List of top Mathematics Questions

The particular solution of the differential equation \( x \, dy + 2y \, dx = 0 \), when \( x = 2 \) and \( y = 1 \) is

The differential equation obtained by eliminating the arbitrary constant from the equation \[ y^2 = (2x+c)^5 \] is

The statement pattern \( \sim (p \vee q) \vee (\sim p \wedge q) \) is equivalent to

Evaluate \( \int_{-4}^{4} \log \left( \frac{8 - x}{8 + x} \right) dx \)

If \( y\sqrt{1-x^2} + x\sqrt{1-y^2} = 1 \), then \( \dfrac{dy}{dx} = \)

If the tangent to the curve given by \( x = t^2 - 1 \) and \( y = t^2 - t \) is parallel to the x-axis, then the value of \( t \) is

If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is

If the line \[ \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \quad \text{is parallel to the plane} \quad \vec{r} \cdot (3i - 2j + mk) = 10, \] then the value of \( m \) is

If \[ A = \{x, y, z\}, \quad B = \{1, 2\}, \text{ then the total number of relations from set } A \text{ to set } B \text{ are} \]

With usual notations, in \( \triangle ABC \), if \( a = 2 \), \( b = 3 \), \( c = 5 \) and \[ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = \frac{k}{7} + \frac{30}{30}, \] then \( k = \)

The centre and radius of a circle \[ x = 4a \left( \frac{1 - t^2}{1 + t^2} \right), \quad y = \frac{8at}{1 + t^2} \] are respectively

If \(2\sin^2 x + 7\cos x = 5\), then the permissible value of \(\cos x\) is

If \(\vec u = \hat i - 2\hat j + \hat k\), \(\vec v = 3\hat i + \hat k\) and \(\vec w = \hat j - \hat k\), then the volume of the parallelepiped with \(\vec u \times \vec v\), \(\vec u + \vec w\) and \(\vec v + \vec w\) as coterminous edges is

If \(P(3,2,6)\), \(Q(1,4,5)\) and \(R(3,5,3)\) are the vertices of \(\triangle PQR\), then the measure of \(\angle PQR\) is

The cartesian co-ordinates of the point whose polar co-ordinates are \( \left( \frac{1}{2}, 120^\circ \right) \text{ are}

The shortest distance between the lines \( 1 + x = 2y = -12z \) and \( x = y + 2 = 6z - 6 \) is

If \( A + B + C = 180^\circ \), then the value of \( \tan \left( \frac{A}{2} \right) \tan \left( \frac{B}{2} \right) + \tan \left( \frac{B}{2} \right) \tan \left( \frac{C}{2} \right) + \tan \left( \frac{C}{2} \right) \tan \left( \frac{A}{2} \right) \) is

The acute angle between the line \[ \vec{r} = (i + 2j + k) + \lambda (i + j + k) \] and the plane \[ \vec{r} \cdot (2i - j + k) = 5 \] is

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get at least one correct answer is

\(y = mx + \dfrac{2}{m}\) is the general solution of

The bacteria increases at the rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours, then the number of bacteria in $12$ hours will be

Evaluate the integral \[ \int \frac{1 + 2e^{-x}}{1 - 2e^{-x}} \, dx \]

If \( x = a(1 - \cos\theta) \), \( y = a(\theta - \sin\theta) \), then \( \frac{d^2y}{dx^2} = \)

If \( f : \mathbb{R} \rightarrow \mathbb{R} \) such that \[ f(x) = \frac{e^{x} + e^{-x}}{e^{x} - e^{-x}}, \] then \( f \) is

If \( f : \mathbb{R} \to \mathbb{R}, g : \mathbb{R} \to \mathbb{R} \) are defined by \[ f(x) = x^2 - 3x + 4 \quad \text{and} \quad g(x) = 2x + 1, \quad \text{then the value of} \quad x \text{ for which} \quad f(x) = f \circ g(x) \text{ is} \]