JEE Main 2021 (Online) 20th July Morning Shift

In the given reaction
3-Bromo-2, 2-dimethyl butane \(\buildrel {{C_2}{H_5}OH} \over \longrightarrow \mathop {'A'}\limits_{(Major\,\Pr oduct)}\) Product A is :

To synthesize 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate ___________ equivalents of CH3MgBr Reagent will be required. (Integer value)

Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

Among the given species the Resonance stabilised carbocations are :

Identify the incorrect statement from the following

The number of lone pairs of electrons on the central I atom in I\(_3^ -\) is ____________.

2SO2(g) + O2(g) \(\rightleftharpoons\) 2SO3(g)In an equilibrium mixture, the partial pressures are PSO3 = 43 kPa; PO2 = 530 Pa and PSO2 = 45 kPa. The equilibrium constant KP = ___________ \(\times\) 10\(-\)2. (Nearest integer)

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation, 10% of the virus is inactivated. The rate constant for viral inactivation is ___________ \(\times\) 10\(-\)3 min$$-$...

Green chemistry in day-to-day life is in the use of :

The correct structure of Rhumann's Purple, the compound formed in the reaction of ninhydrin with proteins is :

Compound A is converted to B on reaction with CHCl3 and KOH. The compound B is toxic and can be decomposed by C. A, B and C respectively are :

The number of nitrogen atoms in a semicarbazone molecule of acetone is ______________.

According to the valence bond theory the hybridization of central metal atom is dsp2 for which one of the following compounds?

The correct order of intensity of colors of the compounds is :

The spin-only magnetic moment value for the complex [Co(CN)6]4\(-\) is __________ BM.[At. no. of Co = 27]

For above chemical reactions, identify the correct statement from the following :

Given below are two statements : One is labelled as Assertion A and other is labelled as Reason R. Assertion A : The dihedral angles in H2O2 in gaseous phase is 90.2\(^\circ\) and in solid phase is 111.5\(^\circ\).Reason R : The change in d...

The metal that can be purified economically by fractional distillation method is :

The species given below that does NOT show disproportionation reaction is :

Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and P4O10 (in 4 : 1 ratio) is :

Orlon fibres are made up of :

An inorganic Compound 'X' on treatment with concentrated H2SO4 produces brown fumes and gives dark brown ring with FeSO4 in presence of concentrated H2SO4. Also Compound 'X' gives precipitate 'Y', when its solution in dilute HCl is treated ...

The set in which compounds have different nature is :

A s-block element (M) reacts with oxygen to form an oxide of the formula MO2. The oxide is pale yellow in colour and paramagnetic. The element (M) is :

Given below are two statements. One is labelled as Assertion A nd the other is labelled as Reason R.Assertion A : Sharp glass edge becomes smooth on heating it upto its melting point.Reason R : The viscosity of glass decreases on melting.Ch...

At 20\(^\circ\) C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The mole fraction of benzene in the vapour phase at 20\(^\circ\) above an equimolar mixture of benzene and methyl benzene is _____________ $...

250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl. The number of unreacted HCl molecules in the solution after complete reaction is ___________ \(\times\) 1021. (Nearest integer)(NA = 6.022 \(\times\) 1023)

An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol\(-\)1) needed to meet this energy requirement is ____________ g.(Use : \(\Delta\)CH(glucose) = \(-\)2700 kJ mol\(-\)1)

The Azimuthal quantum number for the valence electrons of Ga+ ion is ___________.(Atomic number of Ga = 31)

The conditions given below are in the context of observing Tyndall effect in colloidal solutions :(A) The diameter of the colloidal particles is comparable to the wavelength of light used.(B) The diameter of the colloidal particles is much ...

Let P be a plane passing through the points (1, 0, 1), (1, \(-\)2, 1) and (0, 1, \(-\)2). Let a vector \(\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k\) be such that \(\overrightarrow a\) is parallel to the ...

Let \(A = [{a_{ij}}]\) be a 3 \(\times\) 3 matrix, where \({a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr { - x} & , & {if\,\left| {i - j} \right| = 1} \cr {2x + 1} & , & {otherwise.} \cr } } \right.\)Let a function f...

Let 'a' be a real number such that the function f(x) = ax2 + 6x \(-\) 15, x \(\in\) R is increasing in \(\left( { - \infty ,{3 \over 4}} \right)\) and decreasing in \(\left( {{3 \over 4},\infty } \right)\). Then the function g(x) = ax2 $$-$...

Let T be the tangent to the ellipse E : x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = \(\sqrt 5\) is \(\alpha\)\(\sqrt 5\) + \(\beta\) + \(\gamma\) cos\(-\)1$$\left( ...

The coefficient of x256 in the expansion of (1 \(-\) x)101 (x2 + x + 1)100 is :

The number of rational terms in the binomial expansion of \({\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}\) is _______________.

If z and \(\omega\) are two complex numbers such that \(\left| {z\omega } \right| = 1\) and \(\arg (z) - \arg (\omega ) = {{3\pi } \over 2}\), then \(\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)\) is :...

Let a be a positive real number such that \(\int_0^a {{e^{x - [x]}}} dx = 10e - 9\) where [ x ] is the greatest integer less than or equal to x. Then a is equal to:

The value of the integral \(\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx}\) is equal to:

Let y = y(x) be the solution of the differential equation \(x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( {{y \over x}} \right) - x} \right)dx\), \(- 1 \le x \le 1\), \(y\left( {{1 \over 2}} \right) = {\pi \over 6}\). Then t...

Let y = y(x) be the solution of the differential equation \({e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy = 0\), y(1) = \(-\)1. Then the value of (y(3))2 is equal to :

Let [ x ] denote the greatest integer \(\le\) x, where x \(\in\) R. If the domain of the real valued function \(f(x) = \sqrt {{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}}\) is (\(-\) \(\infty\), a) \(]\cup\) [b, c) $$\cup...

The number of real roots of the equation \({\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4}\) is :

Let a function f : R \(\to\) R be defined as \(f(x) = \left\{ {\matrix{ {\sin x - {e^x}} & {if} & {x \le 0} \cr {a + [ - x]} & {if} & {0 < x < 1} \cr {2x - b} & {if} & {x \ge 1} \cr } } \right.\) where [ x ] is the greatest...

If the value of \(\mathop {\lim }\limits_{x \to 0} {(2 - \cos x\sqrt {\cos 2x} )^{\left( {{{x + 2} \over {{x^2}}}} \right)}}\) is equal to ea, then a is equal to __________.

The Boolean expression \((p \wedge \sim q) \Rightarrow (q \vee \sim p)\) is equivalent to :

Let \(A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]\), a\(\in\)R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of deter...

Let \(A = \left( {\matrix{ 1 & { - 1} & 0 \cr 0 & 1 & { - 1} \cr 0 & 0 & 1 \cr } } \right)\) and B = 7A20 \(-\) 20A7 + 2I, where I is an identity matrix of order 3 \(\times\) 3. If B = [bij], then b13is equal to ___________...

Let a, b, c, d in arithmetic progression with common difference \(\lambda\). If \(\left| {\matrix{ {x + a - c} & {x + b} & {x + a} \cr {x - 1} & {x + c} & {x + b} \cr {x - b + d} & {x + d} & {x + c} \cr } } \right| = 2\), t...

Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :