List of top Questions asked in JEE Main

Let S be the set of all \(\lambda \in R\) for which the system of linear equations

\(2x - y + 2z = 2\)
\(x - 2y + \lambda z = -4\)
\(x + \lambda y + z = 4\)

has no solution. Then the set S :

The domain of the function
\(f(x) = \sin^{-1}\left(\frac{|x| + 5}{x^2 + 1}\right)\)
is \((-\infty, -a] \cup [a, \infty)\). Then a is equal to :

Let A be a \(2 \times 2\) real matrix with entries from \(\{0, 1\}\) and \(|A| \ne 0\). Consider the following two statements :

(P) If \(A \ne I_2\), then \(|A| = -1\)
(Q) If \(|A| = 1\), then \(\operatorname{tr}(A) = 2\),

where \(I_2\) denotes \(2 \times 2\) identity matrix and \(\operatorname{tr}(A)\) denotes the sum of the diagonal entries of A. Then :

If p(x) be a polynomial of degree three that has a local maximum value 8 at \(x = 1\) and a local minimum value 4 at \(x = 2\); then p(0) is equal to :

If \(R = \{(x, y) : x, y \in Z,\ x^2 + 3y^2 \le 8\}\) is a relation on the set of integers Z, then the domain of \(R^{-1}\) is :

Let \(y = y(x)\) be the solution of the differential equation,
\(\frac{2 + \sin x}{y + 1}\cdot\frac{dy}{dx} = -\cos x\),
\(y \gt 0\), \(y(0) = 1\).
If \(y(\pi) = a\) and \(\frac{dy}{dx}\) at \(x = \pi\) is b, then the ordered pair (a, b) is equal to :

Let \(\alpha \gt 0\), \(\beta \gt 0\) be such that
\(\alpha^3 + \beta^2 = 4\). If the maximum value of the term independent of x in
the binomial expansion of \(\left(\alpha x^{\frac19} + \beta x^{-\frac16}\right)^{10}\)
is \(10k\),
then k is equal to :

If a function f(x) defined by
\(f(x) = \begin{cases} ae^{x} + be^{-x}, & -1 \le x \lt 1 \\ cx^2, & 1 \le x \le 3 \\ ax^2 + 2cx, & 3 \lt x \le 4 \end{cases}\)
be continuous for some \(a, b, c \in R\) and \(f'(0) + f'(2) = e\), then the value of \(a\) is :

Let \(X = \{x \in N : 1 \le x \le 17\}\) and
\(Y = \{ax + b : x \in X \text{ and } a, b \in R,\ a \gt 0\}\). If mean
and variance of elements of Y are 17 and 216
respectively then \(a + b\) is equal to :

The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :

Let \(\alpha\) and \(\beta\) be the roots of the equation
\(5x^2 + 6x - 2 = 0\). If \(S_n = \alpha^n + \beta^n\), \(n = 1, 2, 3, \ldots\), then :

Area (in sq. units) of the region outside
\(\frac{|x|}{2} + \frac{|y|}{3} = 1\)
and inside the ellipse
\(\frac{x^2}{4} + \frac{y^2}{9} = 1\)
is :

A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ/mol) for this process is closest to__________.
(Given, \(R = 8.3\ \mathrm{J\ mol^{-1}\ K^{-1}}\), \(\ln\left(\frac{3}{2}\right) = 0.4\), \(e^{-3} = 4.0\))

10.30 mg of \(\mathrm{O_2}\) is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of \(\mathrm{O_2}\) in ppm is__________.

The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is ____________.

Which polymer has 'chiral' monomer(s) ?

Amongst the following, the form of water with the lowest ionic conductance at 298 K is :

Which of the following has the shortest C-Cl bond?

The isomer(s) of \(\mathrm{[Co(NH_3)_4Cl_2]}\) that has/have a Cl-Co-Cl angle of 90\(^\circ\), is/are :

The reaction of \(\mathrm{H_3N_3B_3Cl_3}\) (A) with \(\mathrm{LiBH_4}\) in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A) with (C) leads to \(\mathrm{H_3N_3B_3(Me)_3}\). Compounds (B) and (C) respectively, are :

5 g of zinc is treated separately with an excess of
(a) dilute hydrochloric acid and
(b) aqueous sodium hydroxide.
The ratio of the volumes of \(\mathrm{H_2}\) evolved in these two reactions is :

A, B and C are three biomolecules. The results of the tests performed on them are given below:

	Molisch's Test	Barfoed Test	Biuret Test
A	Positive	Negative	Negative
B	Positive	Positive	Negative
C	Negative	Negative	Positive

A, B and C are respectively :

The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol\(^{-1}\), respectively. How many moles of HCl and \(\mathrm{H_2SO_4}\), respectively, will be needed to react completely with 1 mole of the metal hydroxide ?

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?

In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength \(\lambda\) is used. Then the value of \(\lambda\) is (in nm) __________.