JEE Main 2020 (Online) 4th September Evening Slot

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line \({x \over 2} = {y \over 3} = {z \over { - 6}}\) is :

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x2–1 below the x-axis, is :

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n + 5 are in the ratio 5 : 10 : 14, then the largest coefficient in this expansion is :

The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x2 + y2 – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the point :

Let PQ be a diameter of the circle x2 + y2 = 9. If \(\alpha\) and \(\beta\) are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of \(\alpha\beta\) is _____.

If a and b are real numbers such that \({\left( {2 + \alpha } \right)^4} = a + b\alpha\) where \(\alpha = {{ - 1 + i\sqrt 3 } \over 2}\) then a + b is
equal to :

Let {x} and [x] denote the fractional part of x and the greatest integer \(\le\) x respectively of a real number x. If \(\int_0^n {\left\{ x \right\}dx} ,\int_0^n {\left[ x \right]dx}\) and 10(n2 – n), \(\left( {n \in N,n > 1} \right)\) ...

The integral \(\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}\)
is equal to:

The solution of the differential equation
\({{dy} \over {dx}} - {{y + 3x} \over {{{\log }_e}\left( {y + 3x} \right)}} + 3 = 0\) is:
(where c is a constant of integration)

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is \({1 \over 2}\). If P(1, \(\beta\)), \(\beta\) > 0 is a point on this ellipse, then the equation of the normal to it at P is :

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°,then PC (in m) is equal to :

Let \(f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)\) be a differentiable function such that f(1) = e and \(\mathop {\lim }\limits_{t \to x} {{{t^2}{f^2}(x) - {x^2}{f^2}(t)} \over {t - x}} = 0\). If f(x) = 1, then x is equal ...

The function \(f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.\) is :

Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is:

If the system of equations
x+y+z=2
2x+4y–z=6
3x+2y+\(\lambda\)z=\(\mu\)
has infinitely many solutions, then

Suppose the vectors x1, x2 and x3 are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b1, b2 and b3 respectively. if
$${x_1} = \left[ {\matrix{
1 \cr
1 \cr
1 \cr

} } \...

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is _______...

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws total a of 6 before B throws a total of 7 and B wins t...

Let \(\lambda \ne 0\) be in R. If \(\alpha\) and \(\beta\) are the roots of the equation, x2 - x + 2\(\lambda\) = 0 and \(\alpha\) and \(\gamma\) are the roots of the equation, \(3{x^2} - 10x + 27\lambda = 0\), then $${{\beta \gamma...

Let a1, a2, ..., an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + .... + an. If a1 = 1, an = 300 and 15 \(\le\) n \(\le\) 50, then the ordered pair (Sn-4, an–4) is equal to:

The minimum value of 2sinx + 2cosx is :

Let \(\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T\) where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi’s and exac...

If the variance of the following frequency
distribution :
Class         : 10–20 20–30 30–40

Frequency :    2          x          2
is 50, then x is equal to____

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

If \(\overrightarrow a = 2\widehat i + \widehat j + 2\widehat k\), then the value of
$${\left| {\widehat i \times \left( {\overrightarrow a \times \widehat i} \right)} \right|^2} + {\left| {\widehat j \times \left( {\overrightarrow a \t...