List of top Questions asked in NPAT- 2020

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 \( |x - y| \)?
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:
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 \( (m - n) \)?
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.
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') = ?
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:
Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( \frac{4}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:

You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
 If the breadth of a rectangle is 10 cm, then what is its length?
Statements:
I. If the length of the rectangle is increased by 25% and its breadth by 20%, its area increases by 70 cm\textsuperscript{2}.
II. The length remaining the same, if its breadth is increased by 20%, the ratio of the new area to the original area becomes 6:5.
In a year, out of 160 games to be played, a cricket team wants to win 80% of them. Out of 90 games already played, the success rate is \( 66\frac{2}{3} %\). What should be the success rate for the remaining games in order to reach the target?
Select the Venn diagram that best represents the relationship between the following classes.
Wolves, Goats, Mammals

If the signs ‘×’ and ‘+’ are interchanged in each of the given equations, then which one equation would be correct?
Question :
How is Q exactly related to P? Statements:
I. P’s father is the son of Q’s mother.
II. P’s sister R is the daughter of Q’s husband.
The sum of the first 10 terms of the series \[ \frac{7}{3} + \frac{7}{15} + \frac{1}{5} + \frac{1}{9} + \dots \quad \text{where} \quad \text{HCF}(a,b) = 1. \] What is the value of \( |a - b| \)?

You are given a question and two statements. Identify which of the statements is/are sufficient/necessary to answer the question.
 Which is the heaviest of the four objects X, Y, Z and M?
Statements:
I. X and Z together weigh as much as Y and M together. X is twice as heavy as M and half as heavy as Z.
II. X is twice as heavy as M and half as heavy as Y, while Z is one and a half times as heavy as X.
You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
Six friends A, B, C, D, E and F are sitting in a row. D is at one of the extreme ends. Who is exactly at the other end?
Statements:
I. B is sitting to the immediate left of D and F is to the immediate right of C. There are two persons between F and E. C is to the right of D and there are two persons between C and B. B is to the immediate left of A.
II. C is sitting to the immediate right of D and there are two persons between C and B. B is sitting to the immediate left of A.
Consider the given statement and decide which of the given assumptions is/are implicit in the statement.
Statement:
This year the state will not import onions from other states.
Assumptions:
I. The onion production in the state would meet the consumer needs.
II. The quality of onions grown in other states is poor.
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') = ?

Six friends A, B, C, D, E and F are sitting in a straight line. A is third to the right of F. D is to the immediate left of F and is at one end of the row. B is sitting between A and C. There is one person between B and E. Who is sitting at the other end?
If \( \sec \theta + \tan \theta = p \), then \( \frac{\sin \theta - 1}{\sin \theta + 1} \) is equal to: