Mathematics Class XI

Question 1 of 25

1. Question
1 point(s)
The median and standard deviation of distribution are $ 20 $ and $ 4 $ respectively. If each item is increased by $ 2 $, the new median is _______
- $ 20 $
- $ 22 $
- $ 24 $
- $ 26 $
Correct

Incorrect

Hint

Since each value is increased by $2$ , therefore the median value is also increased by $2$ .
So, median $=20+2=22$
Question 2 of 25

2. Question
1 point(s)
Range of the data $ 4,7,8,9,10,12,13 $ and $ 17 $ is_______
- $ 4 $
- $ 17 $
- $ 13 $
- $ 21 $
Correct

Incorrect

Hint

Maximum value $=17$
Minimum value $=4$
$\begin{aligned} \text{Range}&=\text{Max. value}-\text{Min. value}\\&=17-4=13 \end{aligned}$
Question 3 of 25

3. Question
1 point(s)
If the difference of male and median of data is $ 24 $, then the difference of median and mean is________
- $ 12 $
- $ 24 $
- $ 8 $
- $ 36 $
Correct

Incorrect

Hint

$\begin{aligned} &\text{Mode}-\text{Median}=24\\&\Longrightarrow \text{Mode}=\text{Median}+24\\&\text{Mode}=3\text{Median}-2\text{Mean}\\&\Longrightarrow \text{Median}+24=3\text{Median}-2\text{Mean}\\&\Longrightarrow 2\text{Median}-2\text{Mean}=24\\&\Longrightarrow \text{Median}-\text{Mean}=12 \end{aligned}$
Question 4 of 25

4. Question
1 point(s)
If $ r $ is the correlation coefficient, then ________
- $ |r|\leq 1 $
- $ |r|\geq 1 $
- $ r\leq 1 $
- $ r\geq 1 $
Correct

Incorrect

Hint

If $r$ is the correlation coefficient then $|r|\leq 1$
Question 5 of 25

5. Question
1 point(s)
The median and standard deviation of a distribution are $ 24 $ and $ 8 $ respectively. If each item is decreased by $ 4 $, the new median and standard deviation are________
- $ 24,4 $
- $ 20,4 $
- $ 20,8 $
- $ 24,8 $
Correct

Incorrect

Hint

Since each value is decreased by $4$ , therefore the median value is also decreased by $4$ .
So, new median $=24-4=20$
Variance is independent of the change of origin, hence SD remains same.
$\therefore\text{Median}=20,SD=8$
Question 6 of 25

6. Question
1 point(s)
If the standard deviation of the data is $ 9 $, then variance is _______
- $ 9 $
- $ 18 $
- $ 81 $
- None of these
Correct

Incorrect

Hint

$\begin{aligned} SD(\sigma)&=9\\\text{Variance}(\sigma^2)&=9^2=81 \end{aligned}$
Question 7 of 25

7. Question
1 point(s)
If the mean of the following data is $ 20.6 $, then the value of $ P $ is______
- $ 10 $
- $ 15 $
- $ 30 $
- $ 20 $
Correct

Incorrect

Hint

$\begin{aligned} &\text{Mean}\ (\overline{x})=\dfrac{\Sigma f_ix_i}{\Sigma f_i}\\&\Longrightarrow 20.6=\dfrac{30+150+25P+175+175}{50}\\&\Longrightarrow 20.6\times 50=530+25P\\&\Longrightarrow 25P=1030-530=500\\&\Longrightarrow P=\dfrac{500}{25}=20 \end{aligned}$
Question 8 of 25

8. Question
1 point(s)
The mean of first $ n $ natural numbers is $ \dfrac{5n}{9} $, then $ n $ is_______
- $ 5 $
- $ 4 $
- $ 9 $
- $ 10 $
Correct

Incorrect

Hint

Mean of first $'n'$ natural numbers
$\begin{aligned} &=\dfrac{n(n+1)}{2n}=\dfrac{n+1}{2}\\&\Longrightarrow \dfrac{n+1}{2}=\dfrac{5n}{9}\\&\Longrightarrow 9n+9=10n\\&\Longrightarrow n=9 \end{aligned}$
Question 9 of 25

9. Question
1 point(s)
If one of the observation is zero, then geometric mean is ________
- $ \dfrac{(\text{Sum of Observation})}{n} $
- $ (\text{Multiplication of Observation})^n $
- $ (\text{Multiplication of observation})^{\frac{1}{n}} $
- $ 0 $
Correct

Incorrect

Hint

Let the observations are $0,a,b,c,...$ up to $n$
Now, geometric mean
$\begin{aligned} &=(0\times a\times b\times c\times...\text{up to}\ n)^{\frac{1}{n}}\\&=0^{\frac{1}{n}}=0 \end{aligned}$
Question 10 of 25

10. Question
1 point(s)
Which is measure of dispersion method?
- Range
- Quartile Deviation
- Mean Deviation
- All of above
Correct

Incorrect

Hint

Range, quartile deviation, mean deviation all are the measure of dispersions method.
Question 11 of 25

11. Question
1 point(s)
If a variable takes discrete values $ x+4,~x-\dfrac{7}{2},~x-\dfrac{5}{2},~x-3,~x-2,~x+\dfrac{1}{2},~x-\dfrac{1}{2},~x+5(x > 0) $, then the median is_______
- $ x-\dfrac{1}{2} $
- $ x-\dfrac{5}{4} $
- $ x-2 $
- $ x+\dfrac{5}{4} $
Correct

Incorrect

Hint

Arranging the discrete values in ascending order, we have $x-\dfrac{7}{2},x-3,x-\dfrac{5}{2},x-2,x-\dfrac{1}{2},x+\dfrac{1}{2},x+4,x+5$ .
Total observations $=8$
Median $=$ AM of $4^{th}$ and $5^{th}$ observations
$\begin{aligned} &=\text{AM of}\ (x-2)\ \text{ and }\ \left( x-\dfrac{1}{2} \right)\\&=\dfrac{x-2+x-\dfrac{1}{2}}{2}=\dfrac{2x-\dfrac{5}{2}}{2}\\&=x-\dfrac{5}{4} \end{aligned}$
Question 12 of 25

12. Question
1 point(s)
If co-variance between two variable is $ 0 $, then the correlation coefficient between them is______
- $ 0 $
- Nothing can be said
- Positive
- Negative
Correct

Incorrect

Hint

$\begin{aligned} r_{(x,y)}&=\dfrac{\text{Cov}(x,y)}{(S_x\times S_y)}\\r_{(x,y)}&=\text{Correlation of the variable}\ x\ \text{and}\ y\\\text{Cov}(x,y)&=\text{Covariance of the variables}\ x\ \text{and}\ y\\S_x&=\text{Sample S.D. of the random variable}\ x\\S_y&=\text{Sample S.D. of the random variable}\ y \end{aligned}\\\begin{aligned} &\text{Given,Cov}(n,y)=0\\&\text{Then}\ r(x,y)=0 \end{aligned}$
Question 13 of 25

13. Question
1 point(s)
Variance is indipendent of change of _______
- Origin only
- Scale only
- Origin and Scale both
- None of these
Correct

Incorrect

Hint

Variance is independent of change of origin only.
Question 14 of 25

14. Question
1 point(s)
Let $ x_1,x_2,…,x_n $ be $ n $ observations and $ \overline{x} $ be the arithmetic mean. Then standard deviation is_______
- $ \Sigma(x_1-\overline{x})^2 $
- $ \Sigma(x_i-\overline{x})^{\frac{2}{n}} $
- $ \sqrt{\Sigma(x_i-\overline{x})^{\dfrac{2}{n}}} $
- None of these
Correct

Incorrect

Hint

$\begin{aligned} &\text{Mean}=\overline{x}\\&\text{SD}=\sqrt{\dfrac{\Sigma x_i-\overline{x}}{n}} \end{aligned}$
Question 15 of 25

15. Question
1 point(s)
The mean of a group of $ 100 $ observations was found to be $ 20 $. Later on, it was founded that three observations were incorrect, which was recorded as $ 21,21 $ and $ 18 $. Then the mean if the incorrect observation are omitted_______
- $ 18 $
- $ 20 $
- $ 22 $
- $ 24 $
Correct

Incorrect

Hint

$\begin{aligned} &\Sigma\dfrac{x_i}{100}=20\Longrightarrow \Sigma x_i=2000\\&3\ \text{observations}21,21\ \text{and}\ 18\ \text{are recorded incorrectly.}\\&\text{So}\ \Sigma x_i=2000-21-21-18=1940 \end{aligned}\\\begin{aligned} \text{Now Mean}&=\dfrac{\Sigma x_i}{97}\\&=\dfrac{1940}{97}=20 \end{aligned}$
Question 16 of 25

16. Question
1 point(s)
Range of a data is calculated as_______
- Max Value $ + $ Min Value
- Max Value $ – $ Min Value
- $ \dfrac{\{\text{max value}+\text{Min value}\}}{2} $
- $ \dfrac{\{\text{max value}-\text{Min value}\}}{2} $
Correct

Incorrect

Hint

$\text{Range}=\text{Max.value}-\text{Min value}$
Question 17 of 25

17. Question
1 point(s)
If the variance of the data is $ 169 $ then the standard deviation of the data is______
- $ 11 $
- $ 12 $
- $ 13 $
- $ 15 $
Correct

Incorrect

Hint

$\begin{aligned} \text{Varience}(\sigma^2)&=169\\\text{SD}(\sigma)&=\sqrt{169}=13 \end{aligned}$
Question 18 of 25

18. Question
1 point(s)
The mean deviation from the mean for the following data: $ 4,7,8,9,10,12,13 $ and $ 17 $ is
- $ 2 $
- $ 3 $
- $ 4 $
- $ 5 $
Correct

Incorrect

Hint

$\begin{aligned} \text{Mean}&=\dfrac{1}{8}\{ 4+7+8+9+10+12+13+17 \}\\&=\dfrac{80}{8}=10\\|x_i-\text{Mean|}&=|4-10|+|7-10|+|8-10|+|9-10|+|10-10|+|+|12-10|+|13-10|+|17-10|\\&=6+3+2+1+0+2+3+7\\&=24\\\therefore MD&=\dfrac{|x_i-\text{Mean}|}{n}=\dfrac{24}{8}=3 \end{aligned}$
Question 19 of 25

19. Question
1 point(s)
The mean of $ 1,3,4,5,7,4 $ is $ m $, the numbers $ 3,2,2,4,3,3,P $ have mean $ m=1 $ and median $ q $. Then $ P+q= $______
- $ 4 $
- $ 5 $
- $ 6 $
- $ 7 $
Correct

Incorrect

Hint

$\begin{aligned} &\dfrac{1+3+4+5+7+4}{6}=m\Rightarrow m=\dfrac{24}{6}=4\\&\dfrac{3+2+2+4+3+3+P}{7}=m-1\Longrightarrow \dfrac{17+P}{7}=4-1\\&\Longrightarrow 17+P=21\Longrightarrow P=4\\&\text{The numbers}\ 2,2,3,3,3,4,4\ \text{have median}\ q.\\&\Longrightarrow \dfrac{(7+1)}{2^{th}}\text{term}=q\\&\Longrightarrow 4^{th}\text{term}=q\\&\Longrightarrow q=3\\&\therefore P+q=4+3=7 \end{aligned}$
Question 20 of 25

20. Question
1 point(s)
If the difference between mode and median of a data is $ 12 $, then the difference of median and mean is_______
- $ 6 $
- $ 8 $
- $ 12 $
- $ 10 $
Correct

Incorrect

Hint

$\begin{aligned} &\text{Mode}-\text{Median}+12\\&\Longrightarrow \text{Mode} =\text{Median}+12\\&\text{Mode}=3\text{Median}-2\text{Mean}\\&\Longrightarrow \text{Median}+12=3\text{Median}-2\text{Mean}\\&\Longrightarrow 2\text{Median}-2\text{Mean}=12\\&\Longrightarrow \text{Median}-\text{Mean}=\dfrac{12}{2}=6 \end{aligned}$
Question 21 of 25

21. Question
1 point(s)
The geometric mean of series having mean $ =25 $ and harmonie mean $ =16 $ is_______
- $ 16 $
- $ 20 $
- $ 25 $
- $ 30 $
Correct

Incorrect

Hint

$\begin{aligned} &GM^2=AM\times HM\\&\Longrightarrow GM^2=25\times16=400\\&\Longrightarrow GM=\sqrt{400}=20 \end{aligned}$
Question 22 of 25

22. Question
1 point(s)
Mean of the first $ ‘n’ $ terms of the arithmetic progression $ a+(a+d)+(a+2d)+… $ is________
- $ a+\dfrac{nd}{2} $
- $ a+(n-1)d $
- $ a+\dfrac{(n-1)d}{2} $
- $ a+nd $
Correct

Incorrect

Hint

Mean of the first $'n'$ terms of the
$\begin{aligned} AP&=\dfrac{1}{n}\{ a+(a+d)+(a+2d)+...+[a+(n-1)d] \}\\ &=\dfrac{1}{n}\left[ \dfrac{n}{2}\{ 2a+(n-1)d \} \right]\\&=\dfrac{1}{2}\{ 2a+(n-1)d \}\\&=a+\dfrac{(n-1)d}{2} \end{aligned}$
Question 23 of 25

23. Question
1 point(s)
In a series, the coefficient of variation is $ 50 $ and standard deviation is $ 20 $, then the arithmetic mean is________
- $ 20 $
- $ 40 $
- $ 50 $
- $ 60 $
Correct

Incorrect

Hint

$\begin{aligned} &\dfrac{SD}{AM}\times 100=CV\\&\Longrightarrow \dfrac{20}{AM}\times 100=50\\&\Longrightarrow \dfrac{20}{AM}=\dfrac{50}{100}\\&\Longrightarrow AM=2\times 20=40\\&\text{So, the AM is}\ 40 \end{aligned}$
Question 24 of 25

24. Question
1 point(s)
If the correlation coefficient between two variables is $ 1 $, then the two least squares of regression are________
- Parallel
- at right angles
- Coincident
- None of these
Correct

Incorrect

Hint

If the correlation coefficient between two variable is $1$ , then the two least square lines of regression are coincident.
Question 25 of 25

25. Question
1 point(s)
The geometric mean of having mean $ 18 $ and harmonic mean $ =8 $ is________
- $ 8 $
- $ 9 $
- $ 10 $
- $ 12 $
Correct

Incorrect

Hint

$GM^2=AM\times HM\\\begin{aligned}\Longrightarrow GM^2&=18\times 8\\&=144\end{aligned}\\\Longrightarrow GM=\sqrt{144}=12$