If A = {1, 2, 4}, B = {2, 4, 5}, c = {2, 5}, then (A - B) × (B - C) is
- ✓{(1, 4)}
- B(2, 5)
- C{(1, 2), (1, 5), (2, 5)}
- D(1, 4)
Answer: A.
View full solution →Question types
Model Paper 7 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 7 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In how many ways can the letters of the word 'PENCIL' be arranged so that N is always next to E?
- A1440
- ✓120
- C240
- D720
Answer: B.
View full solution →Time value of money supports the comparison of cash flows recorded at different time period by
i. Discounting all cash flows to a common point of time
ii. Compounding all cash flows to a common point of time
iii. Using either Discounting all cash flows to a common point of time or Compounding all cash flows to a common point of time
iv. not Discounting all cash flows to a common point of time nor Compounding all cash flows to a common point of time
i. Discounting all cash flows to a common point of time
ii. Compounding all cash flows to a common point of time
iii. Using either Discounting all cash flows to a common point of time or Compounding all cash flows to a common point of time
iv. not Discounting all cash flows to a common point of time nor Compounding all cash flows to a common point of time
- ✓Statement (c) is correct
- BStatement (b) is correct.
- CStatement (a) is correct.
- DStatement (d) is correct.
Answer: A.
View full solution →If A and B are two events, then $P (\bar{A} \cap B)=$
- ✓$P ( B )- P ( A \cap B )$
- B$P(\bar{A}) P(\bar{B})$
- C1 - P(A) - P(B)
- D$P ( A )+ P ( B )- P ( A \cap B )$
Answer: A.
View full solution →Four cards are drawn from a well-shuffled pack of 52 cards. The probability of obtaining 3 diamonds and one spade is:
- ✓$\frac{{ }^{13} C _3 \times{ }^{13} C _1}{{ }^{52} C _4}$
- B$\frac{{ }^{13} C _3 \times{ }^{10} C _1}{{ }^{52} C _4}$
- C$\frac{{ }^{26} C_2 \times{ }^{26} C_2}{{ }^{52} C_1}$
- D$\frac{{ }^{26} C _4}{{ }^{52} C _4}$
Answer: A.
View full solution →Assertion (A): The sum of first 6 terms of the GP 4, 16, 64, ... is equal to 5460.
Reason (R): Sum of first n terms of the G.P is given by $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$, where a = first term r = common ratio and
|r| > 1.
Reason (R): Sum of first n terms of the G.P is given by $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$, where a = first term r = common ratio and
|r| > 1.
- ✓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 →Assertion (A): The variance of 10 observations is 6. If each observation is multiplied by 3, then new variance is 54.
Reason (R): If $\sigma^2$ is the variance of $n$ observations $x _1, x _2, \ldots, x _{ n }$, then variance of the observations $ax _1, ax _2 \ldots$, $ax _{ n }$ is $a ^2 \sigma^2$.
Reason (R): If $\sigma^2$ is the variance of $n$ observations $x _1, x _2, \ldots, x _{ n }$, then variance of the observations $ax _1, ax _2 \ldots$, $ax _{ n }$ is $a ^2 \sigma^2$.
- ✓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 437 into the binary number.
Find the derivative of the given function: $\left(x^2+1\right)(x-2)$
View full solution →If $xy ^2=1$, prove that $2 \frac{d y}{d x}+ y ^3=0$.
View full solution →A clock gains 4 seconds in 3 minutes and was set right at 9:00 a.m. What time will it show at 11:00 p.m. on the same day?
In a certain language if LUCKNOW is coded as NWEMPQY, how is DELHI coded?
A and B are two sets such that n(A - B) = 14 + x, n(B - A) = 3x and $n ( A \cap B )= x$. Draw a Venn diagram to illustrate this information. If n(A) = n(B), find
i. the value of x
ii. $n(A \cup B)$
View full solution →i. the value of x
ii. $n(A \cup B)$
Mr. Rajesh in Bengaluru, Karnataka consumed 159 kL of water in a month. Calculate the water bill for the month. The tariff plan of Bengaluru is as given below:
Meter rent = ₹ 56 per month; Sewerage charges are flat ₹ 14 if the consumption is less than 8 KL and 25% of the consumption charges if the consumption is more than 8 kL.
| Units of Consumption (in kL): | up to 8 | Aug-25 | 25-50 | > 50 |
| Price per kL consumed : | ₹ 7 | ₹ 11 | ₹ 25 | ₹ 45 |
In what time will ₹ 25000 amount to ₹ 35000 at 6% compounded quarterly?
Find the domain and range of f(x) = |2x - 3| - 3.
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. Pandey lives in Lucknow, Uttar Pradesh. The reading of the electric meter of his house is found to be 5678 units. If the previous month's reading was 4803 units and the connected load is 4 kW, calculate his electricity bill for that month.
Tariff plan is given below.
Energy charges
Fixed charges ₹ 110 per kW/month
Energy tax is 5% of tariff rates
Surcharge is ₹ 0.26 per unit
Tariff plan is given below.
Energy charges
| Number of units | 0-150 | 151-300 | 301-500 | > 500 |
| Price per unit (in ₹) | ₹ 5.50 | ₹ 6 | ₹ 6.50 | ₹ 7 |
Energy tax is 5% of tariff rates
Surcharge is ₹ 0.26 per unit
The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results:
Number of observations = 25, mean = 18.2 seconds, standard deviation = 3.25 seconds.
Further, another set of 15 observations $x _1, x _2, \ldots, x _{15}$, also in seconds, is now available and we have $\sum_{i=1}^{15} x_i=279$ and $\sum_{i=1}^{15} x_i^2=5524$. Calculate the standard derivation based on all 40 observations.
View full solution →Number of observations = 25, mean = 18.2 seconds, standard deviation = 3.25 seconds.
Further, another set of 15 observations $x _1, x _2, \ldots, x _{15}$, also in seconds, is now available and we have $\sum_{i=1}^{15} x_i=279$ and $\sum_{i=1}^{15} x_i^2=5524$. Calculate the standard derivation based on all 40 observations.
Using short cut method, find the mean, variance and standard deviation for the data:
| Class | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |
| Frequency | 64 | 132 | 153 | 140 | 51 |
For what integers m and n does $\lim _{x \rightarrow 0} f(x)$ and $\lim _{ x \rightarrow 1} f( x )$ exist, if $f(x)=\left\{\begin{array}{lc}m x^2+n, & x<0 \\ n x+m, & 0 \leq x \leq 1 \\ n x^2+m, & x>1\end{array}\right.$
View full solution →In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
Read the text carefully and answer the questions
A shopkeeper sells three types of flower seeds $A _1, A_2$, and $A _3$ 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 a randomly chosen seed to germinate.
(b) Calculate the probability that it is of the type A2 given that randomly chosen seed does not germinate.
(c) Calculate the probability that it will not germinate given that the seed is of type $A _1$.
View full solution →A shopkeeper sells three types of flower seeds $A _1, A_2$, and $A _3$ 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 a randomly chosen seed to germinate.
(b) Calculate the probability that it is of the type A2 given that randomly chosen seed does not germinate.
(c) Calculate the probability that it will not germinate given that the seed is of type $A _1$.
Read the text carefully and answer the questions
In XI standard, teacher was discussing about Spearman's Rank Correlation Coefficient in Statistics. Following points were discussed in the class about the same topic:
When we are finding correlation between two qualitative characteristics, say, beauty and intelligence, we take recourse to using rank correlation coefficient. Rank correlation can also be applied to find the level of agreement (or disagreement) between two judges so far as assessing a qualitative characteristic is concerned. As compared to product moment correlation coefficient, rank correlation is easier to compute, it can also be advocated to get a first hand impression about the correlation between a pair of variables. Spearman's rank correlation coefficient is given by
$r _{ S }=1-\frac{6 \Sigma d^2}{n\left(n^2-1\right)}$
where,
d = difference between ranks of corresponding x and y
n = number of pairs of values (x,y) in the data
When the rank are repeated, the Spearman's rank correlation coefficient formula is given by
$r _{ S }=1-\frac{6\left[\Sigma d^2+\frac{\left(m_1^3-m_1\right)}{12}+\frac{\left(m_2^3-m_2\right)}{12}+\ldots \ldots\right]}{n\left(n^2-1\right)}$
where, $m _1, m_2 \ldots$, are the number of repetitions of ranks and $\frac{m_1^3-m_1}{12} \ldots$ their corresponding correlation factors.
For example: Ranks obtained by 10 students are given below:
View full solution →In XI standard, teacher was discussing about Spearman's Rank Correlation Coefficient in Statistics. Following points were discussed in the class about the same topic:
When we are finding correlation between two qualitative characteristics, say, beauty and intelligence, we take recourse to using rank correlation coefficient. Rank correlation can also be applied to find the level of agreement (or disagreement) between two judges so far as assessing a qualitative characteristic is concerned. As compared to product moment correlation coefficient, rank correlation is easier to compute, it can also be advocated to get a first hand impression about the correlation between a pair of variables. Spearman's rank correlation coefficient is given by
$r _{ S }=1-\frac{6 \Sigma d^2}{n\left(n^2-1\right)}$
where,
d = difference between ranks of corresponding x and y
n = number of pairs of values (x,y) in the data
When the rank are repeated, the Spearman's rank correlation coefficient formula is given by
$r _{ S }=1-\frac{6\left[\Sigma d^2+\frac{\left(m_1^3-m_1\right)}{12}+\frac{\left(m_2^3-m_2\right)}{12}+\ldots \ldots\right]}{n\left(n^2-1\right)}$
where, $m _1, m_2 \ldots$, are the number of repetitions of ranks and $\frac{m_1^3-m_1}{12} \ldots$ their corresponding correlation factors.
For example: Ranks obtained by 10 students are given below:
| 3 | 4 | 7 | 8 | 9 |
| 7 | 3 | 4 | 1 | 1 |
Read the text carefully and answer the questions
A market is in the form of a triangle whose vertices are B(-2, 0), C(1, 12). The third vertex A of this trianagle lies on the mid point of the line joining the points (2, 1) and (4, 13).
(a) What will be the coordinates of A?
(b) Find the slope of the line joining the points B and C?
(c) Equation of the line joining the points B and C?
OR
Does point A lies on the line BC?
A market is in the form of a triangle whose vertices are B(-2, 0), C(1, 12). The third vertex A of this trianagle lies on the mid point of the line joining the points (2, 1) and (4, 13).
(a) What will be the coordinates of A?
(b) Find the slope of the line joining the points B and C?
(c) Equation of the line joining the points B and C?
OR
Does point A lies on the line BC?
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