JEE Main 2019 (Online) 11th January Evening Slot

Two lines \({{x - 3} \over 1} = {{y + 1} \over 3} = {{z - 6} \over { - 1}}\) and \({{x + 5} \over 7} = {{y - 2} \over { - 6}} = {{z - 3} \over 4}\) intersect at the point R. The reflection of R in the xy-plane has coordinates :

If the point (2, \(\alpha\), \(\beta\)) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2\(\alpha\) – 3\(\beta\) is equal to

Let f(x) = \({x \over {\sqrt {{a^2} + {x^2}} }} - {{d - x} \over {\sqrt {{b^2} + {{\left( {d - x} \right)}^2}} }},\,\,\) x \(\, \in\) R, where a, b and d are non-zero real constants. Then :

The area (in sq. units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is :

Let (x + 10)50 + (x \(-\) 10)50 = a0 + a1x + a2x2 + . . . . + a50x50, for all x \(\in\) R; then \({{{a_2}} \over {{a_0}}}\) is equal to

Let Sn = 1 + q + q2 + . . . . . + qn and Tn = 1 + \(\left( {{{q + 1} \over 2}} \right) + {\left( {{{q + 1} \over 2}} \right)^2}\) + . . . . . .+ \({\left( {{{q + 1} \over 2}} \right)^n}\) where q is a real number and q \(\ne\) 1. If...

Let z be a complex number such that |z| + z = 3 + i (where i = \(\sqrt { - 1}\)). Then |z| is equal to :

The integral  \(\int\limits_{\pi /6}^{\pi /4} {{{dx} \over {\sin 2x\left( {{{\tan }^5}x + {{\cot }^5}x} \right)}}}\)  equals :

The solution of the differential equation,
\({{dy} \over {dx}}\) = (x – y)2, when y(1) = 1, is :

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following poi...

The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3,
whenever k is a multiple of 4, is :

Let a function f : (0, \(\infty\)) \(\to\) (0, \(\infty\)) be defined by f(x) = \(\left| {1 - {1 \over x}} \right|\). Then f is :

A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the
eccentricity of the hyperbola is :

If   \(\int {{{x + 1} \over {\sqrt {2x - 1} }}} \,dx\) = f(x) \(\sqrt {2x - 1}\) + C, where C is a constant of integration, then f(x) is equal to :

All x satisfying the inequality (cot–1
x)2– 7(cot–1 x) + 10 > 0, lie in the interval :

\(\mathop {\lim }\limits_{x \to 0} {{x\cot \left( {4x} \right)} \over {{{\sin }^2}x{{\cot }^2}\left( {2x} \right)}}\) is equal to :

Let K be the set of all real values of x where the function f(x) = sin |x| – |x| + 2(x – \(\pi\)) cos |x| is not differentiable. Then the set K is equal to :

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

Let A and B be two invertible matrices of order 3 \(\times\) 3. If det(ABAT) = 8 and det(AB–1) = 8,
then det (BA–1 BT) is equal to :

If  \(\left| {\matrix{ {a - b - c} & {2a} & {2a} \cr {2b} & {b - c - a} & {2b} \cr {2c} & {2c} & {c - a - b} \cr } } \right|\)
      = (a + b + c) (x + a + b + c)2, x \(\ne\) 0,
then x is equal to :

If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x – a2) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left( {{{mean\,\,of\,X} \over {s\tan dard\,\,deviation\,\,of\,X}}} \right...

Let  S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

Given \({{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}\) for a \(\Delta\)ABC with usual notation.
If   \({{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },\) then the ordered triad ($$\alpha...

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation x2
sin \(\theta\) – x(sin \(\theta\) cos \(\theta\) + 1) + cos \(\theta\) = 0 (0 < \(\theta\) < 45o), and \(\alpha\) < \(\beta\). Then $$\sum\limits_{n = 0}^\inft...

Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \({{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}}\) is :

If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the
equation of the diagonal AD is :

Let \(\sqrt 3 \widehat i + \widehat j,\)    \(\widehat i + \sqrt 3 \widehat j\)  and   \(\beta \widehat i + \left( {1 - \beta } \right)\widehat j\) respectively be the position vectors of the points A, B and C with respect to the origin O. ...