List of top Mathematics Questions

Evaluate: \(\displaystyle \int e^x \left( \sin^{-1} x + \frac{1}{\sqrt{1 - x^2}} \right) dx = \)
Evaluate: \(\displaystyle \int \sqrt{a^2 - x^2} \, dx = \)
The equation of the \( xy \)-plane is:
If \( P(A) = \frac{6}{11} \), \( P(B) = \frac{5}{11} \), and \( P(A \cup B) = \frac{7}{11} \), then \( P(A \cap B) \) is:
If \( P(A) = \frac{1}{3} \), \( P(B) = \frac{1}{4} \), and \( P(A \cap B) = \frac{1}{5} \), then \( P(B|A) \) is:
The direction cosines of the \( z \)-axis are:
A coin is tossed 10 times. The probability of getting exactly six heads is:
The distance between the points \( (4, 3, 7) \) and \( (1, -1, -5) \) is:
The rate of change of the area of a circle with respect to its radius \( r \) (in cm\(^2\)/cm) at \( r = 6 \) cm is:
The slope of the tangent to the curve \( y = 2x^P + 3\sin x \) at \( x = 0 \) is:
If events \( A \) and \( B \) are independent, then:
The probability of drawing a king from a pack of 52 cards is:
Which of the following rational number has terminating decimal?
Three numbers are chosen at random from 1 to 20. The probability that their sum is divisible by 3 is:
By taking out a hemisphere from both the ends of a wooden solid cylinder, an item is formed. If the height of the cylinder is 10 cm and radius of the base is 3.5 cm, find the total surface area of the item.
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pillar are $45^\circ$ and $60^\circ$ respectively. Find the height of the pillar.
A flagstaff stands on a tower. At a distance 10 m from the tower, the angles of elevation of the top of the tower and flagstaff are $45^\circ$ and $60^\circ$ respectively. Find the length of the flagstaff.
Find the sum of 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.
Solve the following equations: \[ \dfrac{3}{2}x - \dfrac{5}{3}y = -2, \quad \dfrac{x}{3} + \dfrac{y}{2} = \dfrac{13}{6} \]
If the perimeter of a garden of area 800 m$^2$ is 120 m and its length is twice the breadth, then find its length and breadth.
Solve the quadratic equation \(2x^2 - 5x + 3 = 0\).
The sum of the digits of a two-digit number is 9. 9 times of this number is equal to 2 times the number formed by reversing the digits. Find the number.
$D$ is a point on the side $BC$ of a triangle $ABC$ such that $\angle ADC = \angle BAC$. Prove that $CA^2 = CB \cdot CD$.

Find the mode from the following table: 

Prove that $\sqrt{3}$ is an irrational number.