1
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let f : R $$\to$$ R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(x) f(y) for all x, y$$\in$$ R.

Then, the value of loge(f(4)) is ...........
2
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respectively, where O(0, 0, 0) is the origin. Let $$S\left( {{1 \over 2},{1 \over 2},{1 \over 2}} \right)$$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If p = SP, q = SQ, r = SR and t = ST, then the value of |(p $$\times$$ q) $$\times$$ (r $$\times$$ t)| is ............
3
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
The number of distinct solutions of the equation

$${5 \over 4}{\cos ^2}\,2x + {\cos ^4}\,x + {\sin ^4}\,x + {\cos ^6}\,x + {\sin ^6}\,x\, = \,2$$

in the interval $$\left[ {0,\,2\pi } \right]$$ is
4
IIT-JEE 2011 Paper 1 Offline
Numerical
+4
-0
The positive integer value of $$n\, > \,3$$ satisfying the equation $${1 \over {\sin \left( {{\pi \over n}} \right)}} = {1 \over {\sin \left( {{{2\pi } \over n}} \right)}} + {1 \over {\sin \left( {{{3\pi } \over n}} \right)}}$$ is
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination