List of top Questions asked in NPAT- 2020

Let \( A = \{1, 2, 5, 6\} \), \( B = \{1, 2, 3\} \), and \( C = (A \cap B) \cup (B \cap A) \). Which of the following is INCORRECT?
Let \( A = \{1,2,5,6\}, B = \{1,2,3\} \) and \( C = (A \times B) \cap (B \times A) \). Which of the following is INCORRECT?
A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
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?
Let \( U \) be the universal set, \( A \), \( B \), and \( C \) are the sets such that \( C \) is a subset of \( A \) and \( B \cap C = \emptyset \). If \( n(U) = 105 \), \( n(A) = 58 \), \( n(B) = 50 \), \( n(A \cap B) = 20 \) and \( n(A \cap C) = 32 \), then \( n(A \cup B) - n(B \cap C') = ? \)
If \( U = \{ x \ | \ x \in \mathbb{N}, x \leq 10 \} \) is the universal set, and \( A = \{ 1, 3, 5, 7, 9 \} \), \( B = \{ 2, 4, 6, 8, 10 \} \), and \( C = \{ 1, 2, 3, 4 \} \), the number of elements in \( A - (B \cap C) - (B' \cap C') \) where \( B' \) and \( C' \) are the complements of B and C, respectively is:
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 $(2p - 3q)$?
A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?
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:
Find the figure that will come next in the following figure series.
figure that will come next
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

Study the given symbols:

A @ B means A is not smaller than B.
A # B means A is not greater than B.
A & B means A is neither smaller than nor equal to B.
A % B means A is neither greater than nor equal to B.
A $ B means A is neither smaller than nor greater than B.

Statements: A) S & W
B) T $ Z
C) W @ T

Conclusions:

Z # W
T % S
S & Z
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 \[ \text{(take } \pi = \frac{22}{7}) \]
An integer is selected at random from the set \(\{100, 101, 102, \ldots, 999\}\). What is the probability that the sum of the digits of the selected number is the same as the product of its digits?
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
What is the value of \( \frac{4 \times (2.83)^2 - 3 \times 2.96 \times 2.22}{(2 - 0.78) \times (5.05)} \)?
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:

Let \( x \) be the median of the data: \[ \{20, 50, 60, 53, 77, 88, 90, 40, 30, 70, 25, 45, 64, 72, 8, 15, 85, 60, 55, 28\} \] If \( y \) is the median of the same dataset when 25 and 28 are replaced by 52 and 82 respectively, then what is the value of \( |x - y| \)?

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 \( f\left(1 - \frac{1}{x} \right) = \frac{5x + 1}{x}, \, x \neq 0 \), then \( f(x) = k - x \). What is the value of \( k \)?