**1**

In a circular field, AOB and COD are two mutually perpendicular diameters having length of 4 meters. X is the mid-point of OA. Y is the point on the circumference such that ∠YOD = 30°. Which of the following correctly gives the relation among the three alternate paths from X to Y?

**2**

If x and y are real numbers, then the minimum value of x^{2} + 4xy + 6y^{2} – 4y + 4 is

**3**

Let X be a four-digit positive integer such that the unit digit of X is prime and the product of all digits of X is also prime. How many such integers are possible?

**4**

There are two types of employees in Sun Metals, general graduates and engineers. 40% of the employees in Sun Metals are general graduates, and 75% of the engineers earn more than Rs. 5 lakh/year. )f 5??% of the organisation??s employees earn more than Rs. 5 lakh/year, what proportion of the general graduates employed by the organisation earn Rs. 5 lakh or less?

**5**

In an equilateral triangle ABC, whose length of each side is 3 cm, D is the point on BC such that BD = 1/2 CD. What is the length of AD?