List of top Questions asked in NPAT- 2020

Let \( A = \{ 1, 2, 5 \} \), \( B = \{ 1, 2, 3, 4 \} \), and \( C = \{ 2, 5, 6 \} \) be the three sets. If \( D = [A \times (B \cap C)] \cap [(A - B) \times C] \), then which of the following is true?
In an examination, 82% of students passed in Mathematics, 70% passed in Science and 13% failed in both the subjects. If 299 students passed in both the subjects, then the total number of students who appeared in the examination is:
The number of elements in sets X and Y are $p$ and $q$ respectively. The total number of subsets of X is 112 more than that of Y. What is the value of $(2p - 3q)$?
Let \( U \) be the universal set, and \( A, B, C \) are the sets such that \( C \subset A \) and \( B \cap C = \emptyset \). If \( n(U) = 105 \), \( n(A) = 58 \), \( n(B) = 50 \), \( n(A \cap B) = 20 \) and \( n(A \cup C) = 32 \), then \( n(A \cup B) - n(B \cap C) \) is:
Let A = \(\{2, 3, 4, 8, 10\}\), B = \(\{3, 4, 5, 10, 12\}\), and C = \(\{4, 5, 6, 12, 14\}\) be the three sets. If $D = ((A \cup B) \cap (A \cup C)) - (B \cap C)$, then the number of elements in D is:
Select the option that is related to the third figure in the same way as the second figure is related to the first figure.
option that is related to the third figure
Water is flowing at the rate of 4 km/h through a pipe of radius 7 cm into a rectangular tank with length and breadth as 25 m and 22 m, respectively. The time (in hours) in which the level of water in the tank will rise by 28 cm is \[ \text{(take } \pi = \frac{22}{7}) \]
The given pie charts show the percentage distribution of the total employees (executives and non-executives) and that of the executives in different departments of a company. Study the charts and answer the questions that follow.
pie charts show the percentage distribution
The given pie diagram shows the percentage of students in five different universities in an academic year. The table shows the ratio of male to female students and the percentage of foreign students in each university. Study the information and answer the questions that follow.
students in five different universities
The following graph shows the percentage of profit of two Companies C and D over the period of four years.
Study the graph and answer the questions that follow.
profit of two Companies C and D
Consider the following distribution:
mean of the distribution is 8.84 years. 
The mean of the distribution is 8.84 years. The value of x is:

What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
If function $f: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $f(x) = 2x - 3$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $g(x) = x^3 + 5$, then the value of $(f \circ g)^{-1}(-9)$ is:
If \( f(x) = 4x^3 - 8 \), then what is the value of \( f^{-1}(-8) + f^{-1}(24) \)?

The mean deviation about the mean of the dataset \( \{22, 24, 30, 27, 29, 31, 25, 28, 41, 43, 30\} \) is:
There are 980 students in a school, of which 50% play cricket, 30% play basketball and 40% play football. If 60 students play cricket and basketball, 48 students play basketball and football, 180 students play cricket and football, and 35 students play all the three games, then how many students play none of the games?
Let $A = \{2, 4, 6, 9\}$ and $B = \{4, 6, 18, 27, 81\}$. If $C = \{(x, y) \mid x \in A, y \in B$ such that $x$ is a factor of $y$ and $x<y\}$, then $n(C)$ is:
The value of \( \frac{0.35 \times 0.7}{0.63 \times 3.6} + 0.27 (0.83 + 0.16) \) is:
A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
The sum of the first 10 terms of the series \( \frac{7}{3} + \frac{7}{5} + \frac{1}{5} + \frac{1}{9} + \cdots = \frac{a}{b} \), where HCF(a,b) = 1. What is the value of \( |a - b| \)?
Shikha sells an article for ₹253, after giving 12% discount on its marked price. Had she not given any discount, she would have earned a profit of 25% on the cost price. What is the cost price of the article?
If \( \sec \theta = a + \frac{1}{4a^2} \), \( 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{-x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?
The value of \( \frac{(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta)}{\tan^2 \theta + \cot^2 \theta - \sec^2 \theta \csc^2 \theta} \) is: