List of top Questions asked in MET- 2015

The Government is likely to ............. a new rural infrastructure ............... by the end of March.
The company was ............ with a ............ to improve power distribution in rural areas.
State owned banks may lose ................ Government business if they ............. to fulfil their developmental role.
The Finance Minister is ............... that the country will .......... a 9% growth rate.
As public resources are ......... there is a need for ........ of the private sector in development.
A coil having \(n\) turns and resistance \(R\Omega\) is connected with a galvanometer of resistance \(4R\Omega\). This combination is moved in time \(t\) second from a magnetic field \(w_1\) weber to \(w_2\) weber. The induced current in the circuit is
The approximate value of \((1.0002)^{3000}\) is
If \(f(x) = \frac{\sin(e^x - 2) - 1}{\log(x - 1)}\), then \(\lim_{x \to 2} f(x)\) is given by
The radius of the circle passing through the foci of the ellipse \(9x^2 + 16y^2 = 144\) and having its centre at \((0,3)\), is
\(\int_{1}^{4} \log_e [x] dx\) equals
The value of \(\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \sin x^2}{\sin x^2 + \sin(\ln 6 - x^2)} dx\) is

If \[ f(x) = \begin{cases} \dfrac{\sin(\cos x) - \cos x}{(\pi - 2x)^3}, & x \ne \dfrac{\pi}{2} \\ k, & x = \dfrac{\pi}{2} \end{cases} \] is continuous at \( x = \dfrac{\pi}{2} \), then \( k \) is equal to:

If \([\cdot]\) denotes the greatest integer function, then \(f(x) = \left[\frac{1}{2} - x\right] + [x]\)
If \(x_n = \cos \frac{\pi}{3^n} + i \sin \frac{\pi}{3^n}\), then \(x_1 x_2 x_3 ..........\) is equal to
The total number of natural numbers of 6 digits that can be made with digits 1, 2, 3, 4, if all digits are to appear in the same number at least once, is
The number of solutions of the equation \(9x^2 - 18|x| + 5 = 0\) belonging to the domain of definition of \(\log_e \{(x+1)(x+2)\}\), is
If \(2^x + 2^y = 2^{x+y}\), then \(\frac{dy}{dx}\) is equal to
If \(3x + y = 0\) is a tangent to the circle with centre at the point \((2, -1)\), then the equation of the other tangent to the circle from the origin, is
If \(\sin A + \cos A = m\) and \(\sin^3 A + \cos^3 A = n\), then
In \(\triangle ABC\), if \(a = 4\), \(b = 3\), \(\angle A = 60^\circ\). Then, \(c\) is the root of the equation
The sum to \(n\) terms of the series \(\frac{3}{1^2} + \frac{5}{1^2+2^2} + \frac{7}{1^2+2^2+3^2} + ..........\) is
The value of \(\lim_{x \to \infty} \left\{ \frac{a_1^{1/x} + a_2^{1/x} + .......... + a_n^{1/x}}{n} \right\}^x\) is

Evaluate the integral:  

\[ \int \frac{\sec^2 x}{(\sec x + \tan x)^{9/2}} \, dx \]

The centre of the circle passing through \((0,0)\) and \((1,0)\) and touching the circle \(x^2 + y^2 = 9\), is
If the line \(x - 1 = 0\) is the directrix of the parabola \(y^2 - kx + 8 = 0\), then one of the value of \(k\) is