List of top Mathematics Questions

$$ \begin{vmatrix} x-2 & 3x-3 & 5x-5 \\ x-4 & 3x-9 & 5x-25 \\ x-8 & 3x-27 & 5x-125 \end{vmatrix} = 0 $$

Calculate the determinant of the matrix:
 


 

If \( \alpha, \beta \) (\(\alpha<\beta\)) are the values of \( x \) such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of \( 2\alpha + 3\beta + 4\gamma \) is:
A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option is the correct answer. No two students of the class have answered identically and no student has written all correct answers. If every student has attempted all the questions, then the maximum possible number of students who have written the test is:
From a point \( (1,0) \) on the circle \( x^2 + y^2 - 2x + 2y + 1 = 0 \), if chords are drawn to this circle, then locus of the poles of these chords with respect to the circle \( x^2 + y^2 = 4 \) is:
Two pipes A and B together can fill a tank in 40 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in:
If \( A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] \), then \(\text{det} (A - A^T) = \): 
If the line \[ 2x + by + 5 = 0 \] forms an equilateral triangle with \[ ax^2 - 96bxy + ky^2 = 0, \] then \( a + 3k \) is: \
Area of the triangle formed by the points \((-5, -1)\), \((3, -5)\) and \((5, 2)\) is:
If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1<a_2 \), then \( 2a_1 + 3a_2 = \):
For \( \lambda, \mu \in \mathbb{R} \), the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then \( 2a + b = \) ?
The slope of a common tangent to the circles \( x^2 + y^2 - 4x - 8y + 16 = 0 \) and \( x^2 + y^2 - 6x - 16y + 64 = 0 \) is:
If real parts of \( \sqrt{-5 - 12i} \), \( \sqrt{5 + 12i} \) are positive values, the real part of \( \sqrt{-8 - 6i} \) is a negative value. If \[ a + ib = \frac{\sqrt{-5 - 12i} + \sqrt{5 + 12i}}{\sqrt{-8 - 6i}} \] then \( 2a + b \) is:
In \( \triangle ABC \), if \( a = 13 \), \( b = 14 \), and \( \cos \frac{C}{2} = \frac{3}{\sqrt{13}} \), then \( 2r_1 = \):

The numerically greatest term in the expansion of (3x - 16y)15 when x = 2⁄3 and y = 3⁄2 is ?

If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
If tan 48°.tan 23°.tan 42°.tan 67°=tan(A+30°), then the value of A is
Evaluate the integral: \[ \int e^x \left( \frac{x + 2}{(x+4)} \right)^2 dx. \]
If \( a, c, b \) are in GP, then the area of the triangle formed by the lines \( ax + by + c = 0 \) with the coordinate axes is equal to:
Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots \text{n times}) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)
The length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm is:
The range of \( 2 \left| \sin x + \cos x \right| - \sqrt{2} \) is:
Let A= {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A × B define by (a, b)R(c, d) if and only if 3ad – 7bc is an even integer. Then the relation R is
A box contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that the selected ball is not red?
A group of 40 students appeared in an examination of 3 subjects – Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is ________.