Q14 of 52 Page 1

How many three-digit numbers are divisible by 11?

To find: 110 + 121 + 132 + ….... + 990

Given,

a = 110

d = 121 – 110 = 11

a_n = 990

a+(n – 1)d = 990

Therefore,

110 + (n -1) ×11 = 990

(n -1)×11 = 990 – 110 = 880

(n – 1)881/11 = 80

n- 1 = 80

n = 80+1 = 81

As,

S_n = n/2(a₁+a_n)

= 81/2(110+990)

= 81/2(1100) = 81×550 = 44550

If the centroid of ΔABC, in which A(a, b), B(b, c), C(c, a) is at the origin, then calculate the value of (a³ + b³ + c³).

Find the value of k for which the roots of the equation kx(3x – 4) + 4 = 0, are equal.

A box contains 70 cards numbered from 1 to 70. If one card is drawn at random from the box, find the probability that it bears

(i) a perfect square number

(ii) a number divisible by 2 and 3

Find the value of k, for which the points A(6, –1), B(k, –6) and C(0, –7) are collinear.