List of top Mathematics Questions asked in MET

The equation of the parabola whose vertex and focus are \( (0, 4) \) and \( (0, 2) \) respectively, is:

The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates are:

The line \( x + 2y = 4 \) is translated parallel to itself by 3 units in the sense of increasing \( x \) and then rotated by 30° in the anti-clockwise direction about the point where the shifted line cuts the x-axis. The equation of the line in the new position is:

If the equation \( 12x^2 + 7xy - py^2 - 18x + qy + 6 = 0 \) represents a pair of perpendicular straight lines, then

If the roots of the equation \( \frac{\alpha}{x-\alpha} + \frac{\beta}{x-\beta} = 1 \) are equal in magnitude but opposite in sign, then \( \alpha + \beta \) is equal to

The angle of intersection of ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and circle \( x^2 + y^2 = ab \) is:

If \( Z = f(x + ay) + \phi(x - ay) \), then

If \( x + y = 1 \), then \[ \sum_{r=0}^{n} r^2 \cdot n C_r x^r y^{n-r} \quad \text{is equal to:} \]

Let \[ A = \begin{pmatrix} 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} -5 & 0 & \alpha 4 & 2 & 2 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of matrix \( A \), then \( \alpha \) is:

The existence of the unique solution of the system \[ x + y + z = \lambda, \quad 5x - y + \mu z = 10, \quad 2x + 3y - z = 6 \] depends on:

The image of the point with position vector \[ \mathbf{i} + 3 \mathbf{k} \] in the plane \( \mathbf{r} \cdot (\mathbf{i} + \mathbf{j} + \mathbf{k}) = 1 \) is:

The equation of the plane passing through a point \( A(2, -1, 3) \) and parallel to the vectors \[ \mathbf{a} = (3, 0, -1) \quad \text{and} \quad \mathbf{b} = (-3, 2, 2) \] is:

The limit \[ \lim_{x \to 1} \frac{(2x - 3) \sqrt{x - 1}}{2x^2 + x - 3} \] is equal to:

The vectors \( c, a, b \) are such that \( a \cdot b = 2a \cdot c \), \( |c| = 1 \), \( |b| = 4 \), and \( |b \times c| = \sqrt{15} \), if \( b - 2c = \lambda \alpha \), then \( \lambda \) equals:

If \( x = \sqrt{5} + \sqrt{2} \), \( y = \sqrt{5} - \sqrt{2} \), then \[ 3x^2 + 4xy - 3y^2 \quad \text{is equal to:} \]

Which is the correct order for a given number \( \alpha \) in increasing order?

If \( a, b \), and \( c \) are non-collinear vectors such that for some scalars \( x, y, z \), the equation \[ x a + y b + z c = 0, \quad x a + x b + x c = 0, \] then

The square root of \( \sqrt{50} + \sqrt{48} \) is:

Let \( a, b, c \) be the three vectors such that \( c \neq 0 \) and \[ a \cdot b = 2a \cdot c, \quad |c| = |c| = 1, \quad |b| = 4, \quad |b \times c| = \sqrt{15}, \quad \text{if} \quad b - 2c = \lambda \alpha, \quad \text{then} \quad \lambda \quad \text{equals} \]

Let \[ I_1 = \int_{\alpha}^{\pi - \alpha} x \sin x \, dx, I_2 = \int_{\alpha}^{\pi - \alpha} f(\sin x) \, dx \] then \( I_2 \) is equal to:

The area of the figure bounded by \( y = e^x \), \( y = e^{-x} \) and the straight line \( x = 1 \) is:

If \( x \) is real, then the value of \[ \frac{x^2 + 34x - 71}{x^2 + 2x - 7} \] does not lie between:

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line \( y - 4x + 3 = 0 \), is:

The value of \[ \int_0^{\frac{\pi}{2}} | \sin x - \cos x | dx \] is:

The number of solutions of \[ \log_4 (x - 1) = \log_2 (x - 3) \] is/are: