List of top Questions asked in JEE Main

Let \(A=\begin{bmatrix}1&2\\-1&4\end{bmatrix}\). If \(A^{-1}=\alpha I+\beta A,\ \alpha,\beta\in\mathbb{R}\), \(I\) is a \(2\times2\) identity matrix then \(4(\alpha-\beta)\) is equal to :

Let \(f(x)=\begin{vmatrix}\sin^2x&-2+\cos^2x&\cos2x\\2+\sin^2x&\cos^2x&\cos2x\\\sin^2x&\cos^2x&1+\cos2x\end{vmatrix},\ x\in[0,\pi]\). Then the maximum value of \(f(x)\) is equal to ______________.

Let \(f : \mathbb{R} \to \mathbb{R}\) be defined as
\(f(x)=\begin{cases}\dfrac{\lambda\left|x^2-5x+6\right|}{\mu\left(5x-x^2-6\right)}, & x\lt 2\\[2mm] e^{\frac{\tan(x-2)}{x-[x]}}, & x\gt 2\\[2mm] \mu, & x=2\end{cases}\)
where \([x]\) is the greatest integer less than or equal to \(x\). If \(f\) is continuous at \(x=2\), then \(\lambda+\mu\) is equal to :

\(2\mathrm{NO(g)} + \mathrm{Cl_2(g)} \rightleftharpoons 2\mathrm{NOCl(s)}\)
This reaction was studied at \(-10^\circ\) and the following data was obtained

Run	\([\mathrm{NO}]_0\)	\([\mathrm{Cl_2}]_0\)	\(r_0\)
1	0.10	0.10	0.18
2	0.10	0.20	0.35
3	0.20	0.20	1.40

\([\mathrm{NO}]_0\) and \([\mathrm{Cl_2}]_0\) are the initial concentrations and \(r_0\) is the initial reaction rate.
The overall order of the reaction is __________. (Round off to the Nearest Integer).

The major components of German Silver are :

Considering the above reaction, X and Y respectively are :

Consider the above chemical reaction and identify product "A"

Considering the above chemical reaction, identify the product "X" :

The solutions of the equation \(\begin{vmatrix} 1 + \sin^2 x & \sin^2 x & \sin^2 x \\ \cos^2 x & 1 + \cos^2 x & \cos^2 x \\ 4\sin 2x & 4\sin 2x & 1 + 4\sin 2x \end{vmatrix} = 0\), \((0 \lt x \lt \pi)\), are

For the four circles M, N, O and P, following four equations are given :
Circle M : \(x^2 + y^2 = 1\)
Circle N : \(x^2 + y^2 - 2x = 0\)
Circle O : \(x^2 + y^2 - 2x - 2y + 1 = 0\)
Circle P : \(x^2 + y^2 - 2y = 0\)
If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :

Identify A and B in the chemical reaction.

The major product of the following chemical reaction is :

What is 'X' in the given reaction?

The major product of the following reaction is :

Match List I with List II.

	List I		List II
(a)	Rectifier	(i)	Used either for stepping up or stepping down the a.c. voltage
(b)	Stabilizer	(ii)	Used to convert a.c. voltage into d.c. voltage
(c)	Transformer	(iii)	Used to remove any ripple in the rectified output voltage
(d)	Filter	(iv)	Used for constant output voltage even when the input voltage or load current change

Choose the correct answer from the options given below :

The major product of the following reaction is :

Match List - I with List - II.

	List I		List II
(a)	Source of microwave frequency	(i)	Radioactive decay of nucleus
(b)	Source of infrared frequency	(ii)	Magnetron
(c)	Source of Gamma Rays	(iii)	Inner shell electrons
(d)	Source of X-rays	(iv)	Vibration of atoms and molecules
		(v)	LASER
		(vi)	RC circuit

Choose the correct answer from the options given below :

The major product of the following reaction is :

For the following sequence of reactions, the correct products are :

Match List - I and List - II.

	List-I		List-II
(a)	\(\mathrm{R-CO-Cl \rightarrow R-CHO}\)	(i)	\(\mathrm{Br_2/NaOH}\)
(b)	\(\mathrm{R-CH_2-COOH \rightarrow R-CHCl-COOH}\)	(ii)	\(\mathrm{H_2/Pd-BaSO_4}\)
(c)	\(\mathrm{R-CO-NH_2 \rightarrow R-NH_2}\)	(iii)	\(\mathrm{Zn(Hg)/conc.\ HCl}\)
(d)	\(\mathrm{R-CO-CH_3 \rightarrow R-CH_2-CH_3}\)	(iv)	\(\mathrm{Cl_2,\ Red\ P,\ H_2O}\)

Choose the correct answer from the options given below :

Match List - I with List - II.

	List I (Metal)		List II (Ores)
(a)	Aluminium	(i)	Siderite
(b)	Iron	(ii)	Calamine
(c)	Copper	(iii)	Kaolinite
(d)	Zinc	(iv)	Malachite

Choose the correct answer from the options given below :

Identify correct A, B and C in the reaction sequence given below :

Match List - I with List - II.

	List - I		List - II
(a)	\(R_H\) (Rydberg constant)	(i)	\(kg\,m^{-1}s^{-1}\)
(b)	h (Planck's constant)	(ii)	\(kg\,m^2s^{-1}\)
(c)	\(\mu_B\) (Magnetic field energy density)	(iii)	\(m^{-1}\)
(d)	\(\eta\) (coefficient of viscocity)	(iv)	\(kg\,m^{-1}s^{-2}\)

Choose the most appropriate answer from the options given below :

The major product of the following reaction is :
\(\mathrm{CH_3-CH(CH_3)-CH_2-CH_2-COCl}\)
(i) alcoholic \(\mathrm{NH_3}\)
(ii) \(\mathrm{NaOH,\ Br_2}\)
(iii) \(\mathrm{NaNO_2,\ HCl}\)
(iv) \(\mathrm{H_2O}\)
\(\longrightarrow\) Major Product

The major products A and B formed in the following reaction sequence are :