Data Interpretation and Quantitative Ability

**1**

In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other? (1 mark)

**2**

If x = (9 + √ )48 = [x] + f, where [x] is defined as integral part of x and f is a faction, then x(1 – f) equals- (5 marks)

**3**

Let an = 1 1 1 1 1 1 1….. 1, where 1 occurs n number of times. Then,

i. a741 is not a prime.

ii. a534 is not a prime.

iii. a123 is not a prime.

iv. a77 is not a prime. (5 marks)

**4**

A straight line through point P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. lf S is not the centre of the circumcircle, then which of the following is true? (3 marks)

**5**

What is the maximum possible value of (21 Sin X + 72 Cos X)? (3 marks)