Sequences and Series (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

A bag contains 50 tickets, numbered from 1 to 50 . One ticket is drawn at random. What is the probability that: number on the ticket is a perfect square or divisible by 4 ?

Find the derivatives of the following w.r.t. x. : \begin{equation}
\frac{x^2+a^2}{x^2-a^2}
\end{equation}

Two dice are thrown simultaneously 25 times. The following pairs of observations are obtained.
(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) (3, 4) (2, 5) (3, 4) (2, 5) (4, 3) (5, 2) (4, 5) (4, 3) (2, 3) (4, 1)
Prepare a bivariate frequency distribution table for the above data. Also, obtain the marginal distributions.

The city traffic police issued challans for not observing the traffic rules:

Day of the week	Mon	Tue	Wed	Thus	Fri	Sat
No. of challans	40	24	36	58	62	80

Find Q.D.

If p, q, r, s are in G. P., show that p + q, q + r, r + s are also in G.P.

Find the derivatives of the following w.r.t. x. : \begin{equation}
\frac{3 x^2+5}{2 x^2-4}
\end{equation}