JEE Main 2018 (Online) 15th April Evening Slot

A plane bisects the line segment joining the points (1, 2, 3) and (\(-\) 3, 4, 5) at rigt angles. Then this plane also passes through the point :

An angle between the lines whose direction cosines are gien by the equations,
\(l\) + 3m + 5n = 0 and 5\(l\)m \(-\) 2mn + 6n\(l\) = 0, is :

The coefficien of x10 in the expansion of (1 + x)2(1 + x2)3(1 + x3)4 is equal to :

The tangent to the circle C1 : x2 + y2 \(-\) 2x \(-\) 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose center is (3, \(-\)2). The radius of C2 is :

If |z \(-\) 3 + 2i| \(\le\) 4 then the difference between the greatest value and the least value of |z| is :

If   \({I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;\)
   \({I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx\)  and
\({I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;\) then

The value of integral \(\int_{{\pi \over 4}}^{{{3\pi } \over 4}} {{x \over {1 + \sin x}}dx}\) is :

The curve satifying the differeial equation, (x2 \(-\) y2) dx + 2xydy = 0 and passing through the point (1, 1) is :

If    f(x) = sin-1 \(\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),\) then f'\(\left( { - {1 \over 2}} \right)\) equals :

Let f : A \(\to\) B be a function defined as f(x) = \({{x - 1} \over {x - 2}},\) Where A = R \(-\) {2} and B = R \(-\) {1}. Then   f   is :

A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. Fromthe top of T1, if the angle of depression of the foot of T2 is twice the angle of elevation of the top of T2, then the width (in m) o...

A normal to the hyperbola, 4x2 \(-\) 9y2 = 36 meets the co-ordinate axes \(x\) and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the ocus of P is :

If    \(\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C\)
(where C is a constant of integration), then the ordered pair (A, B) is equal to :

\(\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}\) equals :

Let f(x) be a polynomial of degree \(4\) having extreme values at \(x = 1\) and \(x = 2.\)
If   \(\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3\)   then f(\(-\)1) is equal to :

Let f(x) = \(\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {,x = 2} \cr } } \right.\)
Thevaue of k for which f s continuous at x = 2 is :

Consider the following two statements :
Statement p :
The value of sin 120o can be derived by taking \(\theta = {240^o}\) in the equation
2sin\({\theta \over 2} = \sqrt {1 + \sin \theta } - \sqrt {1 - \sin \theta }\)
Statement q :
Th...

Suppose A is any 3\(\times\) 3 non-singular matrix and ( A \(-\) 3I) (A \(-\) 5I) = O where I = I3 and O = O3. If \(\alpha\)A + \(\beta\)A-1 = 4I, then \(\alpha\) + \(\beta\) is equal to :

If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :

Tangents drawn from the point (\(-\)8, 0) to the parabola y2 = 8x touch the parabola at \(P\) and \(Q.\) If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :

The number of four letter words that can be formed using the letters of the word BARRACK is :

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, ...

If f(x) is a quadratic expression such that f (1) + f (2) = 0, and \(-\) 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :

If  a,   b,   c  are in A.P. and  a2,  b2,  c2 are in G.P. such that
a < b < c and   a + b + c = \({3 \over 4},\) then the value of a is :

Let    An = \(\left( {{3 \over 4}} \right) - {\left( {{3 \over 4}} \right)^2} + {\left( {{3 \over 4}} \right)^3}\) \(-\). . . . . + (\(-\)1)n-1 \({\left( {{3 \over 4}} \right)^n}\)    and    Bn = 1 \(-\) An.
Then, the least dd natural numb...

If the mean of the data : 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of this data is :

The foot of the perpendicular drawn from the origin, on the line, 3x + y = \(\lambda\) (\(\lambda\) \(\ne\) 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :

The sides of a rhombus ABCD are parallel to the lines, x \(-\) y + 2 = 0 and 7x \(-\) y + 3 = 0. If the diagonals of the rhombus intersect P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the coordinate of A is :

The number of solutions of sin3x = cos 2x, in the interval \(\left( {{\pi \over 2},\pi } \right)\) is :

If the position vectors of the vertices A, B and C of a \(\Delta\) ABC are respectively \(4\widehat i + 7\widehat j + 8\widehat k,\)    \(2\widehat i + 3\widehat j + 4\widehat k,\) and \(2\widehat i + 5\widehat j + 7\widehat k,\) then the ...