List of top Mathematics Questions

Consider a lottery with three possible outcomes: 

The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.

Let \( f(x) = -3x^2(1 - x) - 3x(1 - x)^2 - (1 - x)^3 \). Then, \( \frac{df(x)}{dx} = \)

Consider a square field ABCD. The diagonal AC is 50 meter. The cost of laying grass in the field is Rs. 5 per square-meter. The total cost for laying grass in the field ABCD is Rs. ________________ (rounded off to two decimal places).

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________.


 

The table shows the data of 450 candidates who appeared in the examination of three subjects – Social Science, Mathematics, and Science. How many candidates have passed in at least one subject?


 

Which one of the following numbers is odd one out?
31541 42651 53791 64871 75981
Let \( f(x, y, z) = x^2 y^3 z \). Then, what is the value of \[ x \frac{\partial f}{\partial x}(x, y, z) + y \frac{\partial f}{\partial y}(x, y, z) + z \frac{\partial f}{\partial z}(x, y, z)? \]
If \( \times \) means \( + \), \( + \) means \( \div \), \( - \) means \( \times \), and \( \div \) means \( - \), then evaluate: 8 \( \times \) 7 \( - \) 8 \( + \) 40 \( \div \) 2.
Given a series \( 5, 8, 11, 14, \dots \), if the \( n \)-th term of the given series is 320, then find \( n \) (where \( n \geq 1 \)):
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
A die is rolled. What is the probability of getting a number less than or equal to 4?
The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of \( x + y \) in the feasible region?
In how many ways can 5 people be arranged in a row?
If \( z = 3 + 4i \), then the modulus of \( z \) is:
The value of the integral \( \int_0^1 x^2 \, dx \) is:
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:
Find the value of the integral: \[ \int_0^e \log_e x \, dx \]

The equation \[ 2 \cos^{-1} x = \sin^{-1} \left( 2 \sqrt{1 - x^2} \right) \] is valid for all values of \(x\) satisfying:

If the 4th, 10th, and 16th terms of a G.P. are \(x\), \(y\), and \(z\) respectively, then
The number of diagonals that can be drawn in an octagon is:
If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:

Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 

 Choose the correct answer from the options given below:

The function f(x) is given by:

For x < 0:
f(x) = ex + ax

For x ≥ 0:
f(x) = b(x - 1)2


The function is differentiable at x = 0. Then,