JEE Main 2019 (Online) 9th January Evening Slot

The equation of the plane containing the straight line \({x \over 2} = {y \over 3} = {z \over 4}\) and perpendicular to the plane containing the straight lines \({x \over 3} = {y \over 4} = {z \over 2}\) and $${x \over 4} = {y \over 2} = {z...

If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :

The area of the region
A = {(x, y) : 0 \(\le\) y \(\le\)x |x| + 1  and  \(-\)1 \(\le\) x \(\le\)1} in sq. units, is :

The coefficient of t4 in the expansion of \({\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}\) is :

If the circles
x2 + y2 \(-\) 16x \(-\) 20y + 164 = r2  
and  (x \(-\) 4)2 + (y \(-\) 7)2 = 36
intersect at two distinct points, then :

Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz\(_0^{81}\) \(-\) 3iz\(_0^{93}\), then arg z is equal to :

Let f be a differentiable function from
R to R such that \(\left| {f\left( x \right) - f\left( y \right)} \right| \le 2{\left| {x - y} \right|^{{3 \over 2}}},\)    for all  \(x,y \in\) R.
If   \(f\left( 0 \right) = 1\)  
then   $$\int\...

If   \(\int\limits_0^{{\pi \over 3}} {{{\tan \theta } \over {\sqrt {2k\,\sec \theta } }}} \,d\theta = 1 - {1 \over {\sqrt 2 }},\left( {k > 0} \right),\) then value of k is :

Let f : [0,1] \(\to\) R be such that f(xy) = f(x).f(y), for all x, y \(\in\) [0, 1], and f(0) \(\ne\) 0. If y = y(x) satiesfies the differential equation, \({{dy} \over {dx}}\) = f(x) with y(0) = 1, then y$$\left( {{1 \over 4}} \righ...

If   x \(=\) 3 tan t and y \(=\) 3 sec t, then the value of \({{{d^2}y} \over {d{x^2}}}\) at t \(= {\pi \over 4},\) is :

Let A = {x \(\in\) R : x is not a positive integer}.
Define a function \(f\) : A \(\to\)  R   as  \(f(x)\) = \({{2x} \over {x - 1}}\),
then \(f\) is :

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

If   \(f\left( x \right) = \int {{{5{x^8} + 7{x^6}} \over {{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} \,dx,\,\left( {x \ge 0} \right),\)
\(f\left( 0 \right) = 0,\)    then the value of \(f(1)\) is :

If  x = sin\(-\)1(sin10) and y = cos\(-\)1(cos10), then y \(-\) x is equal to :

For each x\(\in\)R, let [x] be the greatest integer less than or equal to x.
Then \(\mathop {\lim }\limits_{x \to {0^ - }} \,\,{{x\left( {\left[ x \right] + \left| x \right|} \right)\sin \left[ x \right]} \over {\left| x \right|}}\) is e...

The logical statement
[ \(\sim\) ( \(\sim\) p \(\vee\) q) \(\vee\) (p \(\wedge\) r)] \(\wedge\) (\(\sim\) q \(\wedge\) r) is equivalent to :

If the system of linear equations
x \(-\) 4y + 7z = g
       3y \(-\) 5z = h
\(-\)2x + 5y \(-\) 9z = k
is consistent, then :

If   $$A = \left[ {\matrix{
{{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr
{{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \cr
{{e^t}} & {2{e^{ - t}}\s...

Let A(4, \(-\) 4) and B(9, 6) be points on the parabola, y2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of \(\Delta\)ACB is maximum. Then, the area (in sq. units) of \(\Delta\)ACB, is :

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in...

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not r...

If both the roots of the quadratic equation x2 \(-\) mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :

The number of all possible positive integral values of \(\alpha\)  for which the roots of the quadratic equation, 6x2 \(-\) 11x + \(\alpha\) = 0 are rational numbers is :

Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then \({a \over c}\) equal to :

The sum of the following series
\(1 + 6 + {{9\left( {{1^2} + {2^2} + {3^2}} \right)} \over 7} + {{12\left( {{1^2} + {2^2} + {3^2} + {4^2}} \right)} \over 9}\)
       $$ + {{15\left( {{1^2} + {2^2} + ... + {5^2}} \right)} \over {11}} + ........

A data consists of n observations : x1, x2, . . . . . . ., xn.    
If     \(\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n\)    and
\(\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,\)
then the standard devi...

Let the equations of two sides of a triangle be 3x \(-\) 2y + 6 = 0 and 4x + 5y \(-\) 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is :

If  0 \(\le\) x < \({\pi \over 2}\),  then the number of values of x for which sin x \(-\) sin 2x + sin 3x = 0, is :

Let  \(\overrightarrow a = \widehat i + \widehat j + \sqrt 2 \widehat k,\)   \(\overrightarrow b = {b_1}\widehat i + {b_2}\widehat j + \sqrt 2 \widehat k\),    \(\overrightarrow c = 5\widehat i + \widehat j + \sqrt 2 \widehat k\)   be th...