JEE Main 2020 (Online) 5th September Evening Slot

If for some \(\alpha\) \(\in\) R, the lines
L1 : \({{x + 1} \over 2} = {{y - 2} \over { - 1}} = {{z - 1} \over 1}\) and
L2 : \({{x + 2} \over \alpha } = {{y + 1} \over {5 - \alpha }} = {{z + 1} \over 1}\) are coplanar,
then the line L2
...

If the lines x + y = a and x – y = b touch the
curve y = x2
– 3x + 2 at the points where the
curve intersects the x-axis, then \({a \over b}\) is equal
to _______.

If x = 1 is a critical point of the function
f(x) = (3x2
+ ax – 2 – a)ex
, then :

Which of the following points lies on the
tangent to the curve
x4ey + 2\(\sqrt {y + 1}\) = 3 at the
point (1, 0)?

The area (in sq. units) of the region
A = {(x, y) : (x – 1)[x] \(\le\) y \(\le\) 2\(\sqrt x\), 0 \(\le\) x \(\le\) 2}, where [t]
denotes the greatest integer function, is :

The coefficient of x4
in the expansion of
(1 + x + x2
+ x3)6
in powers of x, is ______.

If the length of the chord of the circle,
x2 + y2 = r2
(r > 0) along the line, y – 2x = 3 is r,
then r2
is equal to :

The value of \({\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}\) is :

Let y = y(x) be the solution of the differential
equation
cosx\({{dy} \over {dx}}\) + 2ysinx = sin2x, x \(\in\) \(\left( {0,{\pi \over 2}} \right)\).
If
y\(\left( {{\pi \over 3}} \right)\) = 0, then y\(\left( {{\pi \over 4}} \right)\) ...

The derivative of
\({\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)\) with respect to \({\tan ^{ - 1}}\left( {{{2x\sqrt {1 - {x^2}} } \over {1 - 2{x^2}}}} \right)\) at x = \({1 \over 2}\) is :

Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the
number of elements in the set C = {f : A \(\to\) B |
2 \(\in\) f(A) and f is not one-one} is ______.

If the line y = mx + c is a common tangent to
the hyperbola
\({{{x^2}} \over {100}} - {{{y^2}} \over {64}} = 1\) and the circle
x2
+ y2
= 36, then which one of the following is
true?

If
\(\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta\) = A\({\log _e}\left| {B\left( \theta \right)} \right| + C\),
where C is a constant of integration, then \({{{B\left( \theta \right)} \over A}}\)
can b...

\(\mathop {\lim }\limits_{x \to 0} {{x\left( {{e^{\left( {\sqrt {1 + {x^2} + {x^4}} - 1} \right)/x}} - 1} \right)} \over {\sqrt {1 + {x^2} + {x^4}} - 1}}\)

The statement
\(\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)\) is :

If the system of linear equations
x + y + 3z = 0
x + 3y + k2z = 0
3x + y + 3z = 0
has a non-zero solution (x, y, z) for some k \(\in\) R,
then x + \(\left( {{y \over z}} \right)\) is equal to :

If a + x = b + y = c + z + 1, where a, b, c, x, y, z
are non-zero distinct real numbers, then
\(\left| {\matrix{ x & {a + y} & {x + a} \cr y & {b + y} & {y + b} \cr z & {c + y} & {z + c} \cr } } \right|\) is equal to :

There are 3 sections in a question paper and
each section contains 5 questions. A candidate
has to answer a total of 5 questions, choosing
at least one question from each section. Then
the number of ways, in which the candidate
can choose t...

In a bombing attack, there is 50% chance that
a bomb will hit the target. Atleast two
independent hits are required to destroy the
target completely. Then the minimum number
of bombs, that must be dropped to ensure that
there is at least 99...

If \(\alpha\) and \(\beta\) are the roots of the equation,
7x2 – 3x – 2 = 0, then the value of
\({\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}\) is equal to :

If the sum of the first 20 terms of the series
\({\log _{\left( {{7^{1/2}}} \right)}}x + {\log _{\left( {{7^{1/3}}} \right)}}x + {\log _{\left( {{7^{1/4}}} \right)}}x + ...\) is 460,
then x is equal to :

If the sum of the second, third and fourth terms
of a positive term G.P. is 3 and the sum of its
sixth, seventh and eighth terms is 243, then the
sum of the first 50 terms of this G.P. is :

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then
a and b are the roots of the equation :

If L = sin2\(\left( {{\pi \over {16}}} \right)\) - sin2\(\left( {{\pi \over {8}}} \right)\) and
M = cos2\(\left( {{\pi \over {16}}} \right)\) - sin2\(\left( {{\pi \over {8}}} \right)\), then :

Let the vectors \(\overrightarrow a\), \(\overrightarrow b\), \(\overrightarrow c\)
be such that
\(\left| {\overrightarrow a } \right| = 2\), \(\left| {\overrightarrow b } \right| = 4\)
and \(\left| {\overrightarrow c } \right| = 4\). ...