What is the value of (Cos²67^o - sin² 23^o)?

In an AP, if the common difference (d) = –4, and the seventh term (a₇) is 4, then find the first term.

Given $∆ABC ~ ∆PQR, if \frac{AB}{PQ} = \frac{1}{3}, then find \frac{ar∆ABC}{ar∆PQR}$

What is the HCF of the smallest prime number and the smallest composite number?

Find the distance of a point P(x, y) from the origin.

6.

If x = 3 is one root of the quadratic equation x²-2kx -6 =0, the find the value of k.

Two different dice are tossed together. Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10, of the numbers on the two dice.

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

An integer is chosen at random between 1 and 100. Find the probability that it is :

(i) divisible by 8

(ii) not divisible by 8

In figure, ABCD is a rectangle. Find the values of x and y.