Mathematics Tes...

If \(\int \sqrt{1+\sin x} f(x) d x=\frac{2}{3}(1+\sin x)^{3 / 2}+c\) then \(f(x)\) is equal to

The number of common tangents that can be drawn to the circles x² + y² - 4x - 6y - 3 = 0 and x² + y² + 2x + 2y + 1 = 0 is :

The equations of the tangents of the parabola y² = 12x, which passes through the point (2,5).

The equations \(x^{2}+x+a=0\) and \(x^{2}+a x+1=0\) have a common real root

Suppose \(f(x)=\tan \left(\sin ^{-1}(2 x)\right)\) then \(f^{\prime}(1 / 4)\) is equal to

There are 4 white and 3 black balls in a box. In another box there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3 then a ball is drawn from the first box but if it shows a number more than 3 then a ball is drawn from the second box. If the ball drawn is black then the probability that the ball was drawn from the first box is

If one of the diagonal of a square is along the line x = 2y and one of its vertices is (3, 0), then its sides through this vertex are given by, the equations-