List of top Questions asked in JEE Main

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle \(60^\circ\) on the circumference of the first circle, then the radius of the arc is:

Let \(A = \{\theta : \sin(\theta) = \tan(\theta)\}\) and \(B = \{\theta : \cos(\theta) = 1\}\) be two sets. Then:

A point on the ellipse, \(4x^2 + 9y^2 = 36\), where the normal is parallel to the line, \(4x - 2y - 5 = 0\), is :

Consider the system of equations : \(x + ay = 0,\ y + az = 0\) and \(z + ax = 0\). Then the set of all real values of 'a' for which the system has a unique solution is:

If for positive integers \(r \gt 1, n \gt 2\), the coefficients of the \((3r)^{\text{th}}\) and \((r+2)^{\text{th}}\) powers of \(x\) in the expansion of \((1 + x)^{2n}\) are equal, then \(n\) is equal to:

The value of \(1^2 + 3^2 + 5^2 + \ldots\ldots + 25^2\) is :

Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is :

5 - digit numbers are to be formed using \(2, 3, 5, 7, 9\) without repeating the digits. If \(p\) be the number of such numbers that exceed \(20000\) and \(q\) be the number of those that lie between \(30000\) and \(90000\), then \(p : q\) is:

If \(p\) and \(q\) are non-zero real numbers and \(\alpha^3 + \beta^3 = -p,\ \alpha\beta = q\), then a quadratic equation whose roots are \(\frac{\alpha^2}{\beta},\ \frac{\beta^2}{\alpha}\) is :

Let \(z\) satisfy \(|z| = 1\) and \(z = 1 - \bar{z}\). Statement 1 : \(z\) is a real number. Statement 2 : Principal argument of \(z\) is \(\frac{\pi}{3}\).

\(\mathrm{H_1}\)-Receptor antagonists is a term associated with :

Which of the following polymer is a polyamide ?

Which of the following is the product of aldol condensation?

Identify the incorrect statement:

The magnetic moment of the complex anion \([\mathrm{Cr(NO)(NH_3)(CN)_4}]^{2-}\) is :

Smoke is an example of :

When a small amount of \(\mathrm{KMnO_4}\) is added to concentrated \(\mathrm{H_2SO_4}\), a green oily compound is obtained which is highly explosive in nature. Compound may be :

Identify incorrect statement :

The numbers of protons, electrons and neutrons in a molecule of heavy water are respectively :

Which of the following statements/relationships is not correct in thermodynamic changes ?

What is the pH of a \(10^{-4}\ \mathrm{M\ OH^-}\) solution at 330 K, if \(K_w\) at 330 K is \(10^{-13.6}\) ?

Given :
\(E^\circ_{\frac{1}{2}\mathrm{Cl_2/Cl^-}} = 1.36\ \mathrm{V},\ E^\circ_{\mathrm{Cr^{3+}/Cr}} = -0.74\ \mathrm{V}\)
\(E^\circ_{\mathrm{Cr_2O_7^{2-}/Cr^{3+}}} = 1.33\ \mathrm{V},\ E^\circ_{\mathrm{MnO_4^-/Mn^{2+}}} = 1.51\ \mathrm{V}\)
The correct order of reducing power of the species \((\mathrm{Cr, Cr^{3+}, Mn^{2+}}\) and \(\mathrm{Cl^-})\) will be :

Which of the following statement is NOT correct?

Which is the correct order of second ionization potential of \(\mathrm{C, N, O}\) and \(\mathrm{F}\) in the following ?

The de Broglie wavelength of a car of mass 1000 kg and velocity 36 km/hr is :