Let $A=\{1,2,3\}$, then the domain of the relation $R=\{(1,1),(2,3),(2,1)\}$ defined on $A$ is
- A$\{1,3\}$
- ✓$\{1,2\}$
- CNone of these
- D$\{2,3\}$
Answer: B.
View full solution →Question types
Model Paper 8 question types
43 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
43
Questions
6
Question groups
5
Question types
01
MCQ
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
7 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 8 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
20 students can compete for a race. The number of ways in which they can win the first three places is (given that no two students finish in the same place).
- A1140
- B8000
- ✓6840
- D6000
Answer: C.
View full solution →The present value of an annuity of ₹ 3993 payable at the end of each year for 3 years, if money is worth $10 \%$ effective.
- A₹ 9039
- B₹ 9903
- ✓₹ 9930
- D₹ 9390
Answer: C.
View full solution →If $A$ and $B$ are independent events, then $P(A \cap B)$ is equal to:
- A$\frac{P(A)}{P(B)}$
- ✓$\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B})$
- C$P(A)-P(B)$
- D$P(A)+P(B)$
Answer: B.
View full solution →There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads $75 \%$ of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?
- ✓$\frac{4}{9}$
- B$\frac{5}{9}$
- C$\frac{1}{9}$
- D$\frac{2}{9}$
Answer: A.
View full solution →Assertion (A): If the product of positive real numbers $a, b, c$ is 27 , then minimum value of $a+b+c$ is 9 .
Reason (R): For positive real numbers, A.M. $\leq$ G.M.
Reason (R): For positive real numbers, A.M. $\leq$ G.M.
- ABoth A and R are true and R is the correct explanation of A .
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of A.
- ✓A is true but R is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →Assertion (A): Mean deviation about median of the following data: 1, 3, 5, 7, 9, 11 is 3.
Reason (R): Median of the observations 1, 3, 5, 7, 9, 11 is 5.
Reason (R): Median of the observations 1, 3, 5, 7, 9, 11 is 5.
- ABoth A and R are true and R is the correct
- BBoth $A$ and $R$ are true but $R$ is not the explanation of $A$. correct explanation of A.
- ✓$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →Convert the decimal number to the binary number: 250
Differentiate the function with respect to $\mathrm{x}: \log \left\{\mathrm{x}+2+\sqrt{x^{2}+4 x+1}\right\}$
View full solution →Find the derivative of the given function: $\frac{a x+b}{c x+d}$
View full solution →A can do a piece of work in 80 days. He works at it for 10 days and then $B$ alone finishes the remaining work in 42 days. In how much time will $A$ and $B$, working together, finish the work?
View full solution →If $A=\{x: x=2 n, n \in Z\}$ and $B=\{x: x=3 n, n \in Z\}$, then find $A \cap B$.
View full solution →For a group of 60 boys students, the mean and S.D. of statistics marks are 45 and 2 respectively. The same figures for a group of 40 girls students are 55 and 3 respectively. What is the mean and S.D. of marks if the two groups are pooled together?
Using logarithmic table, find the value of $\sqrt{\frac{41.32 \times 20.18}{12.69}}$.
View full solution →a. In what time will ₹ 85000 amount to ₹ 157675 at $4.5 \%$ p.a?
b. A sum of ₹ 46875 was lent out at simple interest and at the end of 1 year 8 months the total amount was ₹ 50,000 . Find the rate of interest percent per annum.
View full solution →b. A sum of ₹ 46875 was lent out at simple interest and at the end of 1 year 8 months the total amount was ₹ 50,000 . Find the rate of interest percent per annum.
Find the domain and the range of the given function: $f(x)=\frac{1}{\sqrt{5-x}}$
View full solution →Find the equations of the lines for which $\tan \theta=\frac{1}{2}$, where $\theta$ is the inclination of the line and
i. $y$-intercept is $-\frac{3}{2}$
ii. $x$-intercept is 4
View full solution →i. $y$-intercept is $-\frac{3}{2}$
ii. $x$-intercept is 4
Find the equations of the lines through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $\mathrm{x}-2 \mathrm{y}=3$.
View full solution →Find the mean deviation from the median of the following frequency distribution:
| xi | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| fi | 3 | 8 | 14 | 19 | 7 | 6 | 3 |
Find the mean deviation about the mean for the following data:
| Marks obtained | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 160-70 |
| Number of students | 8 | 6 | 12 | 5 | 2 | 7 |
Evaluate: $\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x}$
View full solution →In a school, there are 1000 students, out of which 430 are girls. It is known that out of $430,10 \%$ of the girls study in class XII, what is the probability that a student chosen randomly studies in class XII, given that the chosen student is a girl?
View full solution →
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