List of top Mathematics Questions asked in MET

The line $\frac{x}{a} - \frac{y}{b} = 1$ cuts the x-axis at P. The equation of the line through P perpendicular to the given line is

If $f(x+y) = f(x) \cdot f(y)$, $f(3) = 3$, $f'(0) = 11$, then $f'(3)$ is equal to

The coefficient of $x$ in the expansion of $(1+x+x^2+x^3)^{-1}$ is

$(p \land q) \lor (\sim p \land \sim q)$ is

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then the value of $x + y + z - xyz$ is

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n(n+1)}$ is equal to

If $4\sin^{-1}x + \cos^{-1}x = \pi$, then $x$ is equal to

$\frac{d}{dx} \left[ \int_0^{x^2} \sin^{-1} \left( \frac{1}{1+t} \right) dt \right]$ is equal to

In the set $Q^+$ of all positive rational numbers, the operation $*$ is defined by the formula $a * b = \frac{ab}{6}$. Then, the inverse of $9$ with respect to $*$ is

If the projection of $\overrightarrow{PQ}$ on OX, OY, OZ are respectively 12, 3 and 4, then the magnitude of $\overrightarrow{PQ}$ is

If $\Delta = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix} = k(a-b)(b-c)(c-a)$, then $k$ is equal to

$\vec{a} = \frac{1}{7}(2\hat{i} + 3\hat{j} + 6\hat{k})$, $\vec{b} = \frac{1}{7}(3\hat{i} - 2\hat{j} + \lambda \hat{k})$. If $\vec{a}$ and $\vec{b}$ are mutually perpendicular, then value of $\lambda$ is

The locus of the point of intersection of two perpendicular tangents to a circle is called

The area bounded by the curve $y = 4x^3 - 3x^2 + 2x + 3$ with x-axis and ordinates corresponding to the minima of y is

$\int \log_e (a^x + x^a) dx$ is equal to

$\lim_{n \to \infty} \left( \frac{1}{4n^2 - 1} + \frac{1}{4n^2 - 4} + \frac{1}{4n^2 - 9} + \ldots + \frac{1}{4n^2 - n^2} \right)$ is equal to

$\int \frac{dx}{x^2 + 4x + 13}$ is equal to

Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is

The differential equation of the family of lines passing through the origin is

If $P = \begin{bmatrix} 0 & i & i \\ -i & 0 & i \\ -i & -i & 0 \end{bmatrix}$ and $Q = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & -i \\ i & i & 0 \end{bmatrix}$, then $PQ$ is equal to

If $x = \sin^{-1}(3t - 4t^3)$ and $y = \cos^{-1}(2t - 1)$, then $\frac{dy}{dx}$ is equal to

If $x^2 + px + q = 0$ is the quadratic equation whose roots are $a - 2$ and $b - 2$, where $a$ and $b$ are the roots of $x^2 - 3x + 1 = 0$, then

If the position vectors of A, B, C are respectively $\hat{i} + \hat{j} - \hat{k}$, $2\hat{i} + 3\hat{j} + \hat{k}$ and $2\hat{i} - \hat{k}$, then the projection of $\overrightarrow{AB}$ on $\overrightarrow{BC}$ is equal to

The area between $y^2 + 4x - 8 = 0$, the x-axis and the line $x = 1$ is

The solution of the equation $(2y-1)dx + (2x-3)dy = 0$ is