Sample QuestionsModel Paper 9 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}^{2}-5 \mathrm{x}+6=0\right\}, \mathrm{B}=\{2,4\}, \mathrm{C}=\{4,5\}$ then $A \times(B \cap C)$ is
- A
$\{(4,2),(4,3)\}$
- B
$\{(2,2),(3,3),(4,4),(5,5)\}$
- C
$\{(2,4),(3,4),(4,4)\}$
- ✓
$\{(2,4),(3,4)\}$
Answer: D.
View full solution →Which of the following is not a binary number?
Answer: A.
View full solution →What sum must be invested at the end of each year to provide funds for the replacement of a machine costing ₹ 8000 at the end of 3 years, if money is worth $5 \%$ effective? (Given $(1.05)^{3}=1.1576$ )
Answer: C.
View full solution →The probability that in the toss of two dice we obtain the sum 7 or 11 is:
- A
$\frac{1}{18}$
- ✓
$\frac{2}{9}$
- C
$\frac{23}{108}$
- D
$\frac{1}{6}$
Answer: B.
View full solution →If $\frac{\log x}{a-b}=\frac{\log y}{b-c}=\frac{\log z}{c-a}$, then xyz is equal to:
Answer: C.
View full solution →Assertion (A): $\left(\sum_{r=0}^{100}{ }^{500-r} C_{3}\right)+{ }^{400} C_{4}={ }^{501} C_{4}$
Reason (R): ${ }^{n} C_{r}+{ }^{n} C_{r-1}={ }^{n+1} C_{r}$
- ✓
Both A and R are true and R is the correct explanation of A .
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
- C
$A$ is true but $R$ is false.
- D
A is false but $R$ is true.
Answer: A.
View full solution →Assertion (A): If $P(A)=0.6$ and $P(B)=0.4$ and $P(A \mid B)=0.4$, then $P(A \cup B)=0.72$.
Reason (R): $\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of A .
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
- C
$A$ is true but $R$ is false.
- D
A is false but R is true.
Answer: A.
View full solution →A bag contains 4 white and 2 black balls. Another contains 3 white and 5 black balls. If one ball is drawn from each bag, find the probability that both are black.
Differentiate $3^{x}+x^{3}+4 x-5$ with respect to $x$.
View full solution →Differentiate the function with respect to $\mathrm{x}: 3 \mathrm{e}^{-3 \mathrm{x}} \log (1+2)$
View full solution →The marks obtained by 15 students in a monthly test are: $11,09,07,03,18,21,13,15,18,04,06,17,22,13,15$
i. Find the average marks of 15 students.
ii. Find the average of their marks when the marks of each student are increased by 2.
View full solution →Find the values of the letter and give a reason for the steps involved.
In a group of students, 225 students know French, 100 know Spanish and 45 know both. Each student knows either French or Spanish. How many students are there in the group.
Find the present value of a regular annuity of ₹ 1000 payable for 3 years at $12 \%$ per annum compounded annually?
View full solution →A family in Agra, U.P consumes 78 SCM of gas in 60 days. The GST is included in the gas charges and the minimum charge is $10 \%$ of the gas consumption charges. The PNG rate in Agra are as follows:| Units of Consumption (in SCM) | Price Per Unit |
| up to 45 SCM/60 days | ₹29,50 |
| above 45 SCM/60 days | ₹42.61 |
Calculate the bimonthly PNG bill of the family. View full solution →Discuss the continuity of the junction $\mathrm{f}(\mathrm{x})$ at $\mathrm{x}=\frac{1}{2}$, where
View full solution →Rohit is the husband of Vanshika. Sumita is the sister of Rohit. Anushka is the sister of Vanshika. How Anushka is related to Rohit?
A retailer buys a TV from a manufacturer for ₹ 25000 . He marks the price of the TV $20 \%$ above his cost price and sells it to a consumer at $10 \%$ discount on the marked price. If the sales are intra-state and rate of GST is 12%, find:
i. the marked price of the TV.
ii. Consumer's cost price of TV inclusive of tax (under GST).
iii. GST paid by the retailer to the Central and State Governments.
View full solution →Calculate Karl Pearson's coefficient of skewness from the following data:
| Profits: (in ₹lacs) | Below 20 | 40 | 60 | 80 | 100 |
| No. of companies: | 8 | 20 | 50 | 64 | 70 |
Find the coefficient of variation for the following data:
| CI | 60-70 | 50-60 | 40-50 | 30-40 | 20-30 | 10-20 |
| Frequencies | 03 | 6 | 10 | 12 | 15 | 6 |
Find the domain of the function $\mathrm{f}(\mathrm{x})=\frac{1}{\log (1-x)}+\sqrt{x+3}$
View full solution →The AM between two positive numbers a and $\mathrm{b}(\mathrm{a}>\mathrm{b})$ is twice their GM. Prove that $\mathrm{a}: \mathrm{b}=(2+\sqrt{3}):(2-\sqrt{3})$.
View full solution →Read the text carefully and answer the questions:
A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of many construction workers not being present for the job is 0.65 . The probability that many are not present and still the work gets completed on time is 0.35 . The probability that work will be completed on time when all workers are present is 0.80 .
Let: $\mathrm{E}_{1}$ : represent the event when many workers were not present for the job;
$\mathrm{E}_{2}$ : represent the event when all workers were present; and
E: represent completing the construction work on time.
(a) What is the probability that all the workers are present for the job?
(b) What is the probability that construction will be completed on time?
(c) What is the probability that many workers are not present given that the construction work is completed on time?
View full solution →Read the text carefully and answer the questions:
In a survey of 200 students it was found that 120 had got grade $\mathbf{A}$ in Mathematics, 90 had got grade $\mathbf{A}$ in Physics and 70 had got grade $\mathbf{A}$ in Chemistry, 50 had got grade $\mathbf{A}$ in Mathematics and Chemistry, 40 had got grade 6 A in Mathematics and Physics, 30 had got grade A in Physics and Chemistry and 10 had got grade $\mathbf{A}$ in all three subjects one student is choosed randomly as a class representative.
(a) The probability that the chosen class representative had got grade $\mathbf{A}$ in at least one of the subject which is?
(b) The probability that the chosen class representative had got grade $\mathbf{A}$ in at least two of the subjects which is?
(c) The probability that the chosen class representative had got grade ' $A$ ' in Mathematics or Chemistry is?
View full solution →Read the text carefully and answer the questions:
Data of all the previous cricket matches are stored to analyze the average batting score of various batsmen. The scores of a batsman in ten innings are:
$38,70,48,34,42,55,63,46,54,44$
(a) What is the median of the data?
(b) What is the mean deviation about the median of the given scores?
(c) If the scores 38 and 34 are replaced by 68 and 74 what will be the mean of the data?
OR
Difference between maximum value of data and minimum vale of data is called? View full solution →Read the text carefully and answer the questions:
The girder of a railway bridge is a parabola with its vertex at the highest point, 10 metres above the ends and span is 100 metres.
(a) Find the equation of bridge.
(b) Find the height of the bridge at 20 metres from the mid-point.
(c) Find the coordinates of the focus of parabola.
OR
Find the length of latus rectum.