List of top Questions asked in MET- 2015

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

The area of the region bounded by the parabola \((y-2)^2 = x-1\), the tangent to the parabola at the point \((2,3)\) and the X-axis, is

Solution of the differential equation \(x = 1 + xy\frac{dy}{dx} + \frac{(xy)^2}{2!}\left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!}\left(\frac{dy}{dx}\right)^3 + ..........\) is

Numbers 1, 2, 3, ..., 100 are written down on each of the cards A, B, and C. One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm) of three sides of a right angled triangle, is

If \([\cdot]\) denotes the greatest integer function, then \(f(x) = \left[\frac{1}{2} - x\right] + [x]\)

If \(f(x) = \min\{1, x^2, x^3\}\), then

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 \(\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \sin x^2}{\sin x^2 + \sin(\ln 6 - x^2)} dx\) is

\(\int_{1}^{4} \log_e [x] dx\) equals

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

If \(f(x) = \frac{\sin(e^x - 2) - 1}{\log(x - 1)}\), then \(\lim_{x \to 2} f(x)\) is given by

If \(\tan A\) and \(\tan B\) are the roots of the equation \(x^2 - ax + b = 0\), then the value of \(\sin^2(A + B)\) is

In a \(\triangle ABC\), if \(a^2 + b^2 + c^2 = ac + \sqrt{3}ab\), then the triangle is

Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be non-zero vectors such that no two are collinear and \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = \frac{1}{3} |\mathbf{b}||\mathbf{c}|\mathbf{a}\). If \(\theta\) is the acute angle between the vectors \(\mathbf{b}\) and \(\mathbf{c}\), then \(\sin \theta\) equals

The distance of the point \((1,1)\) from the line \(2x - 3y - 4 = 0\) in the direction of the line \(x + y = 1\), is