List of top Mathematics Questions

If \(\Delta_1=\begin{vmatrix} x&b&b \\a&x&b\\a&a&x\end{vmatrix}\) and \(\Delta_2=\begin{vmatrix} x&b \\a&x\end{vmatrix}\), then \(\frac{d}{dx}(\Delta_1)\) is equal to

If \(f(x) = \begin{cases}  1 + x & \text{if } 0 \leq x \leq 2 \\ 3 - x & \text{if } 2 < x \leq 3  \end{cases}\) , then \(f[f(x)]\) is

The values of is

If two sides of a triangle are the roots of the equation \(4x^2 - (2\sqrt{6})x + 1 = 0\) and the included angle is 60⁰ , then the third side is

Let f : R $/to$ R be given by f(x) = (x - 1)(x - 2)(x - 5). Define $F\left(x\right) = \int\limits^{x}_{0} f\left(t\right) dt, x > 0.$ Then which of the following options is/are correct?

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

If det $\begin{bmatrix}1&1&2\\ 2&4&9\\ t&t^{2}&1+t^{3}\end{bmatrix} = 0 $ , then the values of t are

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

The probability that a leap year will have 53 Fridays or 53 Saturday is

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 sec, yellow for 5 sec and red for 30 sec. At a randomly chosen time, the probability that the light will not be green is

\[\log(\sin 1^\circ) \times \log(\sin 2^\circ) \times \ldots \times \log(\sin 90^\circ) \text{ is}\]

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is:

A supporting element on a curved opening is called as

A regular hexagonal pyramid is sliced by a plane such that it passes through the centre of its axis. How many additional edges shall be created.

The sum of the values of x satisfying \(\tan(\frac{\pi}{4}+x)+\tan(\frac{\pi}{4}-x)=2\) in the interval \([0,2\pi]\) is:

If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is

Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)

The differential equation of all non vertical lines in a plane is:

The sum of odd integers from 1 to 2001 is:

The function given by: x^myⁿ = (x + y)^m+n is:

A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?

A class has n students, we have to form a team of the students including at least two students and also excluding at least two students. The number of ways of forming the team is

The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?