List of top Questions asked in MET- 2011

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

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

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

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

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

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 value of \( \cos^{-1} \left( \cos \frac{7\pi}{6} \right) \) is

The number of solutions of the equation \( 2 \sin^{-1} \sqrt{x^2 - x + 1} + \cos^{-1} \sqrt{x^2 - x + 2} = \frac{3\pi}{2} \) in the interval \( [0, 5\pi] \) is

The circumcenter of a triangle formed by the lines \( xy + 2x + 2y + 4 = 0 \) and \( x + y + 2 = 0 \) is

Each side of a square subtends an angle of \( 60^\circ \) at the top of a tower \( h \) meters high standing in the center of the square. If \( a \) is the length of each side of the square, then

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

In \( \triangle ABC \), if \( a = 30, b = 24, c = 18 \), then \( r_3 \) is equal to

The number of values of \( x \) in the interval \( [0, 5\pi] \) satisfying the equation \( 3\sin^2 x - 7\sin x + 2 = 0 \) is

The expression \( \left( 1 + \cos \frac{\pi}{8} \right) \left( 1 + \cos \frac{3\pi}{8} \right) \left( 1 + \cos \frac{5\pi}{8} \right) \left( 1 + \cos \frac{7\pi}{8} \right) \) is equal to

ABCD is a rectangular field. A vertical lamp post of height 12 m stands at the corner A. If the angle of elevation of its top from B is 60° and from C is 45°, then the area of the field is

In \( \triangle ABC \), \( \frac{b - c}{r_1} + \frac{c - a}{r_2} + \frac{a - b}{r_3} \) is equal to

The inequality \( n!>2^{n-1} \) is true for

If the circle \( x^2 + y^2 + 2gx + 2fy + c = 0 \) is touched by \( y = x \) at \( P \) such that \( OP = 6\sqrt{2} \), then the value of \( c \) is

The ratio in which the line \( 3x + 4y + 2 = 0 \) divides the distance between \( 3x + 4y + 5 = 0 \) and \( 3x + 4y - 5 = 0 \) is

The coefficient of \( x^4 \) in the expansion of \( (1 + x + x^2 + x^3)^n \) is

If \( 2x + 3b + 6c = 0 \), then at least one root of the equation \( ax^2 + bx + c = 0 \) lies in the interval