List of top Questions asked in NPAT- 2020


Read the given statements and conclusions carefully. Assuming the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements: 1. All instruments are equipment.
2. Some instruments are machines.
3. Some machines are motors.

Conclusions: I. Some motors are instruments.
II. Some machines are equipment.
III. No motor is an instrument.
If the numerator of a fraction (in lowest form) is increased by \( \frac{1}{3} \) of itself and the denominator is decreased by \( \frac{1}{4} \) of itself, the fraction so obtained is \( \frac{21}{64} \). What is the difference between the denominator and the numerator of the original fraction?
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements:
1. All herbs are trees.
2. Some trees are shrubs.
Conclusions:
I. Some herbs are shrubs.
II. Some shrubs are herbs.
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?
The mean of the following distribution is 25. \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0-10 & 14 \\ 10-20 & p \\ 20-30 & 27 \\ 30-40 & 21 \\ 40-50 & 15 \\ \hline \end{array} \]
If the signs ‘+’ and ‘-’ are interchanged in each of the given equations, then which one equation would be correct?
The graphs of \(2x - y = 1\) and \(3x - 2y = -1\) intersect at a point \(P\), which lies on the graph of the equation:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z^2} \), where \( x, y, z \) are positive integers, then the value of \( 2x + 3y - 4z \) is:
From a point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are \(30^\circ\) and \(60^\circ\), respectively. If the height of the bridge from the banks is \( h \) metres and the width of the river is \( k \) metres, then \( h : k \) is equal to:
The expression \( \frac{\sec^6 \theta - \tan^6 \theta - 3 \sec^2 \theta \tan^2 \theta}{1 + 2 \sin^2 \theta - \sin^4 \theta + \cos^4 \theta} \) is equal to:
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 \( f\left(1 - \frac{1}{x} \right) = \frac{5x + 1}{x}, \, x \neq 0 \), then \( f(x) = k - x \). What is the value of \( k \)?
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
A team of four with at least two females is to be selected from among five male players P, Q, R, S and T and three female players K, L and M under the following conditions.
i. R cannot be put with K.
ii. P and M have to be together.
iii. K will always be with T.
iv. S cannot go with N.
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:
In a class of 100 students, 55 students passed in Mathematics and 65 passed in English. Five students failed in both the subjects. Let \( m \) be the number of students who passed in exactly one of the two subjects and \( n \) be the number of students who failed in at least one subject, then what is the value of \( (m - n) \)?
The heights (in cm) of 8 students are recorded as 162, 163, 160, 164, 160, 170, 161, 164. The standard deviation of the data is closest to:
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') = ?
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements :
1. All cars are vehicles.
2. Some four-wheelers are cars.
Conclusions : I. Some four-wheelers are vehicles.
II. Some four-wheelers are not vehicles.
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
X and Y are two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are \( 30^\circ \) and \( 60^\circ \) respectively. The distance of Y from the foot of the pole (in m) is:
In an arithmetic progression, the 4th term equals three times the first term and the 7th term exceeds two times the third term by one. The sum of its first ten terms is: