List of top Mathematics Questions

Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]
If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:
Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
Bag P contains 6 red and 4 blue balls, and Bag Q contains 5 red and 6 blue balls. A ball is transferred from Bag P to Bag Q, and then a ball is drawn from Bag Q. What is the probability that the ball drawn is blue?
The equation of the circle with centre (0,2) and radius 2 is \[ x^2 + y^2 - my = 0. \] The value of \( m \) is:
The sum of the series \[ \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots \] up to 15 terms is:
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?

If \[ \sin x + \cos x = \frac{1}{5} \] then \( \tan 2x \) is: 

In $\triangle ABC$, the midpoints of the sides $AB$, $BC$, and $CA$ are respectively $(1, 0, 0)$, $(0, m, 0)$, and $(0, 0, n)$. Then, $$ \frac{AB^2 + BC^2 + CA^2}{1^2 + m^2 + n^2} \text{ is equal to:} $$ 
Evaluate: \[ \tan (\cos^{-1} \frac{4}{5}) + \tan^{-1} \frac{2}{3} \]
The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:
If \[ \frac{a^n + b^n}{a^{n-1} + b^{n-1}} \] is the arithmetic mean (A.M.) between \( a \) and \( b \), then the value of \( n \) is:

The area of the region bounded by the ellipse $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$ is: 

Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:
If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:

If 

then \( {Adj} (A) \) is equal to:

The integral \[ \int x^n (1 + \log x) \, dx \] is equal to: 

The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:
The distance of the point $(6,-2 \sqrt{2})$ from the common tangent $y=m x+c, m>$, of the curves $x=2 y^2$ and $x=1+y^2$ is :

Let \(P(S)\) denote the power set of \(S = \{1, 2, 3, \ldots, 10\}\). Define the relations \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \[(A \cap B^c) \cup (B \cap A^c) = ,\]and \(A R_2 B\) if\[A \cup B^c = B \cup A^c,\]for all \(A, B \in P(S)\). Then:

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then
What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?
A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?
If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \( 2x + 4y + 5z = 8 \) and \( 3x - 2y + 3z = 5 \), is \( \alpha x + \beta y + \gamma z = 97 \), then \( \alpha + \beta + \gamma \) is: