JEE Main 2019 (Online) 12th January Evening Slot

Let S be the set of all real values of \(\lambda\) such that a plane passing through the points (–\(\lambda\)2, 1, 1), (1, –\(\lambda\)2, 1) and (1, 1, – \(\lambda\)2) also passes through the point (–1, –1, 1). Then S is equal to :

If an angle between the line, \({{x + 1} \over 2} = {{y - 2} \over 1} = {{z - 3} \over { - 2}}\) and the plane, \(x - 2y - kz = 3\) is \({\cos ^{ - 1}}\left( {{{2\sqrt 2 } \over 3}} \right),\) then a value of k is :

The tangent to the curve y = x2 – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point :

If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some a\(\in\)R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $${{f\left( x \right) - 14} \over {{{\left( {x - 1} \right)}^2}}} = 0\left( {...

The total number of irrational terms in the binomial expansion of (71/5 – 31/10)60 is :

If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the
locus of the foot of perpendicular from O on AB is :

Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of
| z1 – z2 | is :

The integral \(\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,\) loge x dx is equal to :

\(\mathop {\lim }\limits_{x \to \infty } \left( {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + {n \over {{n^2} + {3^2}}} + ..... + {1 \over {5n}}} \right)\) is equal to :

If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as \({{{x^2} - 2y} \over x}\), then the curve also passes through the point :

Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If \(\Delta\)S'BS is a right angled triangle with right angle at B and area (\(\Delta\)S'BS) = 8 sq. units, then the length of a latus rectum of...

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30o and the angle of depression of reflection of the cloud in the lake from P be 60o, then the height of the cloud (in meters) from
the surface of the lake is...

The integral \(\int {{{3{x^{13}} + 2{x^{11}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^4}}}} \,dx\) is equal to : (where C is a constant of integration)

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

Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x \(\in\) R R. If h(x) = f(f(x)), then h'(1) is equal to :

The expression \(\sim\) (\(\sim\) p \(\to\) q) is logically equivalent to :

If   A = \(\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]\);
then for all \(\theta\) \(\in\) $$\left( {{{3\pi } \over 4},{{5\pi } \o...

The set of all values of \(\lambda\) for which the system of linear equations
x – 2y – 2z = \(\lambda\)x
x + 2y + z = \(\lambda\)y
– x – y = \(\lambda\)z
has a non-trivial solutions :

The equation of a tangent to the parabola, x2
= 8y, which makes an angle \(\theta\) with the positive directions of x-axis, is :

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men...

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC
nor for NSS is :

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his ...

The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x \(\in\) R, is always positive, is :

If the sum of the first 15 terms of the series \({\left( {{3 \over 4}} \right)^3} + {\left( {1{1 \over 2}} \right)^3} + {\left( {2{1 \over 4}} \right)^3} + {3^3} + {\left( {3{3 \over 4}} \right)^3} + ....\) is equal to 225 k, then k
is equa...

If sin4\(\alpha\) + 4 cos4\(\beta\) + 2 = 4\(\sqrt 2\) sin \(\alpha\) cos \(\beta\); \(\alpha\), \(\beta\) \(\in\) [0, \(\pi\)],
then cos(\(\alpha\) + \(\beta\)) \(-\) cos(\(\alpha\) \(-\) \(\beta\)) is equal to :

If   nC4, nC5 and nC6 are in A.P., then n can be :

Let Z be the set of integers.
If A = {x \(\in\) Z : 2(x + 2) (x2 \(-\) 5x + 6) = 1} and
B = {x \(\in\) Z : \(-\) 3 < 2x \(-\) 1 < 9},
then the number of subsets of the set A \(\times\) B, is

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are
3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors, out of which vectors \(\overrightarrow b\) and \(\overrightarrow c\) are non-parallel. If \(\alpha\) and \(\beta\) are the angles whic...