List of top Questions asked in MET

If \(m\) things are distributed among \(a\) men and \(b\) women, then the chance that the number of things received by men is odd is:

The point on the straight line \(y = 2x + 11\) which is nearest to the circle \(16(x^2 + y^2) + 32x - 8y - 50 = 0\), is

The number of unit vectors perpendicular to \(\vec{a} = \hat{i}+\hat{j}\) and \(\vec{b} = \hat{j}+\hat{k}\) is:

The radius of a cylinder is increasing at \(2\,m/s\) and height is decreasing at \(3\,m/s\). When \(r=3\,m, h=5\,m\), rate of change of volume is:

The solution of differential equation \(y\log x - y\,dx = x\,dy\) is

The locus of the extremities of the latus rectum of the family of ellipses \(b^2x^2 + y^2 = a^2b^2\) having a given major axis is

By trapezoidal rule, approximate value of \(\int_0^6 \frac{dx}{1+x^2}\)

The quadratic equation whose roots are \(\frac{1}{3+\sqrt{2}}\) and \(\frac{1}{3-\sqrt{2}}\), will be:

The sum of the real solutions of equation \(2|x|^2 + 51 = |1 + 20x|\) is

If sum of four numbers in GP is 60 and AM of first and last is 18, then the numbers are:

Who said, “Number of transistors per square inch on integrated circuits double every year…”?

If geometric mean and harmonic mean of two numbers are \(16\) and \(\frac{64}{5}\) respectively, then \(a:b\) is:

If \(\vec{a}, \vec{b}, \vec{c}\) are three non-coplanar vectors, then \([\vec{a}\times\vec{b},\ \vec{b}\times\vec{c},\ \vec{c}\times\vec{a}]\) is equal to:

Evaluate: \[ \cot^{-1}\!\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) \]

If \(1, \omega\) and \(\omega^2\) are the cube roots of unity, then the value of \((1-\omega+\omega^2)(1+\omega-\omega^2)\) is equal to

If \(A(-1,3,2), B(2,3,5), C(3,5,-2)\) are vertices of a triangle ABC, then angles of Triangle ABC are :

The equation of the curve through \((1,0)\), whose slope is \(\frac{y-1}{x^2+x}\), is:

Evaluate: \[ \lim_{x \to 0} \frac{\int_0^{x^2} \sin\sqrt{t}\,dt}{x^3} \]

Number of points where \(f(x)=[\sin x + \cos x]\) is not continuous in \((0,2\pi)\) is:

According to Newton-Raphson method, the value of \(\sqrt{12}\) up to three places of decimal will be

The curve, for which the area of the triangle formed by X-axis, the tangent line at any point \(P\) and line \(OP\) is equal to \(a^2\), is given by

The radical centre of the system of circles, \[ x^2 + y^2 + 4x + 7 = 0,\quad 2(x^2 + y^2) + 3x + 5y + 9 = 0 \] and \(x^2 + y^2 + y = 0\) is

If \[ \lim_{x \to 0} \frac{\sin(\sin x) - \sin x}{ax^3 + bx^5 + c} = -\frac{1}{12}, \] then

Solution of the equation \[ \cos^2 x \frac{dy}{dx} - (\tan 2x)\,y = \cos^4 x,\quad |x|<\frac{\pi}{4}, \] where \(y\!\left(\frac{\pi}{6}\right)=\frac{3\sqrt{3}}{8}\), is given by: