List of top Mathematics Questions

If the zeroes of the quadratic polynomial \(ax^2+bx+c \  (c≠0)\) are equal, then
If secθ+tanθ=k, then secθ-tanθ=?

The area bounded by the parabola \(y = x^2 + 2\) and the lines \(y = x\), \(x = 1\) and \(x = 2\) (in square units) is:

11\( (10P_7) \) =

The integral \(\int e^x \sqrt{e^x} \, dx\) equals:

The minimum value of the function \( f(x) = x^4 - 4x - 5 \), where \( x \in \mathbb{R} \), is:

The integrating factor of the differential equation \[ x \frac{dy}{dx} + 2y = x e^x \] is:
Let

\[ f(x) = \begin{cases} x\left( \frac{\pi}{2} + x \right), & \text{if } x \geq 0 \\ x\left( \frac{\pi}{2} - x \right), & \text{if } x < 0 \end{cases} \]

Then \( f'(-4) \) is equal to:
If \( \overrightarrow{a} \) and \( \overrightarrow{b} \) are two nonzero vectors and if \( |\overrightarrow{a} \times \overrightarrow{b}| = |\overrightarrow{a} \cdot \overrightarrow{b}| \), then the angle between \( \overrightarrow{a} \) and \( \overrightarrow{b} \) is equal to

The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{3}\). If \(\|\vec{a}\| = 5\) and \(\|\vec{b}\| = 10\), then \(\|\vec{a} + \vec{b}\|\) is equal to:

If \( a = \tan^{-1}\left(\frac{4}{3}\right) \) and \( b = \tan^{-1}\left(\frac{1}{3}\right) \), where \( 0<a, b<\frac{\pi}{2} \), then \( a - b \) is:

The value of \( \alpha \) for which the complex number \( \frac{2 - \alpha i}{\alpha - i} \) is purely imaginary, is:

The value of the limit \(\lim_{t \to 0} \frac{(5-t)^2 - 25}{t}\) is equal to:

The critical points of the function \( f(x) = (x-3)^3(x+2)^2 \) are:

The shortest distance between the parallel straight lines \[ \overrightarrow{r_1} = \hat{k} + s(\hat{i} + \hat{j}), \quad t, s \in \mathbb{R} \quad {and} \quad \overrightarrow{r_2} = \hat{j} + t(\hat{i} + \hat{j}), \] is:
If \[ \begin{vmatrix} x & 2 & -1 \\ 1 & x & 5 \\ 3 & 2 & x \end{vmatrix} = 0, \quad \text{then the real value of} \quad x \quad \text{is:} \]
If \( \left( 1 + \cos \frac{\pi}{8} \right) \left( 1 + \cos \frac{7\pi}{8} \right) \) =
\[ \cos^{-1} \left( \cos \left( \frac{-7\pi}{9} \right) \right) = \]

\[ \int \left( \frac{\log_e t}{1+t} + \frac{\log_e t}{t(1+t)} \right) dt \]

For two sets \( A \) and \( B \), we have \( n(A \cup B) = 50 \), \( n(A \cap B) = 12 \), and \( n(A - B) = 15 \). Then \( n(B - A) \) is equal to:
Let \( \vec{a} \) and \( \vec{b} \) be two unit vectors. Let \( \theta \) be the angle between \( \vec{a} \) and \( \vec{b} \). If \( \theta \neq 0 \) or \( \pi \), then

\[ \left| \vec{a} - (\vec{a} \cdot \vec{b}) \vec{b} \right|^2 \] is equal to:

Let \( f(x) = \begin{cases} x^2 - \alpha, & \text{if } x < 1 \\ \beta x - 3, & \text{if } x \geq 1 \end{cases} \). If \( f \) is continuous at \( x = 1 \), then the value of \( \alpha + \beta \) is:

The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
If \( |x| \leq 1 \), then \( \sin \left( 2 \sin^{-1} x + \cos^{-1} x \right) \) is equal to:

Let \(f(x) = a^{3x}\) and \(a^5 = 8\). Then the value of \(f(5)\) is equal to: