List of top Mathematics Questions

The value of the following expression is: \[ \cos \left( \frac{\pi}{2^2} \right) \cdot \cos \left( \frac{\pi}{2^3} \right) \cdot \cos \left( \frac{\pi}{2^4} \right) ... \cdot \cos \left( \frac{\pi}{2^{10}} \right) \]
If \( \cos\theta \), \( \sin\theta \), and \( \cot\theta \) are in geometric progression, then: \[ \sin^9\theta + \sin^6\theta + 3\sin^5\theta + \sin^3\theta + \sin^2\theta = \]
If \( \tan A = \tan \alpha \coth x = \cot \beta \tanh x \), then \( \tan(\alpha + \beta) = \):
In \(\triangle ABC\), if \(\cos A + \cos C = 4 \sin^2 \frac{B}{2}\), then the ratio between the perimeter of the triangle and \((a + c)\) is
If \( \theta = \frac{\pi}{9} \), then \( 1 + 27 \tan^2 \theta - 33 \tan^4 \theta + \tan^6 \theta = \)
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
Evaluate: \( (1 + \cos\frac{\pi}{8})(1 + \cos\frac{2\pi}{8})(1 + \cos\frac{3\pi}{8}) \ldots (1 + \cos\frac{7\pi}{8}) = \)
In \( \triangle ABC \), if \( \cos^2 A + \cos^2 B + \cos^2 C = 1 \), then \( \triangle ABC \) is:
If $ \sin(\alpha + \beta) = 5 \sin(\alpha - \beta) $, then $ \frac{\sin 2\beta}{5 - \cos 2\beta} $ is:
If $ P = \tan 15^\circ + \cot 15^\circ $, $ Q = \tan 22\frac{1}{2}^\circ + \cot 22\frac{1}{2}^\circ $, and $ R = \sin 54^\circ + \sin 18^\circ $, then their ascending order is
Evaluate \( \left[ 1 + \sec 2\theta \right] \left[ 1 + \sec 40^\circ \right] \):
In \(\triangle ABC\), if \(\angle A = 90^\circ\), then \((r_2 - r_1)(r_3 - r_1) = \)
Evaluate the following expression: \[ \sin 21^\circ \cos 9^\circ - \cos 84^\circ \cos 6^\circ \]
If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:
If \( f(a) = \log \left| \frac{1 - a}{1 + a} \right| \) for \( a \neq \{-1, 1\} \), then the set of values of all \( a \), for which \( f\left( \frac{2a}{1 + a^2} \right)>0 \) is:
If \( f(x) = x^3 - x \) and \( g(x) = \sin(2x) \), then \( f(g\left(\frac{\pi}{12}\right)) \) is:
For \( x \in \mathbb{R} \), if \( f(x) = \sqrt{\log_{10} \left( \frac{3-x}{x} \right)} \), then the domain of \( f \) is:
Assertion (A): Every rational function is continuous at every real number \(x\) at which it is defined.
Reason (R): Every rational function is a quotient of two polynomials.
If a set \( A \) has \( n \) elements, then the number of functions defined from \( A \) to \( A \) that are not one-one is:
If \( f:\mathbb{R} \to \mathbb{R} \) is defined by \( f(x+y) = f(x) + f(y) \ \forall x, y \in \mathbb{R} \) and \( f(1) = 7 \), then \(\sum\limits_{r=1}^n f(r) =\)
\(f(x)\) is a continuous function on \(\mathbb{R}\) and \(y = f(x)\) is a curve. If \((\alpha, \beta)\) is a point such that \(\beta = f(\alpha)\) and \(p\alpha + m\beta + n = 0\ (p \ne 0, m \ne 0)\), then which one of the following is True?
Let \( A \subseteq \mathbb{R}, B \subseteq \mathbb{R} \) and \( f : A \to B \) be defined by \( f(x) = x^2 - 3x + 2 \). If \( f \) is a bijection, then
Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
For \( x \in \mathbb{R} \), the minimum value of \( \frac{x^2 + 2x + 5}{x^2 + 4x + 10} \) is: