 'Beti Bachao Ablliyan' by the villages. The ranks are as given below
Village $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
Rank forSwachchata Abhiyan $4$ $8$ $7$ $1$ $9$ $5$ $6$ $2$ $3$
Rank for Beti Bachao Abhiyan $6$ $8$ $5$ $1$ $9$ $7$ $3$ $4$ $2$
Find Rank Correlation Coefficient between the performances of the villages In in two Abhiyans.
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Q 193 Marks Each3 Marks
The data about bi-monthly closing prices of shares of a company in the year $2020$ is given below. Compute the Chain base index number :
Month January March May July September November
price(₹) $22$ $21.20$ $22$ $23$ $24.70$ $26$
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Q 214 Marks Each4 Marks
The profit function of a producer is $40 x+10000-0.1 x^2$. At what production is the profit maximum? Also find this maximum profit.
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Q 224 Marks Each4 Marks
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 $f(x)$.
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Q 244 Marks Each4 Marks
The number of students in classes of higher secondary schools of a city follows normal distribution. Average number of students in the classes is $50$ and standard deviation is $15 .$ If a class is selected at random, then find the following probabilities $(1)$ a class consists of more than $68$ students. $(2)$ a class consists of less than $32$ students.
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Q 254 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.
$(B)$ An amount of purchase of a customer in a Mall of a city follows normal distribution with mean $₹ 800$ and standard deviation $₹ 200$. If a customer is selected at random, then find the probability that the amount of purchases made by him is in between $₹ 850$ to $₹ 1,200$.
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Q 265 Mark Each5 Marks
Find the trend using five yearly moving averages from the following data of profit $($in lakh $₹),$ of a trader, in different years.
Year $2012$ $2013$ $2014$ $2015$ $2016$ $2017$ $2018$ $2019$ $2020$
Profit $($in lakh $₹)$ $15$ $14$ $18$ $20$ $17$ $24$ $27$ $25$ $23$
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Q 275 Mark Each5 Marks
The profit earned $($in lakh $₹)$ by a company making computers is as follows. Find the linear equation for the trend from this data by least square method and estimate the profit for the year $2020 .$
Year $2014$ $2015$ $2016$ $2017$ $2018$
Profit $($in lakh $₹)$ $31$ $35$ $39$ $41$ $44$
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Q 285 Mark Each5 Marks
To know the relationship between the height of father and son, obtain the regression line of height of son on the height of father from the following information of eight pairs of fathers and adult sons :
Height of father $(cm)x$ $167$ $169$ $171$ $168$ $173$ $166$ $167$ $165$
Height of son $(cm ) y$ $158$ $170$ $169$ $172$ $170$ $168$ $164$ $167$
Estimate the height of a son whose father's height is $170 \ cm$.
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Q 295 Mark Each5 Marks
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 $50$ $75$ $60$ $85$ $90$ $40$ $65$ $30$ $45$ $70$


 
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Q 305 Mark Each5 Marks
For six different cities of Gujarat state, the approximate figures regarding their density of population $($per square $km)$ and the death rate $($per thousand$)$ are as given below :
City $A$ $B$ $C$ $D$ $E$ $F$
Density $($per sq.km$.)$ $250$ $500$ $450$ $700$ $600$ $300$
Death rate$($per thousand$)$ $10$ $12$ $10$ $15$ $9$ $12$
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