JEE Main 2020 (Online) 4th September Morning Slot

When neopentyl alcohol is heated with an acid,
it slowly converted into an 85 : 15 mixture of
alkenes A and B, respectively. What are these
alkenes?

An organic compound (A) (molecular formula
C6H12O2) was hydrolysed with dil. H2SO4 to give
a carboxylic acid (B) and an alcohol (C). ‘C’
gives white turbidity immediately when treated
with anhydrous ZnCl2 and conc. HCl. The
organic compound...

[P] on treatment with Br2/FeBr3 in CCl4
produced a single isomer C8H7O2Br while
heating [P] with sodalime gave toluene. The
compound [P] is

The IUPAC name of the following compound is :

Which of the following will react with CHCl3 +
alc. KOH?

What are the functional groups present in the
structure of maltose?

The intermolecular potential energy for the
molecules A, B, C and D given below suggests
that :

For the equilibrium A ⇌ B , the variation of the
rate of the forward (a) and reverse (b) reaction
with time is given by :

If 75% of a first order reaction was completed
in 90 minutes, 60% of the same reaction would
be completed in approximately (in minutes)
_______.
(Take : log 2 = 0.30; log 2.5 = 0.40)

The number of chiral centres present in [B] is
_____.

The pair in which both the species have the
same magnetic moment (spin only) is :

The number of isomers possible for
[Pt(en)(NO2)2] is :

The elements with atomic numbers 101 and 104
belong to, respectively :

\(E_{C{u^{2 + }}|Cu}^0\) = +0.34 V
\(E_{Z{n^{2 + }}|Zn}^0\) = -0.76 V
Identify the incorrect statement from the option
below for the above cell :

The decreasing order of reactivity of the
following organic molecules towards AgNO3
solution is :

Among statements (a) - (d), the correct ones are
(a) Lime stone is decomposed to CaO during
the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted
as an anionic complex.
(c) Nickel is purified by Mond’s...

On heating, lead (II) nitrate gives a brown gas
(A). The gas (A) on cooling changes to a
colourless solid/liquid (B). (B) on heating with
NO changes to a blue solid (C). The oxidation
number of nitrogen in solid (C) is :

The ionic radii of O2–, F–, Na+ and Mg2+ are in
the order :

On combustion of Li, Na and K in excess of air,
the major oxides formed, respectively, are :

At 300 K, the vapour pressure of a solution
containing 1 mole of n-hexane and 3 moles of
n-heptane is 550 mm of Hg. At the same
temperature, if one more mole of n-heptane is
added to this solution, the vapour pressure of
the solution increa...

A 20.0 mL solution containing 0.2 g impure
H2O2 reacts completely with 0.316 g of KMnO4
in acid solution. The purity of H2O2 (in %) is
_____________
(mol. wt. of H2O2 = 34; mol. wt. of
KMnO4 = 158)

The mass of ammonia in grams produced when
2.8 kg of dinitrogen quantitatively reacts with 1
kg of dihydrogen is _______.

The region in the electromagnetic spectrum
where the Balmar series lines appear is :

Match the following :

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For one mole of an ideal gas, which of these
statements must be true?
(a) U and H each depends only on temperature
(b) Compressibility factor z is not equal to 1
(c) CP, m – CV, m = R
(d) dU = CVdT for any process

If the equation of a plane P, passing through the intersection of the planes, x + 4y - z + 7 = 0
and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b \(\in\) R, then the distance of the point
(3, 2, -1) from the plane P is...........

Let f be a twice differentiable function on (1, 6). If f(2) = 8, f’(2) = 5, f’(x) \(\ge\) 1 and f''(x) \(\ge\) 4, for all x \(\in\) (1, 6), then :

Let \({\left( {2{x^2} + 3x + 4} \right)^{10}} = \sum\limits_{r = 0}^{20} {{a_r}{x^r}}\)
Then \({{{a_7}} \over {{a_{13}}}}\) is equal to ______.

The value of \(\sum\limits_{r = 0}^{20} {{}^{50 - r}{C_6}}\) is equal to:

Let \(u = {{2z + i} \over {z - ki}}\), z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :

Let \(f(x) = \left| {x - 2} \right|\) and g(x) = f(f(x)), \(x \in \left[ {0,4} \right]\). Then \(\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx\) is equal to:

Let y = y(x) be the solution of the differential equation, xy'- y = x2(xcosx + sinx), x > 0. if y (\(\pi\)) = \(\pi\) then \(y''\left( {{\pi \over 2}} \right) + y\left( {{\pi \over 2}} \right)\) is equal to :

If \(\left( {a + \sqrt 2 b\cos x} \right)\left( {a - \sqrt 2 b\cos y} \right) = {a^2} - {b^2}\)
where a > b > 0, then \({{dx} \over {dy}}\,\,at\left( {{\pi \over 4},{\pi \over 4}} \right)\) is :

Let \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, \(\phi \left( t \right) = {5 \over {12}} + t - {t^2}\), ...

Let P(3, 3) be a point on the hyperbola, \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). If the normal to it at P intersects the x-axis
at (9, 0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :

Let \(f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)}\). Then f(3) – f(1) is eqaul to :

The integral \(\int {{{\left( {{x \over {x\sin x + \cos x}}} \right)}^2}dx}\) is equal to
(where C is a constant of integration):

Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x) + f(y) + xy2 + x2y, for all real x and y.
\(\mathop {\lim }\limits_{x \to 0} {{f\left( x \right)} \over x} = 1\), then f'(3) is equal to ______.

Given the following two statements:
\(\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)\) is a tautology
\(\left( {{S_2}} \right): \,\,\sim q \wedge \left( { \sim p \leftrightarrow q} \right)\)...

If \(A = \left[ {\matrix{ {\cos \theta } & {i\sin \theta } \cr {i\sin \theta } & {\cos \theta } \cr } } \right]\), \(\left( {\theta = {\pi \over {24}}} \right)\)
and $${A^5} = \left[ {\matrix{
a & b \cr
c & d \cr

}...

If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24, has infinitely many solutions, then a - b is equal to.........

The probability of a man hitting a target is \({1 \over {10}}\). The least number of shots required, so that the
probability of his hitting the target at least once is greater than \({1 \over {4}}\), is ____________.

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If \(\angle BAC = {90^o}\) and area\(\left( {\Delta ABC} \right) = 5\sqrt 5\) s units, then the abscissa of the vertex C is :

Let \(\alpha\) and \(\beta\) be the roots of x2 - 3x + p=0 and \(\gamma\) and \(\delta\) be the roots of x2 - 6x + q = 0. If \(\alpha, \beta, \gamma, \delta\)
form a geometric progression.Then ratio (2q + p) : (2q - p) is:

Let [t] denote the greatest integer \(\le\) t. Then the equation in x,
[x]2 + 2[x+2] - 7 = 0 has :

If 1+(1–22.1)+(1–42.3)+(1-62.5)+......+(1-202.19)= \(\alpha\) - 220\(\beta\), then an ordered pair \(\left( {\alpha ,\beta } \right)\) is equal to:

A survey shows that 63% of the people in a city read newspaper A whereas 76% read
newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations
are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A
and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m)
above the line AC is :

Let x0 be the point of Local maxima of \(f(x) = \overrightarrow a .\left( {\overrightarrow b \times \overrightarrow c } \right)\), where \(\overrightarrow a = x\widehat i - 2\widehat j + 3\widehat k\), $$\overrightarrow b = - 2\widehat ...