List of top Questions asked in MHT CET- 2021

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

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 $\lambda =$

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

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 $\text{Var}(X) =$

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

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

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

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

What is the volume of unit cell of a metal (at. mass $25\text{ g mol}^{-1}$) having BCC structure and density $3\text{ g cm}^{-3}$ ?

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

Which among following monomers is used to prepare PVC?

What is the work done when a gas is compressed from $2.5 \times 10^{-2}\text{ m}^3$ to $1.3 \times 10^{-2}\text{ m}^3$ at constant external pressure of $4.05\text{ bar}$?

What is boiling point of a decimolal aqueous solution of glucose if molal elevation constant for water is $0.52^\circ\text{C kg mol}^{-1}$?

Dissociation constant of propionic acid is $1.32 \times 10^{-5}$. Calculate the degree of dissociation of acid in $0.05\text{ M}$ solution.

Identify homoleptic complex from following :

Identify the product obtained when phenol reacts with concentrated sulphuric acid at $293\text{ K}$ ?

An element with simple cubic close structure has edge length of unit cell $3.86\ \text{\AA}$. What is the radius of atom?

In a first order reaction, concentration of reactant is reduced to (1/8)th of concentration in 23.03 minutes. What is half-life period of reaction?

What is the number of $\text{-CH}_2\text{-}$ groups present in dodecane?

Which among the following statements is NOT true?

Identify the reactant, reagent and condition of Kolbe's reaction from following.

The wavelength of a spectral line of caesium is $460\text{ nm}$. What is the frequency of spectral line?

Select the catalyst used in hydrogenation of ethene.