List of top Mathematics Questions asked in MET

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

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

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 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

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

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:

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

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:

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

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:

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 :

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

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

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:

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

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

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

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