JEE Main 2019 (Online) 9th April Evening Slot

The vertices B and C of a \(\Delta\)ABC lie on the line,
\({{x + 2} \over 3} = {{y - 1} \over 0} = {z \over 4}\) such that BC = 5 units. Then the
area (in sq. units) of this triangle, given that the
point A(1, –1, 2), is :

Let P be the plane, which contains the line of
intersection of the planes, x + y + z – 6 = 0 and
2x + 3y + z + 5 = 0 and it is perpendicular to the
xy-plane. Then the distance of the point (0, 0, 256)
from P is equal to :

A water tank has the shape of an inverted right
circular cone, whose semi-vertical angle is
\({\tan ^{ - 1}}\left( {{1 \over 2}} \right)\). Water is poured into it at a constant
rate of 5 cubic meter per minute. The the rate
(in m/min.), at...

The area (in sq. units) of the region
A = {(x, y) : \({{y{}^2} \over 2}\) \(\le\) x \(\le\) y + 4} is :-

If some three consecutive in the binomial
expansion of (x + 1)n is powers of x are in the ratio
2 : 15 : 70, then the average of these three
coefficient is :-

A rectangle is inscribed in a circle with a diameter
lying along the line 3y = x + 7. If the two adjacent
vertices of the rectangle are (–8, 5) and (6, 5), then
the area of the rectangle (in sq. units) is :

The common tangent to the circles x 2 + y2 = 4 and
x2 + y2 + 6x + 8y – 24 = 0 also passes through the
point :

Let z \(\in\) C be such that |z| < 1.
If \(\omega = {{5 + 3z} \over {5(1 - z)}}\)z, then :

If f : R \(\to\) R is a differentiable function and
f(2) = 6, then \(\mathop {\lim }\limits_{x \to 2} {{\int\limits_6^{f\left( x \right)} {2tdt} } \over {\left( {x - 2} \right)}}\) is :-

The value of the integral \(\int\limits_0^1 {x{{\cot }^{ - 1}}(1 - {x^2} + {x^4})dx}\) is :-

If \(\cos x{{dy} \over {dx}} - y\sin x = 6x\), (0 < x < \({\pi \over 2}\))
and \(y\left( {{\pi \over 3}} \right)\) = 0 then \(y\left( {{\pi \over 6}} \right)\) is equal to :-

If the tangent to the parabola y2 = x at a point
(\(\alpha\), \(\beta\)), (\(\beta\) > 0) is also a tangent to the ellipse,
x2 + 2y2 = 1, then \(\alpha\) is equal to :

The domain of the definition of the function
\(f(x) = {1 \over {4 - {x^2}}} + {\log _{10}}({x^3} - x)\) is

Two poles standing on a horizontal ground are of
heights 5m and 10 m respectively. The line joining
their tops makes an angle of 15º with ground. Then
the distance (in m) between the poles, is :-

\(\int {{e^{\sec x}}}\) \((\sec x\tan xf(x) + \sec x\tan x + se{x^2}x)dx\)
= esecxf(x) + C then a possible choice of f(x) is :-

If the function \(f(x) = \left\{ {\matrix{ {a|\pi - x| + 1,x \le 5} \cr {b|x - \pi | + 3,x > 5} \cr } } \right.\)
is
continuous at x = 5, then the value of a – b is :-

If \(f(x) = [x] - \left[ {{x \over 4}} \right]\) ,x \(\in\)
4
, where [x] denotes the
greatest integer function, then

If p \(\Rightarrow\) (q \(\vee\) r) is false, then the truth values of p,
q, r are respectively :-

If the system of equations 2x + 3y – z = 0, x + ky
– 2z = 0 and 2x – y + z = 0 has a non-trival solution
(x, y, z), then \({x \over y} + {y \over z} + {z \over x} + k\)
is equal to :-

The total number of matrices
\(A = \left( {\matrix{ 0 & {2y} & 1 \cr {2x} & y & { - 1} \cr {2x} & { - y} & 1 \cr } } \right)\)
(x, y \(\in\) R,x \(\ne\) y) for which ATA = 3I3 is :-

The area (in sq. units) of the smaller of the two
circles that touch the parabola, y2 = 4x at the point
(1, 2) and the x-axis is :-

If m is chosen in the quadratic equation
(m2 + 1)
x2 – 3x + (m2 + 1)2 = 0
such that the sum of its
roots is greatest, then the absolute difference of
the cubes of its roots is :-

The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 +....
upto 11th term is :-

Some identical balls are arranged in rows to form
an equilateral triangle. The first row consists of one
ball, the second row consists of two balls and so
on. If 99 more identical balls are addded to the total
number of balls used in formin...

If the sum and product of the first three term in
an A.P. are 33 and 1155, respectively, then a value
of its 11th term is :-

Two newspapers A and B are published in a city.
It is known that 25% of the city populations reads
A and 20% reads B while 8% reads both A and
B. Further, 30% of those who read A but not B
look into advertisements and 40% of those who
read ...

The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then \({y \over x}\) is equal to

If the two lines x + (a – 1) y = 1 and
2x + a2y = 1 (a\(\in\)R – {0, 1}) are perpendicular, then
the distance of their point of intersection from the
origin is :

The value of sin 10º sin30º sin50º sin70º is :-

If a unit vector \(\overrightarrow a\) makes angles \(\pi\)/3 with \(\widehat i\) , \(\pi\)/ 4
with \(\widehat j\) and \(\theta\)\(\in\)(0, \(\pi\)) with \(\widehat k\), then a value of \(\theta\)
is :-