CBSE[Outside Delhi]_X_Mathematics_2018_Set_III

What is the value of (cos²67°–sin²23°)?

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

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

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

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

Two different dice are tossed 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 Fig. 1, ABCD is a rectangle. Find the value of x and y.