List of top Questions asked in JEE Main

Statement-1: The function \(x^2(e^x+e^{-x})\) is increasing for all \(x \gt 0\).
Statement-2: The functions \(x^2e^x\) and \(x^2e^{-x}\) are increasing for all \(x \gt 0\) and the sum of two increasing functions in any interval \((a,b)\) is an increasing function in \((a,b)\).

For \(a \gt 0,\ t \in \left(0, \dfrac{\pi}{2}\right)\), let \(x = \sqrt{a^{\sin^{-1}t}}\) and \(y = \sqrt{a^{\cos^{-1}t}}\), Then, \(1 + \left(\dfrac{dy}{dx}\right)^2\) equals :

If the system of linear equations :
\(x_1 + 2x_2 + 3x_3 = 6\)
\(x_1 + 3x_2 + 5x_3 = 9\)
\(2x_1 + 5x_2 + ax_3 = b\)
is consistent and has infinite number of solutions, then :

If \(\int \frac{x^2-x+1}{x^2+1}\,e^{\cot^{-1}x}\,dx = A(x)\,e^{\cot^{-1}x}+C\), then \(A(x)\) is equal to :

If \(p, q, r\) are 3 real numbers satisfying the matrix equation, \([p\ q\ r]\begin{bmatrix}3&4&1\\3&2&3\\2&0&2\end{bmatrix} = [3\ \ 0\ \ 1]\) then \(2p + q - r\) equals :

Let \(f(x) = -1 + |x - 2|\), and \(g(x) = 1 - |x|\); then the set of all points where \(f\!og\) is discontinuous is :

The statement \(p \to (q \to p)\) is equivalent to :

Mean of 5 observations is 7 . If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is :

The acute angle between two lines such that the direction cosines \(l, m, n\), of each of them satisfy the equations \(l + m + n = 0\) and \(l^2 + m^2 - n^2 = 0\) is :

Statement-1: The number of common solutions of the trigonometric equations \(2\sin^2\theta - \cos 2\theta = 0\) and \(2\cos^2\theta - 3\sin\theta = 0\) in the interval \([0, 2\pi]\) is two.
Statement-2: The number of solutions of the equation, \(2\cos^2\theta - 3\sin\theta = 0\) in the interval \([0, \pi]\) is two.

The number of solutions of the equation, \(\sin^{-1}x = 2\tan^{-1}x\) (in principal values) is :

If the 7th term in the binomial expansion of \(\left(\dfrac{3}{\sqrt[3]{84}} + \sqrt{3}\ln x\right)^9\), \(x \gt 0\), is equal to 729 , then \(x\) can be:

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :

The sum \(\dfrac{3}{1^2} + \dfrac{5}{1^2+2^2} + \dfrac{7}{1^2+2^2+3^2} + \cdots\) upto 11-terms is :

Given sum of the first \(n\) terms of an A.P. is \(2n + 3n^2\). Another A.P. is formed with the same first term and double of the common difference, the sum of \(n\) terms of the new A.P. is :

If a complex number \(z\) statisfies the equation \(x + \sqrt{2}|z + 1| + i = 0\), then \(|z|\) is equal to :

If \(\alpha\) and \(\beta\) are roots of the equation \(x^2 + px + \frac{3p}{4} = 0\), such that \(|\alpha - \beta| = \sqrt{10}\), then \(p\) belongs to the set :

If a polythene sample contains two monodisperse fractions in the ratio 2 : 3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be :

Aryl fluoride may be prepared from arene diazonium chloride using :

In which of the following ionization processes the bond energy has increased and also the magnetic behaviour has changed from paramagnetic to diamagnetic ?

Trigonal bipyramidal geometry is shown by:

Type of isomerism which exists between \([\mathrm{Pd(C_6H_5)_2(SCN)_2}]\) and \([\mathrm{Pd(C_6H_5)_2(NCS)_2}]\) is :

The element with which of the following outer electron configuration may exhibit the largest number of oxidation states in its compounds :

\(+\ \mathrm{HCl} \longrightarrow \mathrm{X}\),
X is:

The instantaneous rate of disappearance of \(\mathrm{MnO_4^-}\) ion in the following reaction is \(4.56\times10^{-3}\ \mathrm{M\,s^{-1}}\)
\(2\mathrm{MnO_4^-} + 10\mathrm{I^-} + 16\mathrm{H^+} \rightarrow 2\mathrm{Mn^{2+}} + 5\mathrm{I_2} + 8\mathrm{H_2O}\)
The rate of appearance \(\mathrm{I_2}\) is :