JEE Main 2020 (Online) 3rd September Morning Slot

The foot of the perpendicular drawn from the
point (4, 2, 3) to the line joining the points
(1, –2, 3) and (1, 1, 0) lies on the plane :

The function, f(x) = (3x – 7)x2/3, x \(\in\) R, is
increasing for all x lying in :

The area (in sq. units) of the region
{ (x, y) : 0 \(\le\) y \(\le\) x2 + 1, 0 \(\le\) y \(\le\) x + 1,
\({1 \over 2}\) \(\le\) x \(\le\) 2 } is :

If the number of integral terms in the expansion
of (31/2 + 51/8)n is exactly 33, then the least value
of n is :

The diameter of the circle, whose centre lies on
the line x + y = 2 in the first quadrant and which
touches both the lines x = 3 and y = 2, is
_______ .

If \({\left( {{{1 + i} \over {1 - i}}} \right)^{{m \over 2}}} = {\left( {{{1 + i} \over {1 - i}}} \right)^{{n \over 3}}} = 1\), (m, n
\(\in\) N) then the
greatest common divisor of the least values of
m and n is _______ .

\(\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx}\) is equal to :

The solution curve of the differential equation,
(1 + e-x)(1 + y2)\({{dy} \over {dx}}\) = y2,
which passes through
the point (0, 1), is :

If y2 + loge (cos2x) = y, \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\), then :

A hyperbola having the transverse axis of
length
\(\sqrt 2\) has the same foci as that of the ellipse
3x2 + 4y2 = 12, then this hyperbola does not
pass through which of the following points?

2\(\pi\) - \(\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \right)\) is equal to :

If \(\mathop {\lim }\limits_{x \to 0} \left\{ {{1 \over {{x^8}}}\left( {1 - \cos {{{x^2}} \over 2} - \cos {{{x^2}} \over 4} + \cos {{{x^2}} \over 2}\cos {{{x^2}} \over 4}} \right)} \right\}\) = 2-k
then the value of k is _______ .

Let [t] denote the greatest integer
\(\le\) t. If for some
\(\lambda\) \(\in\) R - {1, 0}, \(\mathop {\lim }\limits_{x \to 0} \left| {{{1 - x + \left| x \right|} \over {\lambda - x + \left[ x \right]}}} \right|\) = L, then L is
equal ...

The proposition p
\(\to\) ~ (p
\(\wedge\) ~q) is equivalent
to :

If \(\Delta\) = \(\left| {\matrix{ {x - 2} & {2x - 3} & {3x - 4} \cr {2x - 3} & {3x - 4} & {4x - 5} \cr {3x - 5} & {5x - 8} & {10x - 17} \cr } } \right|\) =
Ax3 + Bx2 + Cx + D, then B + C is equal to :

Let A = \(\left[ {\matrix{ x & 1 \cr 1 & 0 \cr } } \right]\), x \(\in\) R and A4 = [aij].
If
a11 = 109, then a22 is equal to _______ .

Let P be a point on the parabola, y2
= 12x and
N be the foot of the perpendicular drawn from
P on the axis of the parabola. A line is now
drawn through the mid-point M of PN, parallel
to its axis which meets the parabola at Q. If the
y-int...

The value of (2.1P0
– 3.2P1 + 4.3P2 .... up to
51th term) + (1! – 2! + 3! – ..... up to 51th term)
is equal to :

A dice is thrown two times and the sum of the
scores appearing on the die is observed to be
a multiple of 4. Then the conditional probability
that the score 4 has appeared atleast once is :

If \(\alpha\) and \(\beta\) are the roots of the equation
x2
+ px + 2 = 0 and \({1 \over \alpha }\) and \({1 \over \beta }\) are the roots of
the equation 2x2
+ 2qx + 1 = 0, then
$$\left( {\alpha - {1 \over \alpha }} \right)\left( {\be...

The value of \({\left( {0.16} \right)^{{{\log }_{2.5}}\left( {{1 \over 3} + {1 \over {{3^2}}} + ....to\,\infty } \right)}}\) is equal to ______.

If the first term of an A.P. is 3 and the sum of
its first 25 terms is equal to the sum of its next
15 terms, then the common difference of this
A.P. is :

Consider the two sets :
A = {m \(\in\) R : both the roots of x2
– (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

For the frequency distribution :
Variate (x) :      x1   x2   x3
....  x15
Frequency (f) : f1
   f2
  f3
...... f15
where 0 < x1
< x2
< x3
< ... < x15 = 10 and
\(\sum\limits_{i = 1}^{15} {{f_i}}\) > 0, the standard deviation cannot be ...

The lines
\(\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)\) and
$$\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} ...