JEE Main 2016

A value of  for which 2 3i sin 1 2i sin       is purely imaginary, is:

The sum of all real values of x satisfying the equation 2x2 4xx 5 5() x   = 1 is:

The system of linear equations x + y  z = 0 x  y  z = 0 x + y  z = 0 has a non-trivial solution for:

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged…

If the number of terms in the expansion of n 2 241 x x  , x  0, is 28, then the sum of the coefficients of all…

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

If the sum of the first ten terms of the series 2 2 23 2 11 2 35 5 5                 + 42 + 244 5 …

Let p =   1 2 2x x0 lim 1 tan x    then long p is equal to:

For x  R, f(x) = |log 2  sin x| and g(x) = f(f(x)), then:

Consider f(x) = tan1 1 sin x 1 sin x    , x  0, 2   . A normal to y = f(x) at x = 6  also passes t…

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a cir…

The integral 12 9 5 3 3 2x 5x (x x 1)   dx is equal to:

1/n 2nn (n 1) (n 2) ...3nlim n     is equal to:

The area (in sq. units) of the region {(x, y) : y2  2x and x2 + y2  4x, x  0, y  0} is:

If a curve y = f(x) passes through the point (1, 1) and satisfies the differential equation, y(1 + xy) dx = x dy, then…

Two sides of a rhombus are along the lines, x  y + 1 = 0 and 7x  y  5 = 0. If its diagonals intersect at (1, 2), t…

The centres of those circles which touch the circle, x 2 + y2  8x  8y  4 = 0, externally and also touch the x-axis,…

If one of the diameters of the circle, given by the equation, x 2 + y2  4x + 6y  12 = 0, is a chord of a circle S, wh…

Let P be the point on the parabola, y 2 = 8x which is at a minimum distance from the centre C of the circle, x 2 + (y +…

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis i…