JEE Main 2020 (Online) 6th September Evening Slot

A plane P meets the coordinate axes at A, B
and C respectively. The centroid of \(\Delta\)ABC is
given to be (1, 1, 2). Then the equation of the
line through this centroid and perpendicular to
the plane P is :

If the tangent to the curve, y = f (x) = xloge x,
(x > 0) at a point (c, f(c)) is parallel to the
line-segment joining the points (1, 0) and
(e, e), then c is equal to :

The set of all real values of \(\lambda\) for which the
function
\(f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\)has exactly one maxima and exactly one
m...

The area (in sq. units) of the region enclosed
by the curves y = x2 – 1 and y = 1 – x2 is equal to :

If the constant term in the binomial expansion
of \({\left( {\sqrt x - {k \over {{x^2}}}} \right)^{10}}\) is 405, then |k| equals :

Let z = x + iy be a non-zero complex number
such that \({z^2} = i{\left| z \right|^2}\), where i = \(\sqrt { - 1}\) , then z lies
on the :

The integral \(\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx\) equals :

If \(y = \left( {{2 \over \pi }x - 1} \right) cosec\,x\) is the solution of the
differential equation, \({{dy} \over {dx}} + p\left( x \right)y = {2 \over \pi } cosec\,x\),
\(0 < x < {\pi \over 2}\), then the function p(x) is equal to :

If the normal at an end of a latus rectum of an
ellipse passes through an extremity of the
minor axis, then the eccentricity e of the ellipse
satisfies :

For a suitably chosen real constant a, let a
function, \(f:R - \left\{ { - a} \right\} \to R\) be defined by
\(f(x) = {{a - x} \over {a + x}}\). Further suppose that for any real
number \(x \ne - a\) and \(f(x) \ne - a\),
(fof)(x) = x. ...

Suppose that a function f : R \(\to\) R satisfies
f(x + y) = f(x)f(y) for all x, y \(\in\) R and f(1) = 3. If \(\sum\limits_{i = 1}^n {f(i)} = 363\) then n is equal to ________ .

The angle of elevation of the summit of a
mountain from a point on the ground is 45°.
After climbing up one km towards the summit
at an inclination of 30° from the ground, the
angle of elevation of the summit is found to be
60°. Then the he...

Let f : R \(\to\) R be a function defined by f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable.
Then :

For all twice differentiable functions f : R \(\to\) R,
with f(0) = f(1) = f'(0) = 0

Consider the statement : ‘‘For an integer n, if n3 – 1 is even, then n is odd.’’ The contrapositive statement of this statement is :

Let \(\theta = {\pi \over 5}\) and \(A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]\). If B = A + A4
, then det (B) :

The sum of distinct values of \(\lambda\) for which the
system of equations\(\left( {\lambda - 1} \right)x + \left( {3\lambda + 1} \right)y + 2\lambda z = 0\)$$\left( {\lambda - 1} \right)x + \left( {4\lambda - 2} \right)y + \left( {\l...

The centre of the circle passing through the
point (0, 1) and touching the parabola y = x2 at the point (2, 4) is :

The number of words (with or without meaning)
that can be formed from all the letters of the
word “LETTER” in which vowels never come
together is ________ .

The probabilities of three events A, B and C are
given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.
If P(A\(\cup\)B) = 0.8, P(A\(\cap\)C) = 0.3, P(A\(\cap\)B\(\cap\)C) = 0.2,
P(B\(\cap\)C) = \(\beta\) and P(A\(\cup\)B\(\cup\)C) ...

If \(\alpha\) and \(\beta\) are the roots of the equation
2x(2x + 1) = 1, then \(\beta\) is equal to :

The common difference of the A.P. b1, b2, … , bm
is 2 more than the common difference of A.P. a1, a2, …, an. If a40 = –159, a100 = –399 and
b100 = a70, then b1
is equal to :

Consider the data on x taking the values 0, 2, 4,
8,....., 2n with frequencies nC0
,
nC1
,
nC2
,....,
nCn
respectively. If the mean of this data is \({{728} \over {{2^n}}}\), then n is equal to _________ .

Let L denote the line in the xy-plane with x and
y intercepts as 3 and 1 respectively. Then the
image of the point (–1, –4) in this line is :

If \(\overrightarrow x\) and \(\overrightarrow y\) be two non-zero vectors such that
\(\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|\) and $${2\overrightarrow x + \lambda \overrightarrow y...