Sample QuestionsModel Paper 6 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the relation $R$ in the set $\{1,2,3,4\}$ given by $R=\{(1,1),(1,2),(1,4),(3,1),(3,2),(4,3),(4,2)\}$ then domain of $R$ is given by
Answer: D.
View full solution →In how many ways can we select 9 balls out of 6 red balls, 5 white balls and 5 blue balls if 3 balls of each colour are selected?
Answer: A.
View full solution →The compound interest on ₹ 30,000 at $7 \%$ per annum is ₹ 4347 . This period (in years) is:
Answer: A.
View full solution →A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
- A
$\frac{1}{4}$
- ✓
$\frac{23}{24}$
- C
$\frac{15}{24}$
- D
$\frac{11}{24}$
Answer: B.
View full solution →X and Y are independent events such that $\mathrm{P}(\mathrm{X} \cap \overline{\mathrm{Y}})=\frac{2}{5}$ and $\mathrm{P}(\mathrm{X})=\frac{3}{5}$. Then $\mathrm{P}(\mathrm{Y})$ is equal to:
- A
$\frac{2}{3}$
- ✓
$\frac{1}{3}$
- C
$\frac{1}{5}$
- D
$\frac{2}{5}$
Answer: B.
View full solution →Assertion (A): If 5 th term of a G.P. is 9 and 11 th term is 16 , then 8 th term is 12 .
Reason (R): In a G.P., $\mathrm{a}_{\mathrm{n}}=\frac{a_{n-k}+a_{n+k}}{2}, \mathrm{n}, \mathrm{k} \in \mathrm{N}$.
View full solution →Assertion(A): For a distribution, if $\Sigma x_{i}^{2}=232, \Sigma x_{i}=16$ and $n=8$, then standard deviation (S.D.) is 5 .
Reason(R): Standard deviation (S.D.) $=\sqrt{\frac{\Sigma x_{i}^{2}}{n}-\left(\frac{\Sigma x_{i}}{n}\right)^{2}}$.
Answer: A.
View full solution →Convert the given decimal number 569 to the binary number.
Differentiate the following function w.r.t. $\mathrm{x}: \frac{\sqrt{x^{2}+1}-x}{\sqrt{x^{2}+1}+x}$
View full solution →Find the derivative of $\frac{x}{2 x+1}$, with respect to x .
View full solution →In covering a distance of 40 km Sachin takes 3 hours more than Utkarsh. If Sachin doubles his speed then he would take 1 hour less than Utkarsh. Find their speeds.
If $A$ and $B$ are two sets such that $n(A)=37, n(B)=26$ and $n(A \cup B)=51$, find $n\{A \cap B)$.
View full solution →Find the correlation coefficient between the heights of husbands and wives based on the following data (given in inches) and interpret the result.
| Couple | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Height of hushand | 76 | 75 | 75 | 72 | 72 | 71 | 71 | 10 | 68 | 68 | 68 | 68 | 67 | 67 | 62 |
| Height of wife | 71 | 70 | 70 | 67 | 71 | 65 | 65 | 67 | 64 | 65 | 65 | 66 | 63 | 65 | 61 |
The population of a town in the year 2014 was 150,500 . If the annual increasing during three successive years he at the rate of $7 \%, 8 \%$ and $6 \%$ respectively, find the population at the end of 2017.
View full solution →Divide ₹ 21866 into two parts such that the amount of one in 3 years is same as the amount of the second in 5 years, the rate of compound interest being $5 \%$ per annum.
View full solution →If $\mathrm{A}=[1,2,3]$ and $\mathrm{f} g, \mathrm{~h}$ and s are relations corresponding to the subsets of $\mathrm{A} \times \mathrm{A}$ indicated against them,
which of $f, g, h$ and $s$ are functions? In case of a function, find its domain and range.
i. $\mathrm{f}=\{(2,1),(3,3)\}$
ii. $g=\{(1,2),(1,3),(2,3),(3,1)\}$
iii. $\mathrm{h}=\{(1,3),(2,1),(3,2)\}$
iv. $s=\{(1,2),(2,2),(3,1)\}$
View full solution →Find the foot of the perpendicular from the point $(3,8)$ to the line $x+3 y=7$.
View full solution →Find the equations of two straight lines passing through $(1,2)$ and making an angle of $60^{\circ}$ with the line $x+y=$ [5]0 . Find also the area of the triangle formed by the three lines.
View full solution →Find the mean deviation about the mean for the data
| Income per day in ₹ | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 |
| Number of persons | 4 | 8 | 9 | 10 | 7 | 5 | 4 | 3 |
Calculate Karl Pearson's coefficient of skewness for the following data:
| CI | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| r | 3 | 6 | 9 | 7 | 4 | 2 |
Evaluate: $\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x}$
View full solution →$60 \%$ students read Hindi newspaper, $40 \%$ students read Tamil newspaper and $20 \%$ students read both Hindi and Tamil newspaper. Find the probability that a student selected at random reads
i. Tamil newspaper given that he has already read Hindi newspaper.
ii. Hindi newspaper given that he has already read Tamil newspaper.
iii. neither Hindi nor Tamil newspaper.
View full solution →Out of 7 boys and 5 girls a team of 7 students is to be made.
(a) Find the number of ways, if team contain at least 3 girls.
(b) Find the number of ways, if team contain exactly 3 girls.
(c) if exactly 3 girls are selected and are arranged in a row for photograph. Find number of ways if all girls and all the boys will stand together.
(d) The number of ways to arrange 3 girls and 4 boys if no two boys and girls will stand together.
