Question

Show that the function f given by f(x) = tan⁻¹ (sin x+ cos x) is decreasing for all $x\in\left({\frac{\pi}{4}},{\frac{\pi}{2}}\right).$

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then find P(A/B).

Find : $\textstyle\int{\frac{d x}{x^{2}+4x+8}}$

Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.

Three cards are drawn without replacement from a pack of 52 cards. Find the probability that (i) the cards drawn are king, queen and jack respectively. (ii) the cards drawn are king, queen and jack.