3 Marks Each

Question 13 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.

Answer

$0.3446$

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Question 23 Marks

Find constant $C$ for the following discrete probability distribution. Hence obtain mean and variance of this distribution.$p(x)=C \cdot 4 p_x, x=0,1,2,3,4 \text {. }$

Answer

$\frac{3964}{4225}$

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Question 33 Marks

Two balanced dice are thrown simultaneously. Find the probability that the sum of numbers on two dice is a multiple of $2$ or $3.$

Answer

$2$ or $3=\frac{2}{3}$

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Question 43 Marks

A problem in Mathematics is given to Dhyan, Kaushal and Namrata to solve. The probabilities of them solving the problem correctly are $\frac{2}{3}, \frac{3}{4}$, and $\frac{1}{2}$ respectively. Find the probability that the problem is solved correctly.OR $4$ couples $($husband-wife$)$ attend a party. Two persons are randomly selected from these $8$ persons. Find the probability that the selected two persons are, $(1)$ husband and wife, $(2)$ One man and one woman who are not husband and wife. Find the probability.

Answer

$(1)\ P ( A )=\frac{m}{n}=\frac{4}{28}=\frac{1}{7}$.
$(2)\ P ( A )=\frac{m}{n}=\frac{16}{28}=\frac{4}{7}$

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Question 53 Marks

Obtain the linear equation for trend for a time seiies with $11:8, Zy=344,2t: 1342$

Answer

$\hat{ y }=65.05-4.9 t$

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Question 63 Marks

If by $y_x=0.8$, then find the value of $b_{v u}$ for the following $u$ and $v$.
$(i)\ u=x-105$ and $v=y-90$.
$(ii)\ u=\frac{ x -1400}{100}$ and $v=\frac{ y -750}{50}$
$(iii)\ u=10(x-4.6)$ and $v=y-75$ OR
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 taluka of Gujarat.

Particulars	Rainfall $(cm.)$ $(X)$	Yield Of size $(Y)$ $($Quintal per hectare$)$
Mean	$82$	$180$
Variance	$64$	$225$

Correlation coefficient $= 0.82$ Obtain the regression lire of $Y$ on $X.$ Estimate the yield of maize when the rainfall is $60 \ cm.$

Answer

$(i)\ 0.8$
$(ii)\ 0.16$
$(iii)\ 0.8$ OR $a=53.72$

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Question 73 Marks

To know the relation between understanding of students in the subject Of Economics and their dancing skill, a sample of eight students is taken and a test is conducted for them. The marks obtained are given below.
Find the tank correlation coefficient between the mat ks obtained in two subjects.

Marks in Economics	$60$	$30$	$10$	$20$	$30$	$50$	$30$	$40$
Marks in Dancing skill	$80$	$20$	$60$	$40$	$12$	$28$	$20$	$15$

Answer

$r =0$

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Question 83 Marks

The chain base index numbers obtained for food items from the year $2010-11$ to $2015-16$ are as follows. Compute the fixed base index numbers. $($Take $2009-10$ as base year$)$

Year	$2010-11$	$2011-12$	$2012-13$	$2013-14$	$2014-15$	$2015-16$
Index number of food items	$134.8$	$115.28$	$115.57$	$107.29$	$109.91$	$112.80$

Answer

Index number $134.8 ; 155.40 ; 179.60$; $192.69 ; 211.79 ; 238.9$

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Statistics 3 Marks Each

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