List of top Questions asked in MET- 2019

Let \(z_1, z_2, z_3\) be three vertices of an equilateral triangle circumscribing the circle \(|z| = 1/2\). If \(z_1 = 1/2 + i\sqrt{3}/2\) and \(z_1, z_2, z_3\) were in anticlockwise sense, then \(z_2\) is

The number of real solutions of the equation \(1 + |e^x - 1| = e^x(e^x - 2)\) is

Let \(f(x) = x^p \cos(1/x)\) when \(x \neq 0\) and \(f(x) = 0\), when \(x = 0\). Then \(f(x)\) will be differentiable at \(x = 0\), if

If \(z = x + iy\), \(z^{1/3} = a - ib\) then \(\frac{x}{a} - \frac{y}{b} = k(a^2 - b^2)\), where \(k\) is equal to

If \(u = x^2 + y^2\) and \(x = s + 3t\), \(y = 2s - t\) then \(\frac{d^2 u}{ds^2}\) is equal to

The derivative of \(f(x) = 3|2 + x|\) at the point \(x_0 = -3\) is

Derivative of the function \(f(x) = \log_5(\log_7 x)\), \(x>7\) is

The length of the axis of the conic \(9x^2 + 4y^2 - 6x + 4y + 1 = 0\) are

The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is

If \(f(x) = \cot^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right)\) and \(g(x) = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)\), then \(\lim_{x \to a} \frac{f(x) - f(a)}{g(x) - g(a)}\), \(0<a<1/2\), is

\(\lim_{x \to -2} \frac{\sin^{-1}(x + 2)}{x^2 + 2x}\) is equal to

If \(c = 2\cos\theta\), then the value of the determinant \(\Delta = \begin{vmatrix} c & 1 & 0 \\ 1 & c & 1 \\ 6 & 1 & c \end{vmatrix}\) is

If \(\cos P = 1/7\) and \(\cos Q = 13/14\), where P and Q both are acute angles. Then the value of \(P - Q\) is

If \(\sec^{-1}x = \csc^{-1}y\), then \(\cos^{-1}(1/x) + \cos^{-1}(1/y)\) is equal to

The equation \(3\cos x + 4\sin x = 6\) has ... solution.

If \(\tan\theta = -4/3\), then the value of \(\sin\theta\) is

If n be any integer, then \(n(n+1)(2n+1)\) is:

The equation of bisectors of the angles between the lines \(|x| = |y|\) are

The base of vertices of an isosceles triangle PQR are Q(1, 3) and R(-2, 7). The vertex P can be

The normal at the point (3, 4) on a circle cuts the circle at the point (-1, -2). Then the equation of the circle is

If the angles between the pair of straight lines represented by the equation \(x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0\) is \(\tan^{-1}(1/3)\). Where \(\lambda\) is a non-negative real number, then \(\lambda\) is

The distance of the line \(2x - 3y = 4\) from the point \((1, 1)\) measured parallel to the line \(x + y = 1\) is

In the oxidation of C\(_6\)H\(_5\)-CH\(_2\)-CH\(_3\) by KMnO\(_4\) the product formed is

C\(_6\)H\(_6\) consists of one ring, while naphthalene consists of two rings. Both of them are aromatic and obey the (4n+2) rule. Thus the number of \(\pi\)-electrons inside rings of C\(_6\)H\(_6\) and naphthalene are respectively

Among H—CHO, CH\(_3\)CHO and C\(_6\)H\(_5\)CHO, which will undergo Cannizzaro's reaction?