JEE Main 2020 (Online) 5th September Morning Slot

If (a, b, c) is the image of the point (1, 2, -3) in the line \({{x + 1} \over 2} = {{y - 3} \over { - 2}} = {z \over { - 1}}\), then a + b + c is :

If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, -4), then PQ2 is equal to:

The natural number m, for which the coefficient of x in the binomial expansion of
\({\left( {{x^m} + {1 \over {{x^2}}}} \right)^{22}}\) is 1540, is .............

If the four complex numbers \(z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)\) and \(z-2Re(z)\) represent the vertices of a square of
side 4 units in the Argand plane, then \(|z|\) is equal to :

The value of \(\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx}\) is:

If y = y(x) is the solution of the differential equation \({{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0\) satisfying
y(0) = 1, then a value of y(loge13) is :

If the co-ordinates of two points A and B are \(\left( {\sqrt 7 ,0} \right)\) and \(\left( { - \sqrt 7 ,0} \right)\) respectively and P is any
point on the conic, 9x2 + 16y2 = 144, then PA + PB is equal to :

If \(\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx}\) = \(g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c\)
where c is a constant of integration,
then g(0) is equal to :

If S is the sum of the first 10 terms of the series
$${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) +...

Let \(f(x) = x.\left[ {{x \over 2}} \right]\), for -10< x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to _____.

If \(\alpha\) is positive root of the equation, p(x) = x2 - x - 2 = 0, then
\(\mathop {\lim }\limits_{x \to {\alpha ^ + }} {{\sqrt {1 - \cos \left( {p\left( x \right)} \right)} } \over {x + \alpha - 4}}\) is equal to :

If the function \(f\left( x \right) = \left\{ {\matrix{ {{k_1}{{\left( {x - \pi } \right)}^2} - 1,} & {x \le \pi } \cr {{k_2}\cos x,} & {x > \pi } \cr } } \right.\) is twice differentiable, then the ordered pair (k1, k2) is equ...

The negation of the Boolean expression x \(\leftrightarrow\) ~ y is equivalent to :

Let \(\lambda \in\) R . The system of linear equations
2x1
- 4x2 + \(\lambda\)x3 = 1
x1 - 6x2 + x3 = 2
\(\lambda\)x1 - 10x2 + 4x3 = 3
is inconsistent for:

If the minimum and the maximum values of the function \(f:\left[ {{\pi \over 4},{\pi \over 2}} \right] \to R\), defined by
$$f\left( \theta \right) = \left| {\matrix{
{ - {{\sin }^2}\theta } & { - 1 - {{\sin }^2}\theta } & 1 \cr
...

If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2, then c is equal to :

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :

Four fair dice are thrown independently 27 times. Then the expected number of times, at
least two dice show up a three or a five, is _________.

The product of the roots of the equation 9x2 - 18|x| + 5 = 0 is :

If 210 + 29.31 + 28
.32 +.....+ 2.39 + 310 = S - 211, then S is equal to :

If \({3^{2\sin 2\alpha - 1}}\), 14 and \({3^{4 - 2\sin 2\alpha }}\) are the first three terms of an A.P. for some \(\alpha\), then the sixth
terms of this A.P. is:

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :

If the line, 2x - y + 3 = 0 is at a distance \({1 \over {\sqrt 5 }}\)
and \({2 \over {\sqrt 5 }}\) from the lines 4x - 2y + \(\alpha\) = 0 and 6x - 3y + \(\beta\) = 0, respectively, then the sum of all possible values of \(\alpha\) and $...

If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\overrightarrow a = \widehat i + \widehat j + n\widehat k\), \(\overrightarrow b = 2\widehat i + 4\widehat j - n\widehat k\) and $$\overrightarrow c = ...