WB JEE 2011
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Determine the sum of imaginary roots of the equation \((2{x^2} + x - 1)(4{x^2} + 2x - 3) = 6\)
If the area of a rectangle is 64 square units, find the minimum value possible for its perimeter.
If \({r^2} = {x^2} + {y^2} + {z^2}\), then prove that \({\tan ^{ - 1}}\left( {{{yz} \over {rx}}} \right) + {\tan ^{ - 1}}\left( {{{zx} \over {ry}}} \right) + {\tan ^{ - 1}}\left( {{{xy} \over {rz}}} \right) = {\pi \over 2}\)
Find the image of the point (\(-\)8, 12) with respect to the line 4x + 7y + 13 = 0.
The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G2 = 27. Find the numbers.
Let R be the set of real numbers and f : R \(\to\) R be such that for all x, y \(\in\) R, \(|f(x) - f(y)| \le |x - y{|^3}\). Prove that f is a constant function.