List of top Mathematics Questions

If \( x + y = 2 \) and \( x^2 + y^2 = 2 \), what is the value of \( xy \)?
About three towns A, B, and C, the information available are: A’s population is twice as B and C’s population is half times as B. Then A’s population compared to C is
If the base of the triangle is 10 cm and the height of the triangle is 12 cm, then the area of the triangle is (in Sq Cm)
The product of three consecutive positive integers is 720. Then the sum of the three numbers is
In a class of 100 students, 73 like apple, 80 like orange, and 52 like grapes. It may be possible that some students do not like any of these three fruits. Find the difference between the maximum and minimum possible number of students who like all three fruits.
The lengths of two sides other than the hypotenuse of a right-angled triangle are 9 cm and 40 cm. The largest side of the triangle is (in cm)
The sum of two numbers is 25 and their product is 144. The smaller number is
Two buses start at 9AM from two different places on a straight road. The buses travel towards each other at uniform speeds of 45 kmph and 55 kmph respectively. If the two places are 200 km apart, the buses will meet at
Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?
A set A has 620 elements and another set B has 380 elements. If the union of the sets A and B has 950 elements, the number of common elements in A and B is equal to
Which one of the following numbers is divisible by 9, 11, and 13?
A person owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is in square meters?
A company plans to produce 1500 units of an item per hour and plans to send out 700 units of the item per hour from the company for sales. The number of units available in the company at the end of 10 hours is
In \(\triangle ABC\), if \(a = 2\), \(b = 3\), and \(\angle C = 60^\circ\), then the value of \(c^{2}\) is:
If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:
Verify that \(\sin 2A = \frac{2 \tan A}{1 + \tan^2 A}\) for \(A = 30^\circ\).

The following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of \(x\) and \(y\).

MarksNumber of Students
10 -- 2012
20 -- 3030
30 -- 40\(x\)
40 -- 5065
50 -- 60\(y\)
60 -- 7025
70 -- 8018
In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to
In two concentric circles centred at O
Three coins are tossed together. The probability that exactly one coin shows head, is
The volume of air in a hollow cylinder is 450 cm\(^3\). A cone of same height and radius as that of cylinder is kept inside it. The volume of empty space in the cylinder is
The volume of air in a hollow cylinder is 450 cm
In \(\triangle ABC, \angle B = 90^\circ\). If \( \frac{AB}{AC} = \frac{1}{2} \), then cos C is equal to
15th term of the A.P. \( \frac{13}{3}, \frac{9}{3}, \frac{5}{3}, \dots \) is

If probability of happening of an event is 57%, then probability of non-happening of the event is

A quadratic polynomial having zeroes 0 and -2, is
To calculate mean of a grouped data, Rahul used assumed mean method. He used \( d = (x - A) \), where A is assumed mean. Then \( \bar{x} \) is equal to