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=?
If \( |x| \leq 1 \), then \( \sin \left( 2 \sin^{-1} x + \cos^{-1} x \right) \) is equal to:

The line \(y = 5x + 7\) is perpendicular to the line joining the points \((2, 12)\) and \((12, k)\). Then the value of \(k\) is equal to:

An assignment of probabilities for outcomes of the sample space \( S = \{1, 2, 3, 4, 5, 6\} \) is as follows:

\[ \begin{array}{c|c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline k & 3k & 5k & 7k & 9k & 11k \end{array} \]

If this assignment is valid, then the value of \( k \) is:

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

Let \( x \text{ and } y \) be two positive real numbers. Then
\[ \left( x + \frac{1}{x} \right) \left( y + \frac{1}{y} \right) \] is greater than or equal to:
 

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

Let \( \overrightarrow{AB} = i + 2j - 2k \) and \( \overrightarrow{AC} = i - j + k. \) Then the area of \( \triangle ABC \) is:

If \( a \text{ and } b \) are A.M. and G.M. of \( x \text{ and } y \) respectively, then \( x^2 + y^2 \) is equal to: 
 

The value of \( x \) that satisfies the equation:

\[ \begin{vmatrix} x & 1 & 1 \\ 2 & 2 & 0 \\ 1 & 0 & -2 \end{vmatrix} = 6 \]

Given that: \[ \frac{1}{\tan A - \tan B} = \]
The solution of the inequality \( |3x - 4| \leq 5 \) is
If \( f(x) = \frac{|x|}{1 + |x|}, \, x \in \mathbb{R} \), then \( f'(-2) \) is equal to:

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

For a hyperbola, the vertices are at \( (6, 0) \) and \( (-6, 0) \). If the foci are at \( (2\sqrt{10}, 0) \) and \( -2\sqrt{10}, 0) \), then the equation of the hyperbola is:

The coefficient of \( x^{17} \) in

\[ (1 - x)^{13} (1 + x + x^2)^{12} \] is:
Let A and B be two events such that \( P(A) = 0.4 \), \( P(B) = 0.5 \) and \( P(A \cap B) = 0.1 \). Then
\[ P(A \mid B) = ? \]

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:

Three dice are thrown simultaneously. The probability that all the three outcomes are the same number, is:

The point of intersection of the lines \(\frac{x-3}{2} = \frac{y-2}{2} = \frac{z-6}{1}\) and \(\frac{x-2}{3} = \frac{y-4}{2} = \frac{z-1}{3}\) is:

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 length of the latus rectum of the parabola \( y^2 = x \) is:
If \( \overrightarrow{a} = \alpha \hat{i} + \beta \hat{j} \) and \( \overrightarrow{b} = \alpha \hat{i} - \beta \hat{j} \) are perpendicular, where \( \alpha \neq \beta \), then \( \alpha + \beta \) is equal to:
Simplify the following expression: \[ (\sec A - \cos A)(\tan A - \cot A) \] The simplified form is: