List of top Questions asked in MHT CET

The radius of a circular plate is increasing at the rate of $0.01\ \text{cm/sec}$. When the radius is $12\ \text{cm}$, the rate at which its area increases is
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
The equation of the common tangent to the circles $x^2 + y^2 - 4x + 10y + 20 = 0$ and $x^2 + y^2 + 8x - 6y - 24 = 0$ is
If $y = x \tan y$, then $\frac{dy}{dx} =$
The differential equation obtained by eliminating A and B from $y = A \cos \omega t + B \sin \omega t$ is
The value of the definite integral $\int_{0}^{\pi} \frac{1}{4 + 3 \cos x} \, dx$ is
The distance between the parallel lines $3x + 4y = 9$ and $6x + 8y = 15$ is
If $\vec{a} = 2\hat{\text{i}} + 3\hat{\text{j}} - \hat{\text{k}}$, $\vec{b} = -\hat{\text{i}} + 2\hat{\text{j}} - 4\hat{\text{k}}$ and $\vec{c} = \hat{\text{i}} + \hat{\text{j}} - 2\hat{\text{k}}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c}) =$
The Cartesian equation of a plane which passes through the points $\text{A}(2, 2, 2)$ and making equal nonzero intercepts on the co-ordinate axes is
If $A = \left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]$, then cofactors of all elements of second row are respectively
The minimum value of the objective function $z = 4x + 6y$ subject to $x + 2y \ge 80$, $3x + y \ge 75$, $x, y \ge 0$ is
If $4ab = 3h^2$, then the ratio of slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is
The joint equation of pair of lines through the origin and having slopes $(1+\sqrt{2})$ and $\frac{1}{(1+\sqrt{2})}$ is
Radium decomposes at the rate proportional to the amount present at any time. If $P\%$ of amount disappears in one year, then amount of radium left after 2 years is
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is 6. Then the probability that it is actually 6 is
The principal solutions of $\cot x = \sqrt{3}$ are
The vectors $\overrightarrow{\text{AB}} = 3\hat{\text{i}} + 4\hat{\text{k}}$ and $\overrightarrow{\text{AC}} = 5\hat{\text{i}} - 2\hat{\text{j}} + 4\hat{\text{k}}$ are the sides of a triangle ABC. The length of the median through A is
The area of the region included between the parabolas $y^2 = 8x$ and $x^2 = 8y$ is
"If two triangles are congruent, then their areas are equal." is the given statement, then the contrapositive of the inverse of the given statement is
Which of following is used for synthesis of adipic acid enzymatically by Drath and Frost?
Identify the product formed when ethyl benzene reacts with nitric acid.
Which among the following is NOT an intensive property?
What is the weight of Al deposited at cathode when 1 ampere current is passed through molten $\text{AlCl}_3$ for 9650 seconds? (At mass of Al = 27)
The solution containing 6 g urea (molar mass 60) per $\text{dm}^3$ of water and another solution containing 9 g of solute A per $\text{dm}^3$ water freezes at same temperature. What is molar mass of A?
Which of the following represents integrated rate law equation for gas phase first order reaction, $\text{A}_{(\text{g})} \rightarrow \text{B}_{(\text{g})} + \text{C}_{(\text{g})}$ if $P_i =$ initial pressure of A and $P =$ total pressure of reaction mixture at time $t$?