List of top Mathematics Questions

If \( |z_1| = 2, |z_2| = 3, |z_3| = 4 \) and \( |2z_1 + 3z_2 + 4z_3| = 4 \), then the absolute value of \( 8z_2z_3 + 27z_1z_3 + 64z_1z_2 \) equals:
If \( z_1, z_2, \dots, z_n \) are complex numbers such that \( |z_1| = |z_2| = \dots = |z_n| = 1 \), then \( |z_1 + z_2 + \dots + z_n| \) is equal to:
If \( z, \bar{z}, -z, -\bar{z} \) forms a rectangle of area \( 2\sqrt{3} \) square units, then one such \( z \) is:
The modulus of the complex number \( z \) such that \( |z + 3 - i| = 1 \) and \( \arg(z) = \pi \) is equal to:
The points represented by the complex numbers \( 1 + i, -2 + 3i, \frac{5}{3}i \) on the Argand plane are:
If \( \tan 15^\circ \) and \( \tan 30^\circ \) are the roots of the equation \( x^2 + px + q = 0 \), then \( pq = \):
Rational roots of the equation \( 2x^4 + x^3 - 11x^2 + x + 2 = 0 \) are:
Roots of the equation \( x^2 + bx - c = 0 \) (\( b, c>0 \)) are:
For real numbers \(x\) and \(y\), we define \(x R y\) iff \(x - y + \sqrt{5}\) is an irrational number. Then, relation \(R\) is:
In four schools \( B_1, B_2, B_3, B_4 \), the number of students is given as follows: \[ B_1 = 12, \quad B_2 = 20, \quad B_3 = 13, \quad B_4 = 17 \] A student is selected at random from any of the schools. The probability that the student is from school \( B_2 \) is:
Let \( f(x) \) be a polynomial function satisfying \[ f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right). \] If \( f(4) = 65 \) and \( I_1, I_2, I_3 \) are in GP, then \( f'(I_1), f'(I_2), f'(I_3) \) are in:
If \( z_r = \cos \frac{r\alpha}{n^2} + i \sin \frac{r\alpha}{n^2} \), where \( r = 1, 2, 3, ..., n \), then the value of \( \lim_{n \to \infty} z_1 z_2 z_3 ... z_n \) is:
Evaluate the limit: \[ L = \lim_{x \to 0} \frac{35^x - 7^x - 5^x + 1}{(e^x - e^{-x}) \ln(1 - 3x)} \]
If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: 
Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to
If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]
The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
The circle touching the y axis at a distance 4 units from the origin and cutting off an intercept 6 from the x axis is: (A) \(x^2 + y^2 \pm 10x - 8y + 16 = 0\)
The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:
If \( \frac{1}{q + r}, \frac{1}{r + p}, \frac{1}{p + q} \) are in A.P., then:
The coefficient of \( x^{50} \) in \( (1 + x)^{101} (1 - x + x^2)^{100} \) is:
The number of different permutations of all the letters of the word "PERMUTATION" such that any two consecutive letters in the arrangement are neither both vowels nor both identical is:
Negation of the statement \( (p \land r) \rightarrow (r \lor q) \) is:
The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
A and B are independent events of a random experiment if and only if: