List of top Questions asked in MHT CET

The complex number with argument $\frac{5\pi}{6}$ at a distance of 2 units from the origin is

If vectors $\bar{a}=2\hat{i}+2\hat{j}+3\hat{k}$, $\bar{b}=-\hat{i}+2\hat{j}+\hat{k}$ and $\bar{c}=3\hat{i}+\hat{j}+2\hat{k}$ are such that $\bar{a}+\lambda\bar{b}$ is perpendicular to $\bar{c}$, then $\lambda =$

If $\bar{a}=3\hat{i}-5\hat{j}, \bar{b}=6\hat{i}+3\hat{j}$ are two vectors and $\bar{c}$ is a vector such that $\bar{c}=\bar{a}\times\bar{b}$, then $|\bar{a}|:|\bar{b}|:|\bar{c}|$ is

The equation of the plane passing through $(-2,2,2)$ and $(2,-2,-2)$ and perpendicular to the plane $9x-13y-3z=0$ is

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is

The area of the region bounded by the curve $y^2 = 4x$ and the line $y = x$ is

The general solution of the differential equation $y(1+\log x)\left(\frac{dx}{dy}\right) - x\log x = 0$ is

If $\frac{\cos(A+B)}{\cos(A-B)} = \frac{\sin(C+D)}{\sin(C-D)}$, then $\tan A \tan B \tan C =$

If $F(\alpha)=\begin{bmatrix}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{bmatrix}$, where $\alpha \in R$, then $[F(\alpha)]^{-1} =$

Negation of the statement $\forall x \in R, x^2+1=0$ is

If the lines $\frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{z-3}{2}$ and $\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles, then $\lambda =$

If the two lines given by $ax^2 + 2hxy + by^2 = 0$ make inclinations $\alpha$ and $\beta$, then $\tan(\alpha + \beta) =$

The differential equation of family of circles whose centres lie on X-axis is

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the store will receive at most one defective bulb is

The vertices of triangle ABC are $A \equiv (3,0,0) ; B \equiv (0,0,4) ; C \equiv (0,5,4)$. Find the position vector of the point in which the bisector of angle A meets BC is

The general solution of the differential equation $(3xy + y^2)dx + (x^2 + xy)dy = 0$ is

The distance between parallel lines $\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 2\hat{k})$ and $\bar{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 2\hat{k})$ is

$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$, then $\tan \theta=$

In a meeting 60\% of the members favour and 40\% oppose a certain proposal. A member is selected at random and we take $X = 0$ if he opposed and $X = 1$ if he is in favour, then $\text{Var}(X) =$

If $e^{-y} \cdot y = x$, then $\frac{dy}{dx}$ is

$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=$

The reaction of propane with bromine in presence of UV light predominantly forms

Which among following monomers is used to prepare PVC?

Oxidation state of Cr in potassium dichromate is

Identify reactant (A) used in the following conversion.
Chlorobenzene + A $\xrightarrow{\text{anhydrous AlCl}_3}$ 1-Chloroacetophenone + 4-Chloroacetophenone