JEE Main 2018 (Online) 16th April Morning Slot

The sum of the intercepts on the coordinate axes of the plane passing through the point (\(-\)2, \(-2,\) 2) and containing the line joining the points (1, \(-\)1, 2) and (1, 1, 1) is :

If the angle between the lines, \({x \over 2} = {y \over 2} = {z \over 1}\)
and \({{5 - x} \over { - 2}} = {{7y - 14} \over p} = {{z - 3} \over 4}\,\,\) is \({\cos ^{ - 1}}\left( {{2 \over 3}} \right),\) then p is equal to :

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 \(-\) 9x2 + 12x + 5 in the interval [0, 3]. Then M \(-\)m is equal to :

If the area of the region bounded by the curves, \(y = {x^2},y = {1 \over x}\) and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :

The coefficient of x2 in the expansion of the product
(2\(-\)x2) .((1 + 2x + 3x2)6 + (1 \(-\) 4x2)6) is :

If a circle C, whose radius is 3, touches externally the circle,
\({x^2} + {y^2} + 2x - 4y - 4 = 0\) at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

The least positive integer n for which \({\left( {{{1 + i\sqrt 3 } \over {1 - i\sqrt 3 }}} \right)^n} = 1,\) is :

If \(f(x) = \int\limits_0^x {t\left( {\sin x - \sin t} \right)dt\,\,\,}\) then :

The differential equation representing the family of ellipse having foci eith on the x-axis or on the \(y\)-axis, center at the origin and passing through the point (0, 3) is :

If \(x = \sqrt {{2^{\cos e{c^{ - 1}}}}}\) and \(y = \sqrt {{2^{se{c^{ - 1}}t}}} \,\,\left( {\left| t \right| \ge 1} \right),\) then \({{dy} \over {dx}}\) is equal to :

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is \({3 \over 2}\) units, then its eccentricity is :

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from 30o to 45o ; then after this, the time taken (in...

The locus of the point of intersection of the lines, \(\sqrt 2 x - y + 4\sqrt 2 k = 0\) and \(\sqrt 2 k\,x + k\,y - 4\sqrt 2 = 0\) (k is any non-zero real parameter), is :

If \(\int {{{\tan x} \over {1 + \tan x + {{\tan }^2}x}}dx = x - {K \over {\sqrt A }}{{\tan }^{ - 1}}}\) \(\left( {{{K\,\tan x + 1} \over {\sqrt A }}} \right) + C,(C\,\,\) is a constant of integration) then the ordered pair (K, A) is equal ...

If the function f defined as
\(f\left( x \right) = {1 \over x} - {{k - 1} \over {{e^{2x}} - 1}},x \ne 0,\) is continuous at
x = 0, then the ordered pair (k, f(0)) is equal to :

\(\mathop {\lim }\limits_{x \to 0} \,\,{{{{\left( {27 + x} \right)}^{{1 \over 3}}} - 3} \over {9 - {{\left( {27 + x} \right)}^{{2 \over 3}}}}}\) equals.

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

Let A = \(\left[ {\matrix{ 1 & 0 & 0 \cr 1 & 1 & 0 \cr 1 & 1 & 1 \cr } } \right]\) and B = A20. Then the sum of the elements of the first column of B is :

The number of values of k for which the system of linear equations,
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :

Let P be a point on the parabola, x2 = 4y. If the distance of P from the center of the circle, x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to ...

Let A, B and C be three events, which are pair-wise independent and \(\overrightarrow E\) denotes the completement of an event E. If \(P\left( {A \cap B \cap C} \right) = 0\) and \(P\left( C \right) > 0,\) then $$P\left[ {\left( {\overline...

If an angle A of a \(\Delta\)ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x2 + 27x + 20 = 0 are :

Let p, q and r be real numbers (p \(\ne\) q, r \(\ne\) 0), such that the roots of the equation \({1 \over {x + p}} + {1 \over {x + q}} = {1 \over r}\) are equal in magnitude but opposite in sign, then the sum of squares of these roots...

Let \({1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,\) (xi \(\ne\) 0 for i = 1, 2, ..., n) be in A.P. such that x1=4 and x21 = 20. If n is the least positive integer for which \({x_n} > 50,\) then $$\sum\limits_{i = 1}^n {\...

The sum of the first 20 terms of the series
\(1 + {3 \over 2} + {7 \over 4} + {{15} \over 8} + {{31} \over {16}} + ...,\) is :

Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) \(\in\) N \(\times\) N : 2x + y = 10} and R2 = {(x, y) \(\in\) N \(\times\) N : x + 2y = 10}. Then :

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow c = \widehat j - \widehat k\) and a vector \(\overrightarrow b\) be such that \(\overrightarrow a \times \overrightarrow b = \overrightarrow c\) and $$\ove...