List of top Questions asked in MHT CET

The equation of the circle whose end points of a diameter are the centres of the circles \[ x^2 + y^2 + 2x - 4y + 1 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 6y + 17 = 0 \] is

The area of the region bounded by the curve \( y = 4x - x^2 \) and the x-axis is

If \[ \mathbf{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} - 4\hat{k}, \quad \mathbf{c} = \hat{i} + \hat{j} + \hat{k} \] then \( (\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{a} \times \mathbf{c}) = \)

The maximum value of the function \( \frac{\log x}{x}, x \neq 0 \) is

The approximate value of \( \cot^{-1} (1 \cdot 001) \) is

The direction cosines of a line which makes equal acute angles with the co-ordinate axes are

With usual notations, if in \( \triangle ABC \), \( s \) is the semi-perimeter and \( (s - a)(s - b) = (s - c) \), then \( \triangle ABC \) is

For the following shaded region, the linear constraints are:

For \( \theta \in \left( 0, \frac{\pi}{2} \right) \), if \( \tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1 \), then \( \theta = \)

If \[ y = \left( \frac{x^2 + 1}{x} \right)^x \text{ and } \frac{dy}{dx} = y \left[ g(x) + \log \left( \frac{x^2}{x+1} \right) \right], \text{ then } g(x) = \]

The solution of \( rdx + (x - r^2) dr = 0 \) is

A metal has half-life period of 10 days. A sample originally has a mass of 1000 mg, then the mass remaining after 50 days is

If \[ A = \{ x / x \text{ is a prime number}, 0 \leq x \leq 9 \}, \text{ then the number of elements of the power set of } A \text{ is} \]

The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are

The symbolic form of the following circuit is (where \( p, q, r \) represent switches \( s_1, s_2, s_3 \) which are closed respectively)

The general solution of \( \tan \theta + \tan 2\theta = \tan 3\theta \)

Which among the following group -15 elements forms hydrogen bonding in its hydride compounds?

An element crystallizes in bcc type of unit cell having atomic radius \( 1.33 \times 10^{-8} \) cm, the edge length of unit cell will be

Which among the following compounds is treated with benzonitrile to obtain benzophenone in dry ether and then acid hydrolysis?

For the following reaction, the relation between \( \Delta H \) and \( \Delta U \) is
\[ \text{2SO}_3(\text{g}) + \text{O}_2(\text{g}) \rightarrow \text{2SO}_3(\text{g}) \]

0.5 molal aqueous solution of a weak acid (HX) is 20% ionised. If Kf of water is 1.86 K kg mol⁻¹, the lowering in freezing point of solution is

What is the number of moles and total number of atoms respectively present in 5.6 cm\(^3\) of ammonia gas at STP?

In aqueous phase the order of basic strength of alkylamine is

An element crystallizes in bcc type of unit cell, the density and edge length of unit cell is 4 g cm\(^{-3}\) and 500 pm respectively. What is the atomic mass of an element?

Which polymer is obtained from monomers 3-Hydroxy butanoic acid and 3-Hydroxy pentanoic acid?