List of top Questions asked in MHT CET- 2020

A force \(F = (10 + 0.5x)\) N acts on a particle in the x-direction. The work done by the force in displacing the particle from \(x = 0\) to \(x = 2\) m is

One end of thick horizontal copper wire of length \(2L\) and radius \(2R\) is welded to the end of another thin horizontal copper wire of length \(L\) and radius \(R\). When they are stretched by applying the same force at the two ends, the ratio of the elongation in the thick wire to that in the thin wire is

Let the physical quantity be \( x = \frac{a^3b^2}{c} \). If the percentage error in the measurement of \( a \), \( b \), and \( c \) is 2%, 3%, and 4% respectively, then the percentage error in the measurement of \( x \) is:

If \( a \), \( b \), \( c \) are non-negative distinct numbers and \( ai + aj + ck \), \( i + j + k \), and \( ci + cj + bk \) are coplanar vectors, then

If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively

A body performing simple harmonic motion has potential energy \(P_1\) at displacement \(x_1\). Its potential energy is \(P_2\) at displacement \(x_2\). The potential energy \(P\) at displacement \((x_1 + x_2)\) is

Find the dimensions of the quantity \( x \) in the equation \( T = 2\pi \left( \frac{ML^3}{3XY} \right)^{\frac{1}{2}} \), where \( T \) is the time period, \( M \) is mass, \( L \) is length, and \( Y \) is the Young’s modulus.

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

A wire has a length of 2 m and resistance of \(10\,\Omega\). It is connected in series with a resistance of \(990\,\Omega\) and a cell of e.m.f. 2 V. The potential gradient along the wire will be

The moduli of elasticity for a substance are Young’s modulus, Bulk modulus and Modulus of rigidity. All the three moduli of elasticity are possessed by

The percentage errors in measurements of mass and speed of a body are 2% and 3% respectively. What is the percentage error in kinetic energy of the body?

In gas phase, the H–O–O–H dihedral bond angle in H\(_2\)O\(_2\) is

If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of \[ f\{f[f(2)]\} \] is

38.4 g of an unknown substance (molar mass \(= 384\ \text{g mol}^{-1}\)) and 116 g of acetone are used to prepare a solution at 313 K. If vapour pressure of pure acetone (molar mass \(= 58\ \text{g mol}^{-1}\)) is 0.842 atm, what is the vapour pressure of the solution?

If \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}, \] then find \((AB)^{-1}\).

The value of \( m \) if the vectors \[ \mathbf{A} = i - j - 6k, \quad \mathbf{B} = i - 3j + 4k, \quad \mathbf{C} = 2i - 5j + mk \] are coplanar, is

The equation of a plane containing the lines \( \vec{r} = (i + 2j - 4k) + \lambda (2i + 3j + 6k) \) and \( \vec{r} = (i + 3j + 4k) + \mu (i + j - k) \) is

Which of the following reactions of alcohols involves breaking of O–H bond?

How much charge in coulombs is required for the reduction of one mole of Al\(^{3+}\) to Al?

A flywheel of mass 2 kg has radius of gyration 0.5 m. If it makes 10 r.p.s., then its rotational kinetic energy will be

For \( f(x) = [x] \), where \( [x] \) is the greatest integer function, which of the following is true, for every \( x \in \mathbb{R} \)?

What is the volume of 1 mole of a crystalline solid having unit cell edge length 16 \(\times\) 10\(^{-10}\) cm, if its unit cell contains 24 molecules?

If \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) represents a joint equation of directrices of the hyperbola \( 16x^2 - 9y^2 = 144 \), then \( g + f - c = \)

Which of the following metals does NOT displace zinc from its solution?

The joint equation of two lines through the origin, each of which makes an angle of \(30^\circ\) with the line \(x + y = 0\), is