Question

Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).

How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.

If P(E) = 6/11, P(F) = 5/11 and P(E ∪ F) = 7/11 then find (i) P(E/F) (ii) P(F/E)

Find the sum of the order and the degree of the following differential equations : ${\frac{d^{2}y}{d x^{2}}}+{3{\sqrt\frac{{d y}}{d x}}}+(1+x)=0$

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.

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

Find : $\textstyle\int$${\frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}}}\,.$