List of top Questions asked in MHT CET

The approximate value of $\log_{10} 998$ is (given that $\log_{10}e=0.4343$)

The value of $\alpha$, so that the volume of the parallelopiped formed by $\hat{i}+\alpha\hat{j}+\hat{k}$, $\hat{j}+\alpha\hat{k}$ and $\alpha\hat{i}+\hat{k}$ becomes maximum, is

The area (in sq. units) of the region bounded by the parabola $x = \frac{y^2}{2}$ and the line $x = y + 4$ is

If $\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}$, then the value of $\cos^{-1}x+\sin^{-1}y$ is

Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^\circ$, then the difference of the remaining angles is

A, B, C are three events, one of which must and only one can happen. The odds in favor of A are $4:6$, the odds against B are $7:3$. Thus, odds against C are

The differential equation of all parabolas, whose axes are parallel to Y-axis, is

Let two non-collinear vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves, so that at any time t the position vector $\overline{OP}$, where O is origin, is given by $\hat{a}\sin t+\hat{b}\cos t.$ when P is farthest from origin O, let M be the length of OP and $\hat{u}$ be the unit vector along $\overline{OP,}$ then

The number of solutions in $[0,2\pi]$ of the equation $16^{\sin^{2}x}+16^{\cos^{2}x}=10$ is

If $Z_{1}=4i^{40}-5i^{35}+6i^{17}+2$, $Z_{2}=-1+i$ where $i=\sqrt{-1}$, then $|Z_{1}+Z_{2}|=$

The value of the integral $\int\frac{x+1}{x(1+xe^{x})^{2dx$ is

If $E_{a}$ and $E_{q}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '$r$' from the centre of the dipole, then}

In potentiometer experiment, the balancing length is $8 \text{ m}$ when two cells $E_{1}$ and $E_{2}$ are joined in series. When two cells are connected in opposition the balancing length is $4 \text{ m}$. The ratio of the e.m.f. of the two cells $\left( \frac{E_{1{E_{2 \right)$ is

The pressure and density of a diatomic gas ($\gamma = \frac{7}{5}$) changes adiabatically from $(P, \rho)$ to $(P', \rho')$. If $\frac{\rho'}{\rho} = 32$ then $\frac{P'}{P}$ should be

In a Binomial distribution with $n=4$ if $2P(X=3)=3P(X=2)$, then the variance is

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1),$ then the third vertex C of the triangle is

What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless?

1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

It is easier to spray water to which soap is added because addition of soap to water}

A coil having an inductance of $\frac{1}{\pi} \text{ H}$ is connected in series with a resistance of $300 \Omega$. If $20 \text{ V}$ from a $200 \text{ Hz}$ source are impressed across the combination, the value of the phase angle between the voltage and the current is

Two wavelengths of sodium light $590 \text{ nm}$ and $596 \text{ nm}$ are used one after another to study diffraction due to single slit of aperture $2 \times 10^{-6} \text{ m}$. The distance between the slit and the screen is $1.5 \text{ m}$. The separation between the positions of first maximum of the diffraction pattern obtained in the two cases is

An ideal refrigerator has freezer at a temperature of $-13^{\circ}\text{C}$. The coefficient of performance of the engine is $5$. The temperature of the air (to which heat is rejected) is

A block of mass '$M$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, $g = 10 \text{ ms}^{-2}, \pi^2 = 10$ )}

Two spherical soap bubbles of radii '$a$' and '$b$' in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to}

A body (mass $m$) starts its motion from rest from a point distant $R_0$ ($R_0>R$) from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ($G =$ universal constant of gravitation, $M =$ mass of earth, $R =$ radius of earth)}