List of top Questions asked in MET

Equation of a plane passing through \((-1,1,1)\) and \((1,-1,1)\) and perpendicular to \(x + 2y + 2z - 5 = 0\) is

What is a compiler?

If \[ \int \sin^2 t \tan^{-1}\sqrt{\frac{1-x}{1+x}}\,dx = A\sin^{-1}x + B\sqrt{1-x^2} + C, \] then \(A+B\) is equal to

Let \[ f(x) = \begin{vmatrix} \sin 3x & 1 & 2\left(\cos \frac{3x}{2} + \sin \frac{3x}{2}\right)^2 \cos 3x & -1 & 2\left(\cos \frac{3x}{2} - \sin \frac{3x}{2}\right)^2 \tan 3x & 4 & 1 + 2\tan 3x \end{vmatrix} \] Then \(f(x)\) is equal to

Condition for line \(lx + my + n = 0\) to be a normal to \(\frac{x^2}{25} + \frac{y^2}{9} = 1\):

The least value of \(a\), for which the function \[ \frac{4}{\sin x} + \frac{1}{1-\sin x} = a \] has at least one solution in the interval \(\left(0,\frac{\pi}{2}\right)\), is:

If one regression coefficient is less than unity, then the other will be:

Three concurrent edges of a parallelepiped are given by \[ \vec{a} = 2\hat{i} - 3\hat{j} + \hat{k},\quad \vec{b} = \hat{i} - \hat{j} + 2\hat{k},\quad \vec{c} = 2\hat{i} + \hat{j} - \hat{k}. \] The volume of the parallelepiped is:

Roots of equation \(x^3 - 6x + 1 = 0\) lie in the interval

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

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

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

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

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

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

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

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

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

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

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