List of top Questions asked in NPAT

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 \( (m - n) \)?
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.
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:
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:
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:
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?
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.
Select the Venn diagram that best represents the relationship between the following classes.
Wolves, Goats, Mammals
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.

If the signs ‘×’ and ‘+’ are interchanged in each of the given equations, then which one equation would be correct?
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 \( |a - b| \)?
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') = ?

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.

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?
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.
If \( \sec \theta + \tan \theta = p \), then \( \frac{\sin \theta - 1}{\sin \theta + 1} \) is equal to:
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?
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: