List of top Questions asked in JEE Main, KCET

Cellulose is an important structural component in plants which is made up of

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is ________ mm.

Find dipole moment of a system consisting of charge $q_1 = 3\,\mu C$ and $q_2 = -9\,\mu C$ with position coordinates $\vec r_1 = 2\hat i + 3\hat j + 3\hat k$ and $\vec r_2 = \hat i + \hat j + \hat k$ respectively.

A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and area of each plate is 'A', the energy stored in the capacitor is

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of CO2(g) formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is: (Given: Molar mass in g mol$^{-1}$: C: 12, H: 1, O: 16)}

Which of the following reaction is correctly matched with their product ?

Let $\alpha$ and $\beta$ be the roots of the equation \[ 2x^2-5x-1=0. \] For $n\in\mathbb{N}$, let \[ P_n=\alpha^n+\beta^n. \] Then the value of \[ \frac{2P_{11}\,(2P_{10}-5P_9)}{P_8\,(5P_{10}+P_9)} \] is equal to:

Let $\vec{a}=2\hat{i}-\hat{j}-\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}+3\hat{k}$. Let $\vec{v}$ be the vector in the plane of $\vec{a}$ and $\vec{b}$, such that the length of its projection on the vector $\vec{c}$ is $\dfrac{1}{\sqrt{14}}$. Then $|\vec{v}|$ is equal to

MnO₄²⁻, in acidic medium, disproportionates to:

What is the mole fraction of water in $10%$ by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and $14 \text{ g mol}^{-1}$ respectively.]

If A =$ \{1, 2, 3, 4, \dots, 10\},$ then the number of non empty subsets of A containing only even number is

Given above is the concentration vs time plot for a dissociation reaction : $A \to nB$. Based on the data of the initial phase of the reaction (initial 10 min), the value of n is ____.

If $\cot x=\dfrac{5}{12}$ for some $x\in\left(\pi,\dfrac{3\pi}{2}\right)$, then \[ \sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right) +\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right) \] is equal to:

If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.

\[ \mathrm{CaCO_3 + 2HCl \rightarrow CaCl_2 + H_2O + CO_2} \] In the above reaction, $90\,\text{g}$ of $\mathrm{CaCO_3}$ is added to $300\,\text{mL}$ of $38.55%$ (w/w) HCl solution with density $1.13\,\text{g mL}^{-1}$. Which of the following option is correct?

IUPAC name of the some alkenes are given below. Find out the correct stability order.
A. 2-Methylbut-2-ene
B. cis-But-2-ene
C. 2,3-Dimethylbut-2-ene
D. Prop-1-ene
Choose the correct answer from the options given below :

A car covers the first half of the distance between two places at 40 km/h and another half at 50 km/h. The average speed of the car is

The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is

Pollen grains are well preserved as fossils because of the presence of ________.

The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of $x$ is

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue ball and one green ball is:

Consider the following statements:
Statement I : If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement II : If $A$ and $B$ are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.

The correct IUPAC name of CH$_3$ - C(CH$_3$)$_{2}$ - O - C$_2$H$_5$ is

If the sum of the first four terms of an A.P. is $6$ and the sum of its first six terms is $4$, then the sum of its first twelve terms is

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is