List of top Mathematics Questions

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
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?
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
Which one of the following numbers is divisible by 9, 11, and 13?
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
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
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?
In \(\triangle ABC\), if \(a = 2\), \(b = 3\), and \(\angle C = 60^\circ\), then the value of \(c^{2}\) is:
Evaluate the integral: $$ \int_0^1 \frac{\ln (1+x)}{1+x^2} \, dx $$
The age ratio of two friends is 4:5. The difference in their ages is 6 years. What is the age of the younger friend?
Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
The general solution of the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \) is:
The general solution of the equation \( \cos(2x) = \frac{1}{2} \) is:
A bag contains 4 red and 6 blue balls. Two balls are drawn one after the other without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?
If vectors \( \vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - \hat{j} + 2\hat{k} \), then the magnitude of the projection of \( \vec{a} \) on \( \vec{b} \) is:
A bag contains 5 red, 4 blue, and 3 green balls. Three balls are drawn at random. What is the probability that at least two balls are of the same color?
If \( f(x) = \lfloor x \rfloor + \lfloor -x \rfloor \), where \( \lfloor \cdot \rfloor \) is the greatest integer function, then the value of \( f(2.5) \) is:
A circle touches the x-axis at point \( (4,0) \) and its center lies on the line \( x + y = 6 \). What is the equation of the circle?
If \( (x - 2) \) is a factor of \( x^3 - 4x^2 + ax + 8 \), find the value of \( a \):
The radius of a sphere is increased by 20%. What is the percentage increase in its volume?
The 10th term of an arithmetic progression is 35 and the 20th term is 65. What is the first term?
A box contains 5 defective and 15 non-defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that at least one bulb is defective?
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is acute, find \( \sin 2\theta \):
The equation of the line passing through the point \((1, 2)\) and perpendicular to the line \(3x + 4y - 12 = 0\) is: