List of top Questions asked in MHT CET

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is ______.

If $\tan^{-1}(x + 1) + \tan^{-1} x + \tan^{-1}(x - 1) = \tan^{-1} 3$, then for $x < 0$ the value of $500x^4 + 270x^2 + 997 = \dots$

Which from following statements is NOT true for phenol?

A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.

A monobasic weak acid dissociates 2% in its 0.002 M solution. Calculate the dissociation constant of weak acid.

A particle starts oscillating simple harmonically from its mean position with time period 'T'. At time $t = T/6$, the ratio of the potential energy to kinetic energy of the particle is \dots

The altitude through vertex A of $\triangle ABC$ with position vectors of points A, B, C as $\vec{a}, \vec{b}, \vec{c}$ respectively is ______.

In Young's double slit experiment, at two points P and Q on screen, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\lambda/4$ respectively. The ratio of intensities at point P to that at Q will be \dots

Heat supplied $dQ$ = increase in internal energy $dU$ is true for \dots

One of the following values of inputs A, B and C respectively gives output (Y) of the following combination of logic gates as '1' is \dots

What is the total number of unit cells shared by each corner particle of bcc unit cell?

The eccentricity of the hyperbola which passes through the points $(3, 0)$ and $(3\sqrt{2}, 2)$ is \dots

Calculate the total volume occupied by all particles in fcc unit cell if volume of unit cell is $6.4 \times 10^{-23}$ cm$^3$.

Calculate the number of unit cells in 1 cm$^3$ volume of metal if unit cell edge length is $1.25 \times 10^{-8}$ cm.

If $\sqrt{y} - \sqrt{y} - \dots = \sqrt{x} + \sqrt{x} + \dots$ then $dy/dx = \dots$

$\int \frac{dx}{(x + a)^{9/7} (x - b)^{5/7}}$ = ______.

$\int \frac{x^4 \cos(\tan^{-1} x^5)}{1 + x^{10}} dx$ equals ______.

If the plane $x/2 - y/3 - z/5 = 1$ cuts the co-ordinate axes in points A, B, C respectively, then the area of the triangle ABC is ______.

The angle $\theta$, at which the curves $y = 3^x$ and $y = 7^x$ intersect, is given by ______.

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students selected at random 4 are swimmers is ______.

The Cartesian equation of the plane $\vec{r} = (2\hat{i} - 3\hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k})$ is \dots}

The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}

Which among the following salts forms basic solution when dissolved in water?

The function $f(x) = x^3 - 6x^2 + ax + b$ satisfies the conditions of Rolle's theorem in $[1, 3]$. Then the values of $a$ and $b$ are respectively \dots

$\int_{\pi/4}^{\pi/2} 2\sin^{-4} x dx = \_\_\_\_\_\_.$
Note: The initial OCR showed "$23.4 \frac{/2}{/4}$". The "4" was a misread coefficient. The mathematical evaluation of the options indicates a coefficient of 2 is present in the intended question.