List of top Mathematics Questions

The straight line \( r = (i - j + k) + \lambda (2i + j - k) \) and the plane \( r \cdot (2i + j - k) = 4 \) are

\[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]

Choose the most appropriate options.
The period of the function \(f(x) = |\sin x| - |\cos x|\) is

$\lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} =\ ?$

\(\lim_{x \to \infty} \frac{\ln x}{x^n}\) is equal to

Find the derivative of \[ y = (1 - x)^m (1 + x)^n \text{ at } x = 0, \text{ where } m, n>0 \]

What is the number of ordered pairs of real numbers (a, b) such that \[ (a + bi)^{2002} = a - bi \]

Find the component of the vector a = (-1, 2, 0) perpendicular to the plane of the vectors \(\mathbf{e}_1(1, 0, 1)\) and \(\mathbf{e}_2(1, 1, 1)\)

A real solution of the equation \[ \cosh x - 5 \sinh x - 5 = 0 \text{ is} \]

\[ \frac{1}{2 \sin 10^\circ} - 2 \sin 70^\circ \text{ is equal to} \]

Given \(\varepsilon = \cos\left(\frac{2\pi k}{n}\right) + i \sin\left(\frac{2\pi k}{n}\right)\), find the value of \[ \prod_{k=0}^{n-1} \left( \varepsilon^2k - 2\varepsilon k \cos \theta + 1 \right) \]

\[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]

If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to

Find the real solution of the system of equations: \[ x^4 + y^4 - x^2 y^2 = 13,\quad x^2 - y^2 + 2xy = 1 \] Satisfying condition: \( xy \geq 0 \)

Find the points of intersection of the given surface $\frac{x^2}{81} + \frac{y^2}{36} + \frac{z^2}{4} = 1$ and the straight line  $\frac{x - 3}{3} = \frac{y - 4}{-6} = \frac{z + 2}{4}$

If \(y^{\frac{1}{m}} + x^{\frac{1}{m}} = 2x\) then

What is the shape of the figure given by the following equations?

What is the equation of the curve traced by point \(M\), if the sum of distances to \(A(-1, -1)\) and \(B(1, 1)\) is constant and equals \(2\sqrt{3}\)?

If \(i = \sqrt{-1}\), then \[ \lim_{n \to \infty} \frac{(n + 2i)(3 + 7in)}{(2 - i)(6n^2 + 1)} \] is equal to:

If \(y = \sec(\tan^{-1} x)\), then \(y\) at \(x = 1\) is equal to term is the sum of two preceding terms. Then, the common ratio of the G.P. is:

Every term of G.P. is positive and also every term is the sum of two preceding terms. Then, the common ratio of the G.P. is

Which of the following complex numbers is conjugate to its square?

Let \( a = \cos \theta_1 + i \sin \theta_1 \), \( b = \cos \theta_2 + i \sin \theta_2 \), \( c = \cos \theta_3 + i \sin \theta_3 \) and \( a + b + c = 0 \), then \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = ? \]