JEE Main 2018 (Online) 15th April Morning Slot

An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z \(-\) 1 = 0 and 5x + 8y + 2z + 14 =0, is :

A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz -plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn par...

If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :

If \(\beta\) is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos \(\theta\), \(\sqrt 3 \sin \theta\)) and (\(-\) 3 sin \(\theta\), \(\sqrt 3 \,\cos \theta\)); $$\theta \in \left( {0,{\pi \over ...

The area (in sq. units) of the region
{x \(\in\) R : x \(\ge\) 0, y \(\ge\) 0, y \(\ge\) x \(-\) 2  and y \(\le\) \(\sqrt x\)}, is :

If n is the degree of the polynomial,
\({\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} +\) \({\left[ {{2 \over {\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}\)
and m is the coefficient of xn in it, ...

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, \(y - 4x + 3 = 0,\) then its radius is equal to :

The set of all \(\alpha\) \(\in\) R, for which w = \({{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}\) is purely imaginary number, for all z \(\in\) C satisfying |z| = 1 and Re z \(\ne\) 1, is :

The value of the integral
\(\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {{{\sin }^4}} x\left( {1 + \log \left( {{{2 + \sin x} \over {2 - \sin x}}} \right)} \right)dx\) is :

Let y = y(x) be the solution of the differential equation \({{dy} \over {dx}} + 2y = f\left( x \right),\) where \(f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.\)...

If   x2 + y2 + sin y = 4, then the value of \({{{d^2}y} \over {d{x^2}}}\) at the point (\(-\)2,0) is :

If \(f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,\) then \(\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}\)

An aeroplane flying at a constant speed, parallel to the horizontal ground, \(\sqrt 3\) kmabove it, is obsered at an elevation of \({60^o}\) from a point on the ground. If, after five seconds, its elevation from the same point, is $${30^o...

If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :

If \(f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,\) (x \(\in\) R \(-\){1, \(-\) 2}), then \(\int f \left( x \right)dx\) is equal to :
(where C is a constant of integration)

Let S = {(\(\lambda\), \(\mu\)) \(\in\) R \(\times\) R : f(t) = (|\(\lambda\)| e|t| \(-\) \(\mu\)). sin (2|t|), t \(\in\) R, is a differentiable function}. Then S is a subset of :

If (p \(\wedge\) \(\sim\) q) \(\wedge\) (p \(\wedge\) r) \(\to\) \(\sim\) p \(\vee\) q is false, then the truth values of \(p, q\) and \(r\) are, respectively :

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y \(-\) z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

Let \(A\) be a matrix such that \(A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]\) is a scalar matrix and |3A| = 108.
Then A2 equals :

Two parabolas with a common vertex and with axes along x-axis and \(y\)-axis, respectively intersect each other in the first quadrant. If the length of the latus rectum of each parabola is \(3\), then the equation of the common tangent to t...

n\(-\)digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

A box 'A' contains \(2\) white, \(3\) red and \(2\) black balls. Another box 'B' contains \(4\) white, \(2\) red and \(3\) black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns ou...

If tanA and tanB are the roots of the quadratic equation, 3x2 \(-\) 10x \(-\) 25 = 0, then the value of 3 sin2(A + B) \(-\) 10 sin(A + B).cos(A + B) \(-\) 25 cos2(A + B) is :

If \(\lambda\) \(\in\) R is such that the sum of the cubes of the roots of the equation,
x2 + (2 \(-\) \(\lambda\)) x + (10 \(-\) \(\lambda\)) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

If x1, x2, . . ., xn and \({1 \over {{h_1}}}\), \({1 \over {{h_2}}}\), . . . , \({1 \over {{h_n}}}\) are two A.P..s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals :

Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number \(\lambda\) and then each of them is decreased by 25, their mean remains the same. Then \(\lambda\) is equal to :

In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of \(\Delta\) ABC (in sq. units) is :

If \(\overrightarrow a ,\,\,\overrightarrow b ,\) and \(\overrightarrow C\) are unit vectors such that \(\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,\) then $$\left| {\overrightarrow a \times \over...