List of top Questions asked in JEE Main

If \(y=y(x)\) is the solution of the differential equation, \(\frac{dy}{dx}+2y\tan x=\sin x,\ y\left(\frac{\pi}{3}\right)=0\), then the maximum value of the function \(y(x)\) over \(\mathbb R\) is equal to:

Consider three observations a, b, and c such that \(b=a+c\). If the standard deviation of \(a+2,\ b+2,\ c+2\) is \(d\), then which of the following is true?

The range of \(a\in\mathbb R\) for which the function \(f(x)=(4a-3)(x+\log_e5)+2(a-7)\cot\left(\frac{x}{2}\right)\sin^2\left(\frac{x}{2}\right)\), \(x\ne2n\pi,\ n\in N\) has critical points, is :

If for \(x\in\left(0,\frac{\pi}{2}\right)\), \(\log_{10}\sin x+\log_{10}\cos x=-1\) and \(\log_{10}(\sin x+\cos x)=\frac12(\log_{10}n-1)\), \(n>0\), then the value of \(n\) is equal to :

Let the functions \(f:\mathbb R\to\mathbb R\) and \(g:\mathbb R\to\mathbb R\) be defined as :
\(f(x)=\begin{cases}x+2, & x<0\\ x^2, & x\ge0\end{cases}\) and
\(g(x)=\begin{cases}x^3, & x<1\\ 3x-2, & x\ge1\end{cases}\)
Then, the number of points in \(\mathbb R\) where \((f\circ g)(x)\) is NOT differentiable is equal to :

If \(n\) is the number of irrational terms in the expansion of \(\left(3^{1/4}+5^{1/8}\right)^{60}\), then \((n-1)\) is divisible by :

The locus of the midpoints of the chord of the circle, \(x^2+y^2=25\) which is tangent to the hyperbola, \(\frac{x^2}{9}-\frac{y^2}{16}=1\) is :

Let a complex number \(z\), \(|z|\neq1\), satisfy \(\log_{\frac{1}{\sqrt2}}\left(\frac{|z|+11}{(|z|-1)^2}\right)\le2\). Then, the largest value of \(|z|\) is equal to ____________.

Let \(A=\begin{bmatrix} i & -i\\ -i & i\end{bmatrix},\ i=\sqrt{-1}\). Then, the system of linear equations \(A^8\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}8\\64\end{bmatrix}\) has :

Let \(S_k=\sum_{r=1}^{k}\tan^{-1}\left(\frac{6^r}{2^{2r+1}+3^{2r+1}}\right)\). Then \(\lim_{k\to\infty}S_k\) is equal to :

The number of elements in the set \(\{x\in\mathbb{R}:(|x|-3)\,|x+4|=6\}\) is equal to :

Let a vector \(\alpha\hat{i}+\beta\hat{j}\) be obtained by rotating the vector \(\sqrt{3}\,\hat{i}+\hat{j}\) by an angle \(45^\circ\) about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices \((\alpha, \beta)\), \((0, \beta)\) and \((0, 0)\) is equal to :

The \(\mathrm{NaNO_3}\) weighed out to make 50 mL of an aqueous solution containing 70.0 mg \(\mathrm{Na^+}\) per mL is _________ g. (Rounded off to the nearest integer)

[Given : Atomic weight in g mol⁻¹ - Na : 23; N : 14; O : 16]

Emf of the following cell at 298K in V is x \(\times\) 10⁻².

\(\mathrm{Zn|Zn^{2+}(0.1\ M)||Ag^{+}(0.01\ M)|Ag}\)

The value of x is _________. (Rounded off to the nearest integer)

[Given : \(E^{\theta}_{Zn^{2+}/Zn} = -0.76\,V;\ E^{\theta}_{Ag^{2+}/Ag} = +0.80\,V;\ \frac{2.303RT}{F} = 0.059\)]

The pH of ammonium phosphate solution, if pk_a of phosphoric acid and pk_b of ammonium hydroxide are 5.23 and 4.75 respectively, is ___________.

The number of octahedral voids per lattice site in a lattice is _________. (Rounded off to the nearest integer)

The number of stereoisomers possible for \(\mathrm{[Co(ox)_2(Br)(NH_3)]^{2-}}\) is ___________. [ox = oxalate]

When 12.2 g of benzoic acid is dissolved in 100 g of water, the freezing point of solution was found to be \(-0.93^\circ\mathrm{C}\) (\(K_f(\mathrm{H_2O}) = 1.86\ \mathrm{K\ kg\ mol^{-1}}\)). The number (n) of benzoic acid molecules associated (assuming 100% association) is ___________.

Match List - I with List - II.

	List - I		List - II
(a)	Sodium Carbonate	(i)	Deacon
(b)	Titanium	(ii)	Castner-Kellner
(c)	Chlorine	(iii)	van-Arkel
(d)	Sodium hydroxide	(iv)	Solvay

Choose the correct answer from the options given below :

If the activation energy of a reaction is 80.9 kJ mol^-1, the fraction of molecules at 700 K, having enough energy to react to form products is \(e^{-x}\). The value of x is __________. (Rounded off to the nearest integer) [Use \(R = 8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}\)]

The average S-F bond energy in kJ mol⁻¹ of \(\mathrm{SF_6}\) is _____________. (Rounded off to the nearest integer)

[Given : The values of standard enthalpy of formation of \(\mathrm{SF_6(g)}\), \(\mathrm{S(g)}\) and \(\mathrm{F(g)}\) are - 1100, 275 and 80 kJ mol⁻¹ respectively.]

In mildly alkaline medium, thiosulphate ion is oxidized by \(\mathrm{MnO_4^-}\) to "A". The oxidation state of sulphur in "A" is __________.

The nature of charge on resulting colloidal particles when \(\mathrm{FeCl_3}\) is added to excess of hot water is :

Match List - I with List - II.

	List - I		List - II
(a)	Siderite	(i)	Cu
(b)	Calamine	(ii)	Ca
(c)	Malachite	(iii)	Fe
(d)	Cryolite	(iv)	Al
		(v)	Zn

Choose the correct answer from the options given below :

Considering the above reaction, the major product among the following is :