The domain of the relation, $R=\{(x, y): x, y \in Z, z x y=4\}$ is
- A$\{-2,-1,1,2,4\}$
- B$\{-2,-1,1,2\}$
- C$\{1,2,4\}$
- ✓$\{-4,-2,-1,1,2,4\}$
Answer: D.
View full solution →Question types
Model Paper 3 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 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
How many even numbers can be formed by using all the digits $2,3,4,5,6$ ?
- ✓72
- B36
- C120
- D24
Answer: A.
View full solution →Mahesh invested an amount of ₹ 10000 in a fixed deposit scheme for 2 years at a compound interest rate $8 \%$ per annum. How much amount will Mahesh get on the maturity of the deposit?
- ✓₹ 11664
- B₹ 11644
- C₹ 11446
- D₹ 11466
Answer: A.
View full solution →A biased coin with probability $\mathrm{p}, 0<\mathrm{p}<1$, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2 / 5$, then p equals
- A$\frac{2}{3}$
- B$\frac{2}{5}$
- ✓$\frac{1}{3}$
- D$\frac{3}{5}$
Answer: C.
View full solution →Three identical dice are rolled. The probability that the same number will appear on each of them is
- A$\frac{1}{6}$
- B$\frac{1}{18}$
- ✓$\frac{1}{36}$
- D$\frac{3}{28}$
Answer: C.
View full solution →Assertion (A): If the sum of first two terms of an infinite GP is 5 and each term is three times the sum of the succeeding terms, then the common ratio is $\frac{1}{4}$.
Reason (R): In an AP 3, 6, 9, 12........... the 10th term is equal to 33 .
Reason (R): In an AP 3, 6, 9, 12........... the 10th term is equal to 33 .
- 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): If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by a, where $a$ is a negative or positive number, then the variance remains unchanged.
Reason (R): Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.
Reason (R): Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.
- ✓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.
- CA is true but R is false.
- DA is false but $R$ is true.
Answer: A.
View full solution →Convert the decimal number to the binary number: 639
Differentiate the given function w.r.t. $\mathrm{x}: \frac{\sqrt{(x-3)\left(x^{2}+4\right)}}{3 x^{2}+4 x+5}$
View full solution →If $\mathrm{y}=\mathrm{x}+\frac{1}{x}$, prove that $x^{2} \frac{d y}{d x}-\mathrm{xy}+2=0$.
View full solution →A clock gains 5 seconds in 2 minutes and was set right at 9:00 a.m. If it shows 2:30 in the afternoon on the same day. What is the correct time?
$A$ and B are brothers. C and D are sisters. A's son is D's brother. How B is related to C?
View full solution →In a class of 50 students, 30 students like Mathematics, 25 like Science, and 16 like both. Find the number of students who like
i. either Mathematics or Science
ii. neither Mathematics nor Science.
i. either Mathematics or Science
ii. neither Mathematics nor Science.
Mr. Sharma in Delhi is using an MTNL connection with a monthly plan of ₹ 240 , which has no free calls. The call charges are ₹ 1 per minute. Calculate the telephone bill payable for Mr. Sharma if he talks for 470 minutes in a month. Assume the broadband charges to be Nil. A GST of $18 \%$ is levied on the total bill amount.
View full solution →A machinery can be purchased by paying ₹ 600,000 now or ₹ 200,000 initially and two instalments of ₹ 300,000 at the end of second year and ₹ 190,000 at the end of 4th year respectively. To pay cash now, the buyer would have to withdraw the money from an investment earning interest at $8 \%$ compounded annually. Which option is better and by how much in present value terms?
View full solution →Find the domain of the function f defined by $f(x)=\sqrt{4-x}+\frac{1}{\sqrt{x^2-1}}$
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?
Mr. Rishabh lives in Bengaluru, Karnataka. He consumed 37 kL of water in one month. Calculate his water bill for that month. Water tariff plan is given below.
Maintenance charge = ₹ 56 per month
Sewerage charges flat ₹ 14 for those whose consumption is upto 8 kL and $25 \%$ of water charges whose consumption is more than 8 kL .
View full solution →| Units of consumption (in kL)upto | upto 8 | 8 to 25 | 25-50 | >50 |
| Price per unit (in ₹) | 7 | 11 | 25 | 45 |
Sewerage charges flat ₹ 14 for those whose consumption is upto 8 kL and $25 \%$ of water charges whose consumption is more than 8 kL .
Find the mean deviation about the median for the following data:
View full solution →| xi | 3 | 6 | 9 | 12 | 13 | 15 | 21 | 22 |
| $f_i$ | 3 | 4 | 5 | 2 | 4 | 5 | 4 | 3 |
Find $\operatorname{Cov}(X, Y)$ between $X$ and $Y$, if:
View full solution →| X: | 1 | 2 | 3 | 4 | 5 |
| Y: | 2 | 4 | 6 | 8 | 10 |
Discuss the continuity of the function $f ( x )$ at $x =1$, defined by $f(x)-\left\{\begin{array}{ll}\frac{3}{2}-x, & \text { if } \frac{1}{2} \leq x < 1 \\ \frac{3}{2}, & \text { if } x-1 \\ \frac{3}{2}+x, & \text { if } 1 < x \leq 2\end{array}\right.$
View full solution →In how many ways can 9 examination papers be arranged so that the best and the worst papers are never together?
Read the text carefully and answer the questions:
Different organisations collect the data and analyse it quantitatively. During one such analysis some mistake crept in. The result given was that mean and variance of 100 observations as 40 and 5.1 but later on rechecking it was found that one observation was mistakenly taken as 50 instead of 40 .
(a) What is incorrect sum of variates?
(b) What is correct sum of observations?
(c) What is incorrect $\Sigma x^{2}$ ?
OR
What is corrected variance?
View full solution →Different organisations collect the data and analyse it quantitatively. During one such analysis some mistake crept in. The result given was that mean and variance of 100 observations as 40 and 5.1 but later on rechecking it was found that one observation was mistakenly taken as 50 instead of 40 .
(a) What is incorrect sum of variates?
(b) What is correct sum of observations?
(c) What is incorrect $\Sigma x^{2}$ ?
OR
What is corrected variance?
Children always keep of thinking something new, sometimes reaching a destination they say we will go by longer sometimes by shorter route, etc.
A child is standing at the point $A(2,3)$ and far away he can notice a straight road path represented by the equation $3 x-4 y-12=0$. He wants to reach path in the minimum possible time.
(a) Find the slope of the path followed by child?
(b) Find the Equation of the path followed by child?
(c) Find the Distance covered by child in reaching the path?
OR
If child wants to reach at point $(4,0)$ on the straight road, then find the equation of path he should follow.
View full solution →A child is standing at the point $A(2,3)$ and far away he can notice a straight road path represented by the equation $3 x-4 y-12=0$. He wants to reach path in the minimum possible time.
(a) Find the slope of the path followed by child?
(b) Find the Equation of the path followed by child?
(c) Find the Distance covered by child in reaching the path?
OR
If child wants to reach at point $(4,0)$ on the straight road, then find the equation of path he should follow.
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