JEE Main 2019 (Online) 9th April Morning Slot

If the line, \({{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 2} \over 4}\) meets the plane,
x + 2y + 3z = 15 at a point P, then the distance of P from the origin is :

A plane passing through the points (0, –1, 0)
and (0, 0, 1) and making an angle \({\pi \over 4}\) with the
plane y – z + 5 = 0, also passes through the
point

If the tangent to the curve, y = x3 + ax – b at
the point (1, –5) is perpendicular to the line,
–x + y + 4 = 0, then which one of the following
points lies on the curve ?

Let S be the set of all values of x for which the
tangent to the curve
y = ƒ(x) = x3 – x2 – 2x at
(x, y) is parallel to the line segment joining the
points (1, ƒ(1)) and (–1, ƒ(–1)), then S is equal
to :

If ƒ(x) is a non-zero polynomial of degree four,
having local extreme points at x = –1, 0, 1; then
the set
S = {x \(\in\) R : ƒ(x) = ƒ(0)}
Contains exactly :

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

If the fourth term in the binomial expansion of \({\left( {{2 \over x} + {x^{{{\log }_8}x}}} \right)^6}\)
(x > 0) is 20 × 87, then a value of
x is :

If a tangent to the circle x2 + y2 = 1 intersects
the coordinate axes at distinct points P and Q,
then the locus of the mid-point of PQ is :

All the points in the set
\(S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )\) lie on a :

The value of \(\int\limits_0^{\pi /2} {{{{{\sin }^3}x} \over {\sin x + \cos x}}dx}\) is

The solution of the differential equation
\(x{{dy} \over {dx}} + 2y\) = x2 (x \(\ne\) 0) with y(1) = 1, is :

If the function ƒ : R – {1, –1} \(\to\) A defined by
ƒ(x) = \({{{x^2}} \over {1 - {x^2}}}\) , is surjective, then A is equal to

Let \(\sum\limits_{k = 1}^{10} {f(a + k) = 16\left( {{2^{10}} - 1} \right)}\) where the function
ƒ satisfies
ƒ(x + y) = ƒ(x)ƒ(y) for all natural
numbers x, y and ƒ(1) = 2. then the natural
number 'a' is

If the line y = mx + 7\(\sqrt 3\) is normal to the
hyperbola
\({{{x^2}} \over {24}} - {{{y^2}} \over {18}} = 1\) , then a value of m is :

The integral \(\int {{\rm{se}}{{\rm{c}}^{{\rm{2/ 3}}}}\,{\rm{x }}\,{\rm{cose}}{{\rm{c}}^{{\rm{4 / 3}}}}{\rm{x \,dx}}}\) is equal to
(Hence C is a constant of integration)

If the function ƒ defined on , \(\left( {{\pi \over 6},{\pi \over 3}} \right)\) by
$$$f(x) = \left\{ {\matrix{
{{{\sqrt 2 {\mathop{\rm cosx}\nolimits} - 1} \over {\cot x - 1}},} & {x \ne {\pi \over 4}} \cr
{k,} & {x = {\pi \ove...

Let ƒ(x) = 15 – |x – 10|; x \(\in\) R. Then the set
of all values of x, at which the function,
g(x) = ƒ(ƒ(x)) is not differentiable, is :

For any two statements p and q, the negation of
the expression
p \(\vee\) (~p \(\wedge\) q) is :

If \(\left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]\)\(\left[ {\matrix{ 1 & 3 \cr 0 & 1 \cr } } \right]\)....$$\left[ {\matrix{
1 & {n - 1} \cr
0 ...

Let \(\alpha\) and \(\beta\) be the roots of the equation
x2 + x + 1 = 0. Then for y \(\ne\) 0 in R,
$$$\left| {\matrix{
{y + 1} & \alpha & \beta \cr
\alpha & {y + \beta } & 1 \cr
\beta & 1 & {y + \alpha } \cr

} } \...

If one end of a focal chord of the parabola,
y2 = 16x is at (1, 4), then the length of this focal
chord is :

A committee of 11 members is to be formed from
8 males and 5 females. If m is the number of ways
the committee is formed with at least 6 males and
n is the number of ways the committee is formed
with at least 3 females, then :

Four persons can hit a target correctly with
probabilities
\({1 \over 2}\), \({1 \over 3}\), \({1 \over 4}\) and
\({1 \over 8}\) respectively. if all hit
at the target independently, then the probability that
the target would be hit, is :

Let p, q \(\in\) R. If 2 - \(\sqrt 3\) is a root of the quadratic
equation, x2 + px + q = 0, then :

Let the sum of the first n terms of a non-constant
A.P., a1, a2, a3, ..... be \(50n + {{n(n - 7)} \over 2}A\), where
A is a constant. If d is the common difference of
this A.P., then the ordered pair (d, a50) is equal to

If the standard deviation of the numbers
–1, 0, 1, k is \(\sqrt 5\) where k > 0, then k is equal to

Slope of a line passing through P(2, 3) and
intersecting the line, x + y = 7 at a distance of
4 units from P, is :

Let S = {\(\theta\) \(\in\) [–2\(\pi\), 2\(\pi\)] : 2cos2\(\theta\) + 3sin\(\theta\) = 0}.
Then the sum of the elements of S is

The value of cos210° – cos10°cos50° + cos250° is

Let \(\overrightarrow \alpha = 3\widehat i + \widehat j\) and \(\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k\)
. If \(\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}}\),
where $${\...