List of top Mathematics Questions

If \( A = \begin{bmatrix} a & 1 & 2 1 & 2 & b c & 1 & 3 \end{bmatrix} \) and \( \text{adj } A = \begin{bmatrix} 7 & -1 & -5 -3 & 9 & 5 1 & -3 & 5 \end{bmatrix} \), then \( a^2 + b^2 + c^2 = \)

The value of the limit \( \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \] is equal to:

The value of the integral \[ \int_{0}^{2} x^8 \left( \frac{4}{x^2} - 1 \right)^{\frac{5}{2}} \, dx \] is equal to:

The value of the integral \[ \int_{-2}^{2} x^4 (4 - x^2)^{\frac{7}{2}} \, dx \] is equal to:

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The value of the integral \(\int_{0}^{3\pi/2} \frac{\cos^3 x}{\cos^3 x + \sin^3 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx\) is equal to:

The value of the integral \(\int_{5}^{9} \frac{\log(3x^2)}{\log(3x^2) + \log(588 - 84x + 3x^2)} \, dx\) is equal to:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{\sin^2 x + 2 \cos^2 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx\) is:

The value of the integral \(\int_{0}^{2} x^2 (2 - x)^5 \, dx\) is:

The value of the integral \( \int_{0}^{4} ||x - 2| - x| dx = \)

If \( [ ] \) denotes the greatest integer function, then \( \int_{1}^{2} [x^2] dx = \)

If the system of equations \( 2x + py + 6z = 8 \), \( x + 2y + qz = 5 \) and \( x + y + 3z = 4 \) has infinitely many solutions, then \( p = \)

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

The value of \(c\) of Lagrange's Mean Value Theorem for \[ f(x)=\sqrt{25-x^2} \] on \([1,5]\) is:

Identify the correct set of molecules with zero dipole moment:

The value of \[ \lim_{n \to \infty} \left\{ \frac{1}{n+m} + \frac{1}{n+2m} + \frac{1}{n+3m} + \dots + \frac{1}{n+nm} \right\} \] is:

In a \(\triangle ABC\), \(a = 1, b = \sqrt{3}\) and \(\angle C = \frac{\pi}{6}\). Then the measure of the third side \(c =\)

If the area of triangle \(ABC\) is \(b^2 - (c - a)^2\), then \(\tan B =\)