List of top Mathematics Questions

If secθ+tanθ=k, then secθ-tanθ=?

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 equation of the line passing through the point \((-9,5)\) and parallel to the line \(5x - 13y = 19\) is:

Find the value of \[ \sin^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right). \] The answer is:

The radius of the circle with centre at \((-4, 0)\) and passing through the point \((2, 8)\) is:

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:

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

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

The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
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
\[ P(A \mid B) = ? \]
Let \( \overrightarrow{AB} = i + 2j - 2k \) and \( \overrightarrow{AC} = i - j + k. \) Then the area of \( \triangle ABC \) is:

Let \( f(x) = \log_e(x) \) and let \( g(x) = \frac{x - 2}{x^2 + 1} \). Then the domain of the composite function \( f \circ g \) is:

The centre of the circle \( (x-3)(x+1)+(y-1)(y+3)=0 \) is:

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 integrating factor of the differential equation \[ x \frac{dy}{dx} + 2y = x e^x \] is:
Let \( A \) and \( B \) be two sets each containing more than one element. If \( n(A \times B) = 155 \), then \( n(A) \) is equal to:
If \[ \sin^{-1} x + \cos^{-1} y = 0, \] then \( x^2 + y^2 \) is equal to:

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

The foci of the ellipse \(\frac{x^2}{49} + \frac{y^2}{24} = 1\) are:

If \( f'(x) = 4x\cos^2(x) \sin\left(\frac{x}{4}\right) \), then \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) 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:

Let \( f(x) = 2 - 7 \sin{\left( \frac{2x}{7} \right)} \). Then the maximum value of \( f(x) \) is:

If \( \sec(\alpha + \beta) = \frac{\sqrt{7}}{\sqrt{3}} \), then \( \sin(\alpha + \beta) + \tan(\alpha + \beta) \) is equal to:
The value of \( \alpha \) for which the complex number \( \frac{2 - \alpha i}{\alpha - i} \) is purely imaginary, is:
Given that: \[ \frac{1}{\tan A - \tan B} = \]