A relation $R$ is defined from $\{2,3,4,5\}$ to $\{3,6,7,10\}$ by $x \mathrm{Ry} \Leftrightarrow \mathrm{x}$ is relatively prime to y . Then, domain of R is
- A$\{3,5\}$
- ✓$\{2,3,4,5\}$
- C$\{2,3,5\}$
- D$\{2,3,4\}$
Answer: B.
View full solution →Question types
Model Paper 2 question types
44 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
44
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)
4 Q→Sample Questions
Model Paper 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following is the correct representation of a binary number?
- ✓$(000)_{2}$
- B110
- C$(110)^{2}$
- D$(124)_{2}$
Answer: A.
View full solution →The effective rate of return which is equivalent to nominal rate of $8 \%$ p.a. compounded quarterly is: [Given $\left.(1.02)^{4}=1.0824\right]$
- A$8.5 \%$
- ✓$8.16 \%$
- C$7.95 \%$
- D$8.24 \%$
Answer: B.
View full solution →If $A$ and $B$ are two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{4}$, then $P\left(\frac{B^{\prime}}{A}\right)$ is
- A$\frac{1}{8}$
- B1
- ✓$\frac{3}{4}$
- D$\frac{1}{4}$
Answer: C.
View full solution →Which of the following is equal to $x$ ?
- A$x^{\frac{12}{7}}-x^{\frac{5}{7}}$
- ✓$\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}$
- C$x^{\frac{12}{7}} \times x^{\frac{7}{12}}$
- D$\sqrt[12]{\left(x^{4}\right)^{\frac{1}{3}}}$
Answer: B.
View full solution →Assertion (A): Suresh plans to go from Lucknow to Kanpur by bus and return back to Lucknow by a different bus. If there are only 10 buses running between Lucknow and Kanpur, then total number of ways in which Suresh can plan his journey is 90.
Reason (R): If an event can occur in $m$ different ways and a second event can occur in $n$ different ways, then either of the two events can occur in $(m+n)$ ways.
Reason (R): If an event can occur in $m$ different ways and a second event can occur in $n$ different ways, then either of the two events can occur in $(m+n)$ ways.
- ✓Both $A$ 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.
- C$A$ is true but $R$ is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A): If $A$ and $B$ are events associated with a random experiment such that $A \subset B$, then $P(B-A)=$ $P(B)-P(A)$.
Reason (R): If $A \subset B$, then $A \cap B=A$.
Reason (R): If $A \subset B$, then $A \cap B=A$.
- ✓Both 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.
- C$A$ is true but $R$ is false.
- DA 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 one is white and one is black.
Differentiate the function $\sqrt{x}\left(2 x^{2}+3\right)$ with respect to x .
View full solution →Find the derivative of the given function from the first principle: $\frac{a x+b}{c x+d}$
View full solution →At what time between 5:00 and 6:00 will the hands of clock be at right angles?
In a certain code language 327 means Truth is eternal, 7983 means 'Enmity is not eternal' and 9426 means Truth does not perish. What does Enmity mean in this language?
In the adjacent Venn diagram, if $n(\xi)=80, n(P)=40, n(Q)=28, n(P \cap Q)=12$ and $n(P \cap R)=10$,
i. mark the number of elements in each region.
ii. determine the value of $n(P \cup Q)$ and $n\left((Q \cup R)^{\prime}\right)$.
View full solution →i. mark the number of elements in each region.
ii. determine the value of $n(P \cup Q)$ and $n\left((Q \cup R)^{\prime}\right)$.
₹ 2000 is invested at annual rate of interest of $10 \%$. What is the amount after two years if compounding is done
(a) Annually(b) semi-annually(c) Quarterly(d) monthly.
View full solution →(a) Annually(b) semi-annually(c) Quarterly(d) monthly.
An industry in Delhi consumed 285kL of water in a month. Calculate the water bill for the month. The tariff plan for the industrial units in Delhi is as given below:
A water cess is levied at 0.20/kL and the sewerage charge is 60% of the consumption charge.
| Monthly Consumption (in kL) | Service Charge | Water Consumption Charge per KL |
| Up to 6 | ₹ 146.41 | ₹17.57 |
| 6-15 | ₹ 292.82 | ₹26.35 |
| 15-25 | ₹585.64 | ₹35.14 |
| 25-50 | ₹1024.87 | ₹87.85 |
| 50-100 | ₹1171.28 | ₹140.56 |
| > 100 | ₹1317.69 | ₹175.69 |
Find $\lim _{x \rightarrow 1} f(x)$, where $f(x)=\left\{\begin{array}{l}x^{2}-1, x \leq 1 \\ -x^{2}-1, x>1\end{array}\right.$
View full solution →Find A and B in the addition
A shopkeeper buys an article whose list price is ₹ 8000 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price. The sales are intra-state and the rate of GST is $18 \%$. If the shopkeeper pay a tax (under GST) of ₹72 to the State Government, find the rate of discount at which he bought the article from the wholesaler.
View full solution →Calculate the standard deviation for the following data:
| Class | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 |
| Frequency | 9 | 17 | 43 | 82 | 81 | 44 | 24 |
Find the domain and range of the real function: $f(x)=\sqrt{9-x^{2}}$
View full solution →If $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}$ be respectively the sums of $\mathrm{n}, 2 \mathrm{n}, 3 \mathrm{n}$ terms of a G.P., then prove that $s_{1}^{2}+s_{2}^{2}=\mathrm{s}_{1}\left(\mathrm{~s}_{2}+\mathrm{s}_{3}\right)$.
View full solution →Read the text carefully and answer the questions:
A shopkeeper sells three types of flower seeds $\mathrm{A}_{1}, \mathrm{~A}_{2}$, and $\mathrm{A}_{3}$. They are sold as a mixture, where the proportions are $4: 4: 2$ respectively. The germination rates of the three types of seeds are $45 \%, 60 \%$ and $35 \%$ respectively.
(a) Calculate the probability of randomly chosen seed to germinate.
(b) Calculate the probability that it is of the type $\mathrm{A}_{2}$ given that randomly chosen seed does not germinate.
(c) Calculate the probability that it will not germinate given that the seed is of type $\mathrm{A}_{1}$.
View full solution →A shopkeeper sells three types of flower seeds $\mathrm{A}_{1}, \mathrm{~A}_{2}$, and $\mathrm{A}_{3}$. They are sold as a mixture, where the proportions are $4: 4: 2$ respectively. The germination rates of the three types of seeds are $45 \%, 60 \%$ and $35 \%$ respectively.
(a) Calculate the probability of randomly chosen seed to germinate.
(b) Calculate the probability that it is of the type $\mathrm{A}_{2}$ given that randomly chosen seed does not germinate.
(c) Calculate the probability that it will not germinate given that the seed is of type $\mathrm{A}_{1}$.
Read the text carefully and answer the questions:
Two students Ankit and Vinod appeared in an examination. The probability that Ankit will qualify the examination is 0.05 and that Vinod will qualify is 0.10 . The probability that both will qualify is 0.02 .
(a) Find the probability that atleast one of them will qualify the exam.
(b) Find the probability that atleast one of them will not qualify the exam.
(c) Find the probability that both Ankit and Vinod will not qualify the exam.
Two students Ankit and Vinod appeared in an examination. The probability that Ankit will qualify the examination is 0.05 and that Vinod will qualify is 0.10 . The probability that both will qualify is 0.02 .
(a) Find the probability that atleast one of them will qualify the exam.
(b) Find the probability that atleast one of them will not qualify the exam.
(c) Find the probability that both Ankit and Vinod will not qualify the exam.
Read the text carefully and answer the questions:
A teacher conducted a surprise test of Mathematics, Physics and Chemistry for class XI on Monday.
The mean and standard deviation of marks obtained by 50 students of the class in three subjects are given below:
A teacher conducted a surprise test of Mathematics, Physics and Chemistry for class XI on Monday.
The mean and standard deviation of marks obtained by 50 students of the class in three subjects are given below:
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
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