List of top Questions asked in JEE Main

Let $f(x)$ be a differentiable function satisfying the equations $\lim_{t \to x} \dfrac{t^2 f(x)-x^2 f(t)}{t-x} = 3$ and $f(1)=2$. Find the value of $2f(2)$.

Let the image of parabola $x^2=4y$ in the line $x-y=1$ be $(y+a)^2=b(x-c)$, where $a,b,c\in\mathbb{N}$. Then $a+b+c$ is equal to

The smallest positive integral value of $a$, for which all the roots of $x^4-ax^2+9=0$ are real and distinct, is equal to

If the equation \[ x^4-ax^2+9=0 \] has four real and distinct roots, then the least possible integral value of $a$ is

Let \( z \) be the complex number satisfying \( |z - 5| \leq 3 \) and having maximum possible positive argument. Then the value of \[ \left| \frac{5z - 12}{5iz + 16} \right|^2 \] is equal to:

Orthocentre of equilateral \(\Delta ABC\) is at the origin. If side \(BC\) lies along \(x + 2\sqrt{2}y = 4\). If coordinates of vertex \(A\) are (a,b). Find the value of \(\lfloor |a + \sqrt{2}b| \rfloor\), where \([ \cdot ]\) denotes G.I.F. :

The largest \( n \in \mathbb{N} \), for which \( 7^n \) divides \( 101! \), is :

The no. of solution in \(x \in \left(-\frac{1}{2\sqrt{6}}, \frac{1}{2\sqrt{6}}\right)\) of equation \(\tan^{-1}4x + \tan^{-1}6x = \frac{\pi}{6}\) is :

If the domain of the function \[ f(x)=\frac{1}{\ln(10-x)}+\sin^{-1}\!\left(\frac{x+2}{2x+3}\right) \] is \[ (-\infty,-a]\ \cup\ (-1,b)\ \cup\ (b,c), \] then find the value of \( (b+c+3a) \).

Let \(Q(a,b,c)\) be the image of the point \(P(3,2,1)\) in the line \[ \frac{x-1}{1}=\frac{y-2}{2}=\frac{z-1}{1}. \] The distance of \(Q\) from the line \[ \frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2} \] is:

Let \[ A=\{z\in\mathbb{C}:|z-2|\le 4\} \quad\text{and}\quad B=\{z\in\mathbb{C}:|z-2|+|z+2|=5\}. \] Then the maximum value of \(|z_1-z_2|\), where \(z_1\in A\) and \(z_2\in B\), is:

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(2x) - 2\sin x}{x^3} \]

An ellipse has its centre at \((1,-2)\), one focus at \((3,-2)\) and one vertex at \((5,-2)\). Then the length of its latus rectum is:

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5\beta}}{2} \] then the value of \( (\alpha + \beta) \) is:

Which of the following statements are TRUE about Haloform reaction?:
A. Sodium hypochlorite reacts with KI to give KOI.
B. KOI is a reducing agent.
C. $\alpha, \beta$-unsaturated methylketone ($\text{CH}_3-\text{CH}=\text{CH}-\text{C=O}-\text{CH}_3$) will give iodoform reaction.
D. Isopropyl alcohol will not give iodoform test.
E. Methanoic acid will give positive iodoform test.

Find out the correct graph for the variation of \( E_{\text{cell}} \) with temperature.

For an ideal gas undergo isothermal reversible process from 0.5Mpa, 20dm$^3$ to 0.2Mpa at 600K. Calculate correct option. [Given $\log 5 = 0.6989, \log 2 = 0.3010$]

Consider the structure of HNO$_3$:
Select the correct option having formal charge of I, II, III and IV respectively.

In the following reaction sequence, identify compound \( (R) \).

An organic compound (A) undergoes the following reactions:

Which of the following is compound (A)?

In the following reaction, \[ {MnO4^{2-} \xrightarrow{H^+} \, ?} \] Manganate ion undergoes disproportionation to form: