List of top Questions asked in MHT CET

If the polar co-ordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$, then its Cartesian co-ordinates are

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

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

In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $\overline{PS} + \overline{QR} = t\overline{MN}$, then $t =$

A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, is

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

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 $[F(\alpha)]^{-1} =$

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

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

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

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

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

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

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

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 $\lambda =$

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 $\text{Var}(X) =$

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

What is the number of electrons passed through an electrolyte solution when 1 ampere current is passed for 16.1 minutes?

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

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

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