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10 questions · timed · auto-graded

Question 11 Mark
Find $f^{\prime}(x)$ for the function $f(x)=21$.
Answer
Derivate of constant number is always zero. So, if function$f(x)=21 \text { the } f^{\prime}(x)>0 .$
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Question 21 Mark
Find the value of $\lim _{x \rightarrow 4} \frac{x^4-81}{x-3}$
Answer
${\left[\lim _{x \rightarrow 3} \frac{x^n-a^n}{x a}=n^{n-1}\right]} \\\lim _{x \rightarrow 3} 4 .(3)^{4-1} ; \quad \lim _{x \rightarrow 3} 4 \cdot(3)^3=108$
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Question 31 Mark
Mean of a normal distribution is $13.25$ and its standard deviation is $10.$ Estimate the value of its third quartile.
Answer
$\lim _{x \rightarrow 3} \frac{x^4-81}{x-3} ; \lim _{x \rightarrow 3} \frac{x^4-3^4}{x-3}$
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Question 41 Mark
Standard score is independent of unit of measurement. Is this statement true or false?
Answer
"Standard score is independent of unit of measurement."
It is a true statement.In a normal distribution $Q _3= m +$ $0.675 \sigma$.
Therefore, $Q _3=13.25+0.675(10)$ $-13.25+6.75=20$.
Thus, estimate value of its third quartile is $20 .$
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Question 51 Mark
State the relation between mean and variance of binomial distribution.
Answer
In binomial distribution value of mean is always greater than its variance.
Hence, $n p>n p q$ OR $n p q$
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Question 61 Mark
State the number of sample points of the random experiment of tossing six balanced coins.
Answer
The number of sample points in the random experiment of tossing six balanced coins is $n=2^6=64$.
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Question 71 Mark
Write the additive model of the time series.
Answer
The additive model of the time series is as follows : $y_t= T _{ t }+ {S _{ t }}^i+ C _{ t }+ R _{ t }$
where, $y_t=$ Variable quantity,
$T _{ t }=\text { Trend, } $
$S _{ t }=\text { Seasonal Component, }$
$C _{ t }=\text { Cyclical component, } $
$R _{ t }=\text { Random component. }$
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Question 81 Mark
The regression co-efficient is independent of which transformation?
Answer
The regression co-efficient is independent from the change of origin.
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Question 91 Mark
Defien correlation.
Answer
If there are simultaneous changes in the values of two variables due to direct or indirect cause effect then it is said that there is correlation between two variables.
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Question 101 Mark
What is a base year ?
Answer
When the price of an item is compared with the price of the same item in some specific $($fixed$)$ year of the past, then that specific year is called the base year.
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1 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip