IIT-JEE 1986

A vector \(\overline a\) has components \(2p\) and \(1\) with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, $$...

The expression \(2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \right)} \right]\) is equal to

Let \(\overrightarrow a = {a_1}i + {a_2}j + {a_3}k,\,\,\,\overrightarrow b = {b_1}i + {b_2}j + {b_3}k\) and \(\overrightarrow c = {c_1}i + {c_2}j + {c_3}k\) be three non-zero vectors such that \(\overrightarrow c\) is a unit vector perp...

The position vectors of the points \(A, B, C\) and \(D\) are \(3\widehat i - 2\widehat j - \widehat k,\,2\widehat i + 3\widehat j - 4\widehat k,\, - \widehat i + \widehat j + 2\widehat k\) and $$4\widehat i + 5\widehat j + \lambda \widehat ...

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit \(- \phi\) and \(+ \phi\). For an angular displacement \(\theta\) \(\left( {\left| \theta \right| < \phi } \right)\),...

A reference frame attached to the earth

The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)