List of top Questions asked in NPAT

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).
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?
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:
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:
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?
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 \( |a - b| \)?
If \( \sec \theta = a + \frac{1}{4a^2} \), \( 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
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:
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 \( (a - b + c) \)?
Let \( U = \{1,2,3,4,5,6,7,8,9\}, A = \{1,2,3,4\}, B = \{2,4,6,8\}, C = \{3,4,5,6\} \). The number of elements in \( A \cap C - (B - C) \), where \( A \cap C \) and \( B - C \) are the complements of \( A \cap C \) and \( B - C \), respectively is:
Given below are five sentences, labelled A, B, C, D and E. They are NOT in a meaningful order. Select the option that arranges the sentences in the correct order to form a meaningful paragraph.
A: Cells called fibroblasts from an animal are used to make sheets of skin.
B: According to a study, yarn grown from human skin cells could be woven or knitted into ‘human textiles’ for tissue grafts or organ repair.
C: Since it is made from animal cells and is not synthetic, scientists believe that it will not be rejected by the immune system of the recipient.
D: These sheets are cut into ribbons and twisted to form various forms of yarn.
E: The threads can then be used in surgery to help treat animals and humans.