JEE Main 2016 (Online) 9th April Morning Slot

The distance of the point (1, − 2, 4) from the plane passing through the point
(1, 2, 2) and perpendicular to the planes x − y + 2z = 3 and 2x − 2y + z + 12 = 0, is :

The shortest distance between the lines \({x \over 2} = {y \over 2} = {z \over 1}\) and
\({{x + 2} \over { - 1}} = {{y - 4} \over 8} = {{z - 5} \over 4}\) lies in the interval :

The minimum distance of a point on the curve y = x2−4 from the origin is :

If the tangent at a point P, with parameter t, on the curve x = 4t2 + 3, y = 8t3−1, t \(\in\) R, meets the curve again at a point Q, then the coordinates of Q are :

The area (in sq. units) of the region described by
A= {(x, y) \(\left| {} \right.\)y\(\ge\) x2 \(-\) 5x + 4, x + y \(\ge\) 1, y \(\le\) 0} is :

For x \(\in\) R, x \(\ne\) -1,
if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 =
\(\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,\) then a17 is equal to :

A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?

The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there \(2\sqrt 2\) units in the south-westwardsdirection. Then its new position in the Argand plane is at the point represe...

If   \(2\int\limits_0^1 {{{\tan }^{ - 1}}xdx = \int\limits_0^1 {{{\cot }^{ - 1}}} } \left( {1 - x + {x^2}} \right)dx,\)
then \(\int\limits_0^1 {{{\tan }^{ - 1}}} \left( {1 - x + {x^2}} \right)dx\) is equalto :

If   f(x) is a differentiable function in the interval (0, \(\infty\)) such that f (1) = 1 and
\(\mathop {\lim }\limits_{t \to x}\)   \({{{t^2}f\left( x \right) - {x^2}f\left( t \right)} \over {t - x}} = 1,\) for each x > 0, then $$f\l...

If the tangent at a point on the ellipse \({{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1\) meets the coordinate axes at A and B, and O is the origin, then the
minimum area (in sq. units) of the triangle OAB is :

For x \(\in\) R, x \(\ne\) 0, Let f0(x) = \({1 \over {1 - x}}\) and
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .
Then the value of f100(3) + f1\(\left( {{2 \over 3}} \right)\) + f2\(\left( {{3 \over 2}} \right)\) is equal to :

Let a and b respectively be the semitransverse and semi-conjugate axes of a
hyperbola whose eccentricity satisfies the equation 9e2 − 18e + 5 = 0. If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 − ...

If   \(\int {{{dx} \over {{{\cos }^3}x\sqrt {2\sin 2x} }}} = {\left( {\tan x} \right)^A} + C{\left( {\tan x} \right)^B} + k,\)
where k is a constant of integration, then A + B +C equals :

If the function
f(x) = \(\left\{ {\matrix{ { - x} & {x < 1} \cr {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \cr } } \right.\)
is differentiable at x = 1, then \({a \over b}\) is equal to :

If    \(\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3},\) then 'a' is equal to :

Consider the following two statements :
P :     If 7 is an odd number, then 7 is
divisible by 2.
Q :    If 7 is a prime number, then 7 is an
odd number
If  V1 is the truth value of the contrapositive of P and V2 is the truth value of contr...

The number of distinct real roots of the equation,
\(\left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0\) in the interval $$\left[ { -...

If P = \(\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\,\)
Q = PAPT, then PT Q2015 P ...

The value of \(\sum\limits_{r = 1}^{15} {{r^2}} \left( {{{{}^{15}{C_r}} \over {{}^{15}{C_{r - 1}}}}} \right)\) is equal to :

If the four letter words (need not be meaningful ) are to be formed using the
letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :

If A and B are any two events such that P(A) = \({2 \over 5}\) and P (A \(\cap\) B) = \({3 \over {20}}\), hen the conditional probability, P(A \(\left| {} \right.\)(A' \(\cup\) B')), where A' denotes the complement of A, is equal to :

If the equations x2 + bx−1 = 0 and x2 + x + b = 0 have a common root different from −1, then \(\left| b \right|\) is equal to :

Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Then x3 + y3 + z3is equal to :

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

If a variable line drawn through the intersection of the lines \({x \over 3} + {y \over 4} = 1\) and \({x \over 4} + {y \over 3} = 1,\) meets the coordinate axes at A and B, (A \(\ne\) B), then the locus of the midpoint of AB is :

The point (2, 1) is translated parallel to the line L : x− y = 4 by \(2\sqrt 3\) units. If the newpoint Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :

The number of x \(\in\) [0,   2\(\pi\) ] for which
\(\left| {\sqrt {2{{\sin }^4}x + 18{{\cos }^2}x} - \sqrt {2{{\cos }^4}x + 18{{\sin }^2}x} } \right| = 1\) is :

If  m and M are the minimum and the maximum values of
4 + \({1 \over 2}\) sin2 2x \(-\) 2cos4 x, x \(\in\) R, then M \(-\) m is equal to :

In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively 3\(\widehat i\) + \(\widehat j\) \(-\) \(\widehat k\),   \(-\)\(\widehat i\) + 3\(\widehat j\) + p\(\widehat k\) and 5\(\widehat i\) + q...