List of top Questions asked in JEE Main

Let $\alpha, \beta$ be roots of $x^2 + \sqrt{2}x - 8 = 0$. If $U_n = \alpha^n + \beta^n$, then \[ \frac{U_{10} + \sqrt{12} U_9}{2 U_8} \] is equal to ________.

If the shortest distance between the lines \[ \frac{x - \lambda}{3} = \frac{y - 2}{-1} = \frac{z - 1}{1} \] and \[ \frac{x + 2}{-3} = \frac{y + 5}{2} = \frac{z - 4}{4} \] is \[ \frac{44}{\sqrt{30}}, \] then the largest possible value of $|\lambda|$ is equal to ________.

Let $[t]$ denote the largest integer less than or equal to $t$. If \[ \int_0^1 \left(\left[x^2\right] + \left\lfloor \frac{x^2}{2} \right\rfloor\right) dx = a + b\sqrt{2} - \sqrt{3} - \sqrt{5} + c\sqrt{6} - \sqrt{7}, \] where $a, b, c \in \mathbb{Z}$, then $a + b + c$ is equal to ________.

The length of the latus rectum and directrices of a hyperbola with eccentricity $e$ are 9 and $x = \pm \frac{4}{\sqrt{3}}$, respectively. Let the line $y - \sqrt{3}x + \sqrt{3} = 0$ touch this hyperbola at $(x_0, y_0)$. If $m$ is the product of the focal distances of the point $(x_0, y_0)$, then $4e^2 + m$ is equal to ________.

If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

If the locus of the point, whose distances from the point $(2, 1)$ and $(1, 3)$ are in the ratio $5 : 4$, is \[ ax^2 + by^2 + cxy + dx + ey + 170 = 0, \] then the value of $a^2 + 2b + 3c + 4d + e$ is equal to:

Considering acetic acid dissociates in water, its dissociation constant is $6.25 \times 10^{-5}$. If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at $-x \times 10^{-1}$ °C, provided pure water freezes at 0 °C. $x = $ _____ (Nearest integer)
Given: $(K_f)_{water} = 1.86$ K kg mol$^{-1}$
density of acetic acid is 1.2 g mol$^{-1}$
molar mass of water = 18 g mol$^{-1}$
molar mass of acetic acid = 60 g mol$^{-1}$
density of water = 1 g cm$^{-3}$
Acetic acid dissociates as CH$_3$COOH $\rightleftharpoons$ CH$_3$COO$^-$ + H$^+$

The product Ⓒ in the following sequence of reactions has _______ π bonds.

In the Claisen-Schmidt reaction to prepare 351 g of dibenzalacetone using 87 g of acetone, the amount of benzaldehyde required is _________g. (Nearest integer)

Using the given figure, the ratio of \(R_f\) values of sample A and sample C is x × 10^–2. Value of x is __________.

In an atom, total number of electrons having quantum numbers n = 4, $|m_l|$ = 1 and $m_s$ = $-\frac{1}{2}$ is ________.

The correct statements from the following are:
(A) The decreasing order of atomic radii of group 13 elements is Tl $>$ In $>$ Ga $>$ Al $>$ B.
(B) Down the group 13 electronegativity decreases from top to bottom.
(C) Al dissolves in dil. HCl and liberate H$_2$, but conc. HNO$_3$ renders Al passive by forming a protective oxide layer on the surface.
(D) All elements of group 13 exhibits highly stable +1 oxidation state.
(E) Hybridisation of Al in [Al(H$_2$O)$_6$]$^{3+}$ ion is sp$^3$d$^2$.
Choose the correct answer from the options given below.

The number of complexes from the following with no electrons in the t$_{2g}$ orbital is _______.
TiCl$_4$, [MnO$_4$]$^{-}$, [FeO$_4$]$^{2-}$, [FeCl$_4$]$^{-}$, [CoCl$_4$]$^{2-}$

The number of moles of methane required to produce 11g \(CO_2\) (g) after complete combustion is:
(Given molar mass of methane in g mol^–1 : 16)

Consider the given chemical reaction :

Product ''A'' is :

Given below are two statements:
Statement I: The metallic radius of Na is 1.86 Å and the ionic radius of Na$^+$ is lesser than 1.86 Å.
Statement II: Ions are always smaller in size than the corresponding elements.
In the light of the above statements, choose the correct answer from the options given below:

Which one of the following reactions is NOT possible?

The metal atom present in the complex MABXL (where A, B, X and L are unidentate ligands and M is metal) involves sp³ hybridization. The number of geometrical isomers exhibited by the complex is:

Identify the major product in the following reaction.

The current in an inductor is given by I = (3t + 8) where t is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self inductance of the inductor _______ mH.

A wire of resistance 20 \(\Omega\) is divided into 10 equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _______ \(\Omega\).

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ______ m.

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _______ N.

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of x is ________.