JEE Main 2020 (Online) 2nd September Morning Slot

The plane passing through the points (1, 2, 1),
(2, 1, 2) and parallel to the line, 2x = 3y, z = 1
also passes through the point :

If p(x) be a polynomial of degree three that has
a local maximum value 8 at x = 1 and a local
minimum value 4 at x = 2; then p(0) is equal to :

If the tangent to the curve y = x + sin y at a point
(a, b) is parallel to the line joining \(\left( {0,{3 \over 2}} \right)\) and \(\left( {{1 \over 2},2} \right)\), then :

Let P(h, k) be a point on the curve
y = x2
+ 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at
P is :

Area (in sq. units) of the region outside
\({{\left| x \right|} \over 2} + {{\left| y \right|} \over 3} = 1\) and inside the ellipse \({{{x^2}} \over 4} + {{{y^2}} \over 9} = 1\) is :

Let
\(\alpha\) > 0,
\(\beta\) > 0 be such that
\(\alpha\)3 + \(\beta\)2 = 4. If the
maximum value of the term independent of x in
the binomial expansion of
$${\left( {\alpha {x^{{1 \over 9}}} + \beta {x^{ - {1 \over 6}}}} \right)^{10}}$...

The number of integral values of k for which
the line, 3x + 4y = k intersects the circle,
x2
+ y2
– 2x – 4y + 4 = 0 at two distinct points is
______.

The value of \({\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}\) is :

The integral \(\int\limits_0^2 {\left| {\left| {x - 1} \right| - x} \right|dx}\) is equal to______.

Let y = y(x) be the solution of the differential
equation,
\({{2 + \sin x} \over {y + 1}}.{{dy} \over {dx}} = - \cos x\), y > 0,y(0) = 1. If y(\(\pi\)) = a and \({{dy} \over {dx}}\) at x =
\(\pi\) is b, then the ordered pair
(a, b) is eq...

A line parallel to the straight line 2x – y = 0 is
tangent to the hyperbola
\({{{x^2}} \over 4} - {{{y^2}} \over 2} = 1\) at the point
\(\left( {{x_1},{y_1}} \right)\). Then \(x_1^2 + 5y_1^2\) is equal to :

The domain of the function
f(x) = \({\sin ^{ - 1}}\left( {{{\left| x \right| + 5} \over {{x^2} + 1}}} \right)\) is (–
\(\infty\), -a]\(\cup\)[a, \(\infty\)). Then a is equal to :

If a function f(x) defined by
\(f\left( x \right) = \left\{ {\matrix{ {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \cr {c{x^2},} & {1 \le x \le 3} \cr {a{x^2} + 2cx,} & {3 < x \le 4} \cr } } \right.\)
be continuous for some $...

If \(\mathop {\lim }\limits_{x \to 1} {{x + {x^2} + {x^3} + ... + {x^n} - n} \over {x - 1}}\) = 820,
(n \(\in\) N) then
the value of n is equal to _______.

The contrapositive of the statement "If I reach the
station in time, then I will catch the train" is :

Let A be a 2 \(\times\) 2 real matrix with entries from
{0, 1} and |A|
\(\ne\) 0. Consider the following two
statements :
(P) If A \(\ne\) I2
, then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,
where I2
denotes 2 \(\times\) 2 identity ...

Let S be the set of all \(\lambda\) \(\in\) R for which the system
of linear equations
2x – y + 2z = 2
x – 2y +
\(\lambda\)z = –4
x +
\(\lambda\)y + z = 4
has no solution. Then the set S :

If the letters of the word 'MOTHER' be permuted
and all the words so formed (with or without
meaning) be listed as in a dictionary, then the
position of the word 'MOTHER' is ______.

Box I contains 30 cards numbered 1 to 30 and
Box II contains 20 cards numbered 31 to 50. A
box is selected at random and a card is drawn
from it. The number on the card is found to be
a non-prime number. The probability that the
card was dr...

Let
\(\alpha\) and
\(\beta\) be the roots of the equation
5x2 + 6x – 2 = 0. If Sn
=
\(\alpha\)n +
\(\beta\)n, n = 1, 2, 3....,
then :

The sum of the first three terms of a G.P. is S and
their product is 27. Then all such S lie in :

If |x| < 1, |y| < 1 and x \(\ne\) y, then the sum to infinity
of the following series
(x + y) + (x2+xy+y2) + (x3+x2y + xy2+y3) + ....

If R = {(x, y) : x, y
\(\in\) Z, x2 + 3y2
\(\le\) 8} is a relation
on the set of integers Z, then the domain of R–1 is :

Let X = {x
\(\in\) N : 1
\(\le\) x
\(\le\) 17} and
Y = {ax + b: x
\(\in\) X and a, b \(\in\) R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors such that
\({\left| {\overrightarrow a - \overrightarrow b } \right|^2}\) + $${\left| {\overrightarrow a - \overrightarrow c } \right|^2}$...