List of top Questions asked in JEE Main

If the area of the region bounded by the curves $ y = 4 - \frac{x^2}{4} $ and $ y = \frac{x - 4}{2} $ is equal to $ \alpha $, then $ 6\alpha $ equals:

Let $ A $ be a $ 3 \times 3 $ matrix such that $ | \text{adj} (\text{adj} A) | = 81.
$ If $ S = \left\{ n \in \mathbb{Z}: \left| \text{adj} (\text{adj} A) \right|^{\frac{(n - 1)^2}{2}} = |A|^{(3n^2 - 5n - 4)} \right\}, $ then the value of $ \sum_{n \in S} |A| (n^2 + n) $ is:

Let the set of all values of $ p \in \mathbb{R} $, for which both the roots of the equation $ x^2 - (p + 2)x + (2p + 9) = 0 $ are negative real numbers, be the interval $ (\alpha, \beta) $. Then $ \beta - 2\alpha $ is equal to:

Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $ \mu $ and $ \sigma $ respectively, then $ 10(\mu + \sigma) $ is equal to:

The integral $ \int_0^\pi \frac{(x + 3) \sin x}{1 + 3 \cos^2 x} \, dx $ is equal to:

Let $ C_1 $ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $ C_2 $ be the circle with center $ (1, 3) $ that touches $ C_1 $ externally at the point $ (\alpha, \beta) $. If $ (\beta - \alpha)^2 = \frac{m}{n} $, and $ \gcd(m, n) = 1 $, then $ m + n $ is equal to:

If for $ \theta \in \left[ -\frac{\pi}{3}, 0 \right] $, the points $ (x, y) = \left( 3 \tan\left( \theta + \frac{\pi}{3} \right), 2 \tan\left( \theta + \frac{\pi}{6} \right) \right) $ lie on $ xy + \alpha x + \beta y + \gamma = 0 $, then $ \alpha^2 + \beta^2 + \gamma^2 $ is equal to:

Let P be the parabola, whose focus is $ (-2, 1) $ and directrix is $ 2x + y + 2 = 0 $. Then the sum of the ordinates of the points on P, whose abscissa is -2, is:

The remainder when $ \left( (64)^{64} \right)^{64} $ is divided by 7 is equal to:

Evaluate the following limit: $ \lim_{x \to 0^+} \frac{\tan\left(5x^{\frac{1}{3}}\right) \log\left(1 + 3x^2\right)}{\left(\tan^{-1}\left(3\sqrt{x}\right)\right)^2 \left(e^{5x^{\frac{4}{3}}} - 1\right)} $

x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)

A metal complex with a formula MC$\ell_4$3NH$_3$ is involved in sp$^3$d$^2$ hybridisation. It upon reaction with excess of AgNO$_3$ solution gives ‘x’ moles of AgCl. Consider ‘x’ is equal to the number of lone pairs of electron present in central atom of BrF$_5$. Then the number of geometrical isomers exhibited by the complex is ________

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12

Consider the following molecule (X).

The Structure X is?

The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively:

‘X’ is the number of electrons in $ t_2g $ orbitals of the most stable complex ion among $ [Fe(NH_3)_6]^{3+} $, $ [Fe(Cl)_6]^{3-} $, $ [Fe(C_2O_4)_3]^{3-} $ and $ [Fe(H_2O)_6]^{3+} $. The nature of oxide of vanadium of the type $ V_2O_x $ is:

Given below are two statements:
Statement (I): The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13.
Statement (II): Melting points and boiling points of group 13 elements are in general much higher than those of the corresponding elements of group 14. Choose the most appropriate answer from the options given below:

Consider the ground state of an atom (Z = 24). How many electrons are arranged with Azimuthal quantum number $ l = 1 $ and $ l = 2 $ respectively?

The correct order of $ [FeF_6]^{3-} $, $ [CoF_6]^{3-} $,$ [Ni(CO)_4] $ and $ [Ni(CN)_4]^{2-} $ complex species based on the number of unpaired electrons present is:

A toxic compound “A” when reacted with NaCN in aqueous acidic medium yields an edible cooking component and food preservative “B”. “B” is converted to “C” by dibromane and can be used as an additive to petrol to reduce emission. “C” upon reaction with oleum at 140°C yields an inhalable anesthetic “D”. Identify “A”, “B”, “C”, and “D”, respectively.

Match List-I with List-II: List-I

The IUPAC name of the following compound is:

Given below are two statements:
Statement (I): Molal depression constant $ k_f $ is given by $ \frac{M_1 R T_f}{\Delta S_{\text{fus}}} $, where symbols have their usual meaning.
Statement (II): $ k_f $ for benzene is less than the $ k_f $ for water.
In light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements:
Statement (I): Alcohols are formed when alkyl chlorides are treated with aqueous potassium hydroxide by elimination reaction.
Statement (II): In alcoholic potassium hydroxide, alkyl chlorides form alkenes by abstracting the hydrogen from the $ \beta $-carbon.
In the light of the above statements, choose the most appropriate answer from the options given below: