List of top Mathematics Questions asked in NIMCET

In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is
If the volume of the parallelepiped whose adjacent edges are \( \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \), \( \vec{b} = \hat{i} + \alpha\hat{j} + 2\hat{k} \), \( \vec{c} = \hat{i} + 2\hat{j} + \alpha\hat{k} \) is 15, then \( \alpha \) is equal to
If \( 0 < P(A) < 1 \) and \( 0 < P(B) < 1 \), and \( P(A \cap B) = P(A)P(B) \), then
There are two circles in xy-plane whose equations are \( x^2 + y^2 - 2y = 0 \) and \( x^2 + y^2 - 2y - 3 = 0 \). A point (x, y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is