List of top Questions asked in MET

A projectile has the maximum range 500 m. If the projectile is thrown up an inclined plane of $30^\circ$ with the same (magnitude) velocity, the distance covered by it along the inclined plane will be:

Two capacitors of capacitances $3~μ F$ and $6~μ F$ are charged to a potential of 12 V each. They are now connected to each other, with the positive plate of each joined to the negative plate of the other. The potential difference across each will be:

White light reflected at normal incidence from a soap film has minima at 6500 Å and maxima at 7500 Å in the visible region with no minimum in between. If $μ$ is 5/3 for the film, the thickness of film is:

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be:

A current carrying coil is bent sharply so as to convert it into a double loop both carrying current in the same direction. If B be the initial magnetic field at the centre, then what will be the final concentric magnetic field?

If 10% of the main current is to be passed through the moving coil galvanometer of resistance $99Ω$, then the required shunt resistance will be:

The ionisation potential of hydrogen atom is 13.6 eV. How much energy need to be supplied to ionise the hydrogen atom in the first excited state?

How does the energy difference between the consecutive energy level vary as the quantum number n increases?

I\(_2\) dissolves in KI solution due to formation of

The approximate value of \((1.0002)^{3000}\) is

\((\mathbf{a} \cdot \hat{\mathbf{i}})(\mathbf{a} \times \hat{\mathbf{i}}) + (\mathbf{a} \cdot \hat{\mathbf{j}})(\mathbf{a} \times \hat{\mathbf{j}}) + (\mathbf{a} \cdot \hat{\mathbf{k}})(\mathbf{a} \times \hat{\mathbf{k}})\) is equal to

If \(A = \{(x,y): x^2 + y^2 = 25\}\) and \(B = \{(x,y): x^2 + 9y^2 = 144\}\); then \(A \cap B\) contains

The value of \(c\) prescribed by Lagrange's mean value theorem, when \(f(x) = \sqrt{x^2 - 4}\), \(a = 2\) and \(b = 3\), is

The mean deviation from the mean of the series \(a, a+d, a+2d, .........., a+2nd\), is

If \(f(x) = x e^{x(1-x)}\), then \(f(x)\) is

If \(\omega\) is an imaginary cube root of unity, then the value of \((1+\omega)(1+\omega^2)(1+\omega^3)(1+\omega^4)(1+\omega^5)..........(1+\omega^{3n})\) is

Let \(X\) denotes the number of times heads occur in \(n\) tosses of a fair coin. If \(P(X=4)\), \(P(X=5)\) and \(P(X=6)\) are in AP, then the value of \(n\) is

If there is a term containing \(x^{2r}\) in \(\left(x + \frac{1}{x^2}\right)^{n-3}\), then

The value of \(\sin^{-1}\left\{\cot\left(\sin^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}\right) + \cos^{-1}\frac{\sqrt{12}}{4} + \sec^{-1}\sqrt{2}\right\}\) is

If \(\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta\), then \(9x^2 - 12xy\cos\theta + 4y^2\) is equal to

If \(\tan(\sec^{-1}x) = \sin\left(\cos^{-1}\frac{1}{\sqrt{5}}\right)\), then \(x\) is equal to

The equation of the tangent to the curve \(y = (2x-1)e^{2(1-x)}\) at the point of its maximum, is

The proposition \((p \rightarrow \neg p) \wedge (\neg p \rightarrow p)\) is

The number of ways in which four letters can be selected from the word 'DEGREE', is

If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is