JEE Main 2019 (Online) 12th April Evening Slot

A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y + 2z – 2 = 0,
passes through the point :

The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines
\(\overrightarrow r = \left( {\widehat i + \widehat j} \right) + \lambda \left( {\widehat i + 2\widehat j - \widehat k} \right)\) and $$\over...

If the area (in sq. units) bounded by the parabola y2
= 4\(\lambda\)x and the line y = \(\lambda\)x, \(\lambda\) > 0, is \({1 \over 9}\)
, then \(\lambda\) is equal to :

If 20C1 + (22) 20C2 + (32) 20C3 + ..... + (202
)
20C20 = A(2\(\beta\)), then the ordered pair (A, \(\beta\)) is equal to :

The term independent of x in the expansion of
\(\left( {{1 \over {60}} - {{{x^8}} \over {81}}} \right).{\left( {2{x^2} - {3 \over {{x^2}}}} \right)^6}\) is equal to :

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the
point :

Let z \(\in\) C with Im(z) = 10 and it satisfies \({{2z - n} \over {2z + n}}\) = 2i - 1 for some natural number n. Then :

A value of \(\alpha\) such that
\(\int\limits_\alpha ^{\alpha + 1} {{{dx} \over {\left( {x + \alpha } \right)\left( {x + \alpha + 1} \right)}}} = {\log _e}\left( {{9 \over 8}} \right)\) is :

The general solution of the differential equation (y2
– x3)dx – xydy = 0 (x \(\ne\) 0) is :
(where c is a constant of integration)

The derivative of \({\tan ^{ - 1}}\left( {{{\sin x - \cos x} \over {\sin x + \cos x}}} \right)\), with respect to \({x \over 2}\)
, where \(\left( {x \in \left( {0,{\pi \over 2}} \right)} \right)\) is :

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from
a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the
top of the tower ...

Let \(a \in \left( {0,{\pi \over 2}} \right)\) be fixed. If the integral
\(\int {{{\tan x + \tan \alpha } \over {\tan x - \tan \alpha }}} dx\) = A(x) cos 2\(\alpha\) + B(x) sin 2\(\alpha\) + C, where C is a
constant of integration, then...

Let f(x) = 5 – |x – 2| and g(x) = |x + 1|, x \(\in\) R. If f(x) attains maximum value at \(\alpha\) and g(x) attains
minimum value at \(\beta\), then
$$\mathop {\lim }\limits_{x \to -\alpha \beta } {{\left( {x - 1} \right)\left( {{x^2}...

\(\mathop {\lim }\limits_{x \to 0} {{x + 2\sin x} \over {\sqrt {{x^2} + 2\sin x + 1} - \sqrt {{{\sin }^2}x - x + 1} }}\) is :

The Boolean expression ~(p \(\Rightarrow\) (~q)) is equivalent to :

A value of \(\theta \in \left( {0,{\pi \over 3}} \right)\), for which
$$\left| {\matrix{
{1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr
{{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \c...

The equation of common tangent to the curves y2
= 16x and xy = –4, is :

The tangents to the curve y = (x – 2)2 – 1 at its points of intersection with the line x – y = 3, intersect at the point :

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can
randomly be selected from this group such that there is at least one boy and at least one girl in each team, is
1750, then n is eq...

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins
Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the
expected gain/loss (in Rs....

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability
that the candidate solve any problem is \({4 \over 5}\)
, then the probability that he is unable to solve less than two
problems...

A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1, 1) and (2, 3). Then the centroid of this triangle is :

If \(\alpha\), \(\beta\) and \(\gamma\) are three consecutive terms of a non-constant G.P. such that the equations \(\alpha\)x
2
+ 2\(\beta\)x + \(\gamma\) = 0 and
x2
+ x – 1 = 0 have a common root, then \(\alpha\)(\(\beta\) + $$\...

If a1, a2, a3, ..... are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P. is :

Let A, B and C be sets such that \(\phi\) \(\ne\) A \(\cap\) B \(\subseteq\) C. Then which of the following statements is not true ?

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and
the perpendicular from the origin to this line makes an angle of 60o with the line x + y = 0. Then an equation
of the line L is ...

If [x] denotes the greatest integer \(\le\) x, then the system of linear equations [sin \(\theta\)]x + [–cos\(\theta\)]y = 0, [cot\(\theta\)]x + y = 0

Let S be the set of all \(\alpha\) \(\in\) R such that the equation, cos2x + \(\alpha\)sinx = 2\(\alpha\)– 7 has a solution. Then S is equal to :

Let \(\alpha\) \(\in\) R and the three vectors \(\overrightarrow a = \alpha \widehat i + \widehat j + 3\widehat k\), \(\overrightarrow b = 2\widehat i + \widehat j - \alpha \widehat k\) and $$\overrightarrow c = \alpha \widehat i - 2\...