List of top Questions asked in MET

DILETTANTE

A person concerned with practical results and values is

A speech by an actor at the end of a play is

The teacher ordered Kamal to leave the room and .......... him to return

A person without manners or polish is

The solution of the differential equation \( \frac{dy}{dx} - \sin x \sin y = 0 \) is

Member of a band of robbers

The inverse of the proportion \( (p \wedge q) \Rightarrow r \) is

If \( \log_3 2 \), \( \log_3 (2^x - 5) \), and \( \log_3 \left( \frac{2^x - 7}{2} \right) \) are in AP, then \( x \) is equal to

If the roots of the cubic equation \( ax^3 + bx^2 + cx + d = 0 \) are in GP, then

The least remainder when \( 17^{30} \) is divided by 5, is

In the group \( G = \{ 1, 2, 3, 4, \times_5 \} \), the solution of \( 2^{-1} \times (3 \times 5^x) = 4 \) is

The diameter of \( 16x^2 - 9y^2 = 144 \) which is conjugate to \( x = 2y \) is

The circle on focal radii of a parabola as diameter touches

\( \frac{\sqrt{3}}{6} + \sqrt{3} + \frac{\sqrt{6}}{3 + \sqrt{2}} \) is equal to

The equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point \( (2, -3) \) and focus at \( (3, -3) \) and one vertex at \( (4, -3) \) is

A circle touches the x-axis and also touches the circle which centre at \( (0, 3) \) and radius 2. The locus of the center of the circle is

The set of points where the function \( f(x) = |x| \) is differentiable, is

If \( f(x) = |x| \sin |x| \), then \( f'(x) \) is equal to

The area bounded by the curve \( y^2 = 2x + 1 \) and the straight line \( x - y - 1 = 0 \) is given by

One diagonal of a square is along the line \( 8x - 15y = 0 \) and one of its vertices is \( (1, 2) \). Then, the equation of the sides of the square passing through this vertex are

The two curves \( x^3 - 3xy^2 + 2 = 0 \) and \( 3x^2y - y^3 = 2 \) are

The limit \( \lim_{n \to \infty} \left[ \sec^2 \frac{\pi}{4n} + \sec^2 \frac{2\pi}{4n} + \dots + \sec^2 \frac{n\pi}{4n} \right] \) is equal to

If \( f(x) = |\cos x| \) and \( g(x) = [x] \), then \( g \circ f(x) \) is equal to

If \( n \in \mathbb{N} \), then \( |\sin nx| \) is