NPAT Common 2020 QP3

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 = $$\left[\left(A \cup B\right)\cap\left(A \cup C\right)\right]-\left(B \cap C\right)$$, then the number of elements in D 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 A = {2,4,6,9} and B = {4,6,18,27,81} be two sets. If C = $$\left\{\left(X,Y\right) \mid x \epsilon A, y \epsilon B \text { such that x is factor of y and x<y}\right\}$$, then n(C) is:

If function $$f:R\rightarrow R$$ is defined by f(x) = 2x - 3 and $$g:R \rightarrow R$$ is defined by$$g(x)=x^{3}+5$$, then the value of $$(f_0 g)^{-1}(-9)$$ is:

If $$f(1-\frac{1}{x})=\frac{5x+1}{x}$$, $$x \neq 0$$, then f(x)=k-x, Where K = ?

If $$f(x)=4x^{3}-8$$, then what is the value of $$f^{-1}(-8)+f^{-1}(24)$$ ?

There are 980 students in a school, out 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 a ll the three games, then how many students play none of the games?

The Value of $$\left(2\frac{2}{3}\times 4\frac{3}{8}\div 2\frac{1}{2}\right) \div \left[\left(2\frac{1}{3}+ 2\frac{1}{2}- \frac{1}{6}\right)\div 2\frac{1}{3}\right]$$ of $$2\frac{4}{5}$$ lies between:

In a class, $$\frac{3}{5}$$ of the total number of students are boys and the rest are girls. $$\frac{4}{5}$$ of the number of girls scored more than 80 marks (out of 150 marks).If $$\frac{3}{5}$$ of the total number of students scored more than 80 marks in the same examination, then what fraction of the total number of boys represent those boys who scored 80 marks or less?

The sum of the three fractions a, b and c, where a < b < c, is $$\frac{37}{24}$$. When a is divided by b, the result is $$\frac{3}{16}$$, which is less than c by $$\frac{9}{16}$$. What is the difference between (a + b) and c?