List of top Questions asked in JEE Main

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ________. (Nearest integer) (Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.

Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is,
Given : Atomic masses of C, H and N are 12, 1 and 14 amu, respectively.
The molar mass of the compound A is 162g mol^–1.

The number of terminal oxygen atoms present in the product B obtained from the following reaction is ______.
FeCr₂O₄ + Na₂CO₃ + O₂ → A + Fe₂O₃ + CO₂
A + H⁺ → B + H₂O + Na⁺

\(\begin{array}{l} \text{Consider a matrix}~A=\begin{bmatrix}\alpha & \beta & \gamma \\\alpha^2 & \beta^2 & \gamma^2 \\\beta+\gamma & \gamma+\alpha & \alpha+\beta \\\end{bmatrix}\end{array}\)

where \(α, β, γ\) are three distinct natural numbers.
If \(\begin{array}{l}\frac{\text{det(adj(adj(adj(adj A))))}}{\left(\alpha-\beta\right)^{16}\left(\beta-\gamma\right)^{16}\left(\gamma-\alpha\right)^{16}}=2^{32}\times3^{16},\end{array}\)
then the number of such 3-tuples \((α, β, γ)\) is _________.

A rolling wheel of \(12\) kg is on an inclined plane at position P and connected to a mass of \(3\) kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.
The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be \(\frac{1}{2}\sqrt{ xgh}\) \(m/s\). The value of x is _________.

In the following nuclear reaction,
\(D \stackrel{α}{⟶} D1 \stackrel{β^-}{⟶} D2 \stackrel{α}{⟶} D3 \stackrel{γ}{⟶} D4\)
Mass number of D is 182 and atomic number is 74. Mass number and atomic number
of D_4, respectively, will be _____.

The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF₄, MnF₃and MnF₂ is____ B.M. [nearest integer]

Let a line L pass through the point intersection of the lines \(bx + 10y – 8 = 0\) and \(2x - 3y = 0, \quad b \in \mathbb{R} - \left\{\frac{4}{3}\right\}\). If the line L also passes through the point \((1, 1)\) and touches the circle \(17(x^2 + y^2) = 16\), then the eccentricity of the ellipse \(\frac{x^2}{5} + \frac{y^2}{5} = 1\) is

Let a vertical tower AB of height 2h stands on a horizontal ground. Let from a point P on the ground a man can see up to height h of the tower with an angle of elevation 2α.
When from P, he moves a distance d in the direction of \(\overrightarrow{AP}\).
he can see the top B of the tower with an angle of elevation α. if \(d = \sqrt7\) h, then tan α is equal to

The intermediate X, in the reaction is:

Let ƒ R ⇒ R be a function defined by

Let ƒ : R ⇒ R be a function defined by

where [t] is the greatest integer less than or equal to t. Let m be the number of points where ƒ is not differentiable and

Then the ordered pair (m, I) is equal to :

The positive value of the determinant of the matrix A, whose
\(\text{Adj}(\text{Adj}(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}\)
is ___.

Let \([t]\) denote the greatest integer less than or equal to \(t\). Then, the value of the integral \(∫_0^1 [ -8x^2 + 6x - 1] dx\) is equal to

For the curve
\(\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}\)

\(\begin{array}{l}\text{the value of}\ 3y’ – y^3y”, \text{at the point}\end{array}\)

\((α, α), α > 0\), on C is equal to ________.

Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

Vulcanization of rubber is carried out by heating a mixture of

17.0 g of NH₃ completely vapourises at – 33.42°C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol^–1. The enthalpy change for the vapourisation of 85 g of NH₃under the same conditions is ____ kJ.

A metallic rod of length \(20\) cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth’s magnetic field at that place is \(4 × 10^{–3}\) T and the angle of dip is \(45º\). The emf induced in the rod is __________mV.

Amongst the following, the major product of the given chemical reaction is

Amongst the following, the major product of