JEE Main 2017 (Online) 9th April Morning Slot

If x = a, y = b, z = c is a solution of the system of linear equations
x + 8y + 7z = 0
9x + 2y + 3z = 0
x + y + z = 0
such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate
axes at A, B and C, then the locus of the centroid of \(\Delta\)ABC is :

If the line, \({{x - 3} \over 1} = {{y + 2} \over { - 1}} = {{z + \lambda } \over { - 2}}\) lies in the plane, 2x−4y+3z=2, then the shortest distance between this line and the line, \({{x - 1} \over {12}} = {y \over 9} = {z \over 4}\) is ...

A tangent to the curve, y = f(x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point :

The function f defined by
f(x) = x3 \(-\) 3x2 + 5x + 7 , is :

The coefficient of x−5 in the binomial expansion of
\({\left( {{{x + 1} \over {{x^{{2 \over 3}}} - {x^{{1 \over 3}}} + 1}} - {{x - 1} \over {x - {x^{{1 \over 2}}}}}} \right)^{10}},\) where x \(\ne\) 0, 1, is :

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60o. If the area of the quadrilateral is \(4\sqrt 3\), then the perimeter
of the quadrilateral is :

A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA⋅PB is equal to :

The equation
Im \(\left( {{{iz - 2} \over {z - i}}} \right)\) + 1 = 0, z \(\in\) C, z \(\ne\) i
represents a part of a circle having radius
equal to :

If    \(\int\limits_1^2 {{{dx} \over {{{\left( {{x^2} - 2x + 4} \right)}^{{3 \over 2}}}}}} = {k \over {k + 5}},\) then k is equal to :

If    \(\mathop {\lim }\limits_{n \to \infty } \,\,{{{1^a} + {2^a} + ...... + {n^a}} \over {{{(n + 1)}^{a - 1}}\left[ {\left( {na + 1} \right) + \left( {na + 2} \right) + ..... + \left( {na + n} \right)} \right]}} = {1 \over {60}}\)
for som...

If 2x = y\({^{{1 \over 5}}}\) + y\({^{ - {1 \over 5}}}\) and
(x2 \(-\) 1) \({{{d^2}y} \over {d{x^2}}}\) + \(\lambda\)x \({{dy} \over {dx}}\) + ky = 0,
then \(\lambda\) + k is equal to :

Let f be a polynomial function such that
f (3x) = f ' (x) . f '' (x), for all x \(\in\) R. Then :

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate
axes and passing through the points (4, −1) and (−2, 2) is :

The function f : N \(\to\) N defined by f (x) = x \(-\) 5 \(\left[ {{x \over 5}} \right],\) Where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :

If \(\,\,\,\) f\(\left( {{{3x - 4} \over {3x + 4}}} \right)\) = x + 2, x \(\ne\) \(-\) \({4 \over 3}\), and
\(\int {}\)f(x) dx = A log\(\left| {} \right.\)1 \(-\) x \(\left| {} \right.\) + Bx + C,
then the ordered pair (A, B) is eq...

A value of x satisfying the equation sin[cot−1 (1+ x)] = cos [tan−1 x], is :

The value of k for which the function
$$f\left( x \right) = \left\{ {\matrix{
{{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr
{k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} ...

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

For two 3 × 3 matrices A and B, let A + B = 2BT and 3A + 2B = I3, where BT is
the transpose of B and I3 is 3 × 3 identity matrix. Then :

If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then \(\left| c \right|\) is equal to :

The number of ways in which 5 boys and 3 girls can be seated on a round table if a
particular boy B1 and a particular girl G1 never sit adjacent to each other, is :

Let E and F be two independent events. The probability that both E and F happen is \({1 \over {12}}\) and the probability that neither E nor F happens is \({1 \over {2}}\), then a value of \({{P\left( E \right)} \over {P\left( F \right)}}\)...

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

The sum of all the real values of x satisfying the equation
2(x\(-\)1)(x2 + 5x \(-\) 50) = 1 is :

If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :

Let
Sn = \({1 \over {{1^3}}}\)\(+ {{1 + 2} \over {{1^3} + {2^3}}} + {{1 + 2 + 3} \over {{1^3} + {2^3} + {3^3}}} + ......... + {{1 + 2 + ....... + n} \over {{1^3} + {2^3} + ...... + {n^3}}}.\)
If 100 Sn = n, then n is equal to :

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If
the incorrect observations are omitted, then the variance of the remaining obs...

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If
one of the sides passing through the origin makes an angle 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices...

If the vector \(\overrightarrow b = 3\widehat j + 4\widehat k\) is written as the
sum of a vector \(\overrightarrow {{b_1}} ,\) paralel to \(\overrightarrow a = \widehat i + \widehat j\) and a vector \(\overrightarrow {{b_2}} ,\) perpe...