**Q1.If p/x+q/y=m and q/x+p/y=n then what is x/y is equal to?**

(a)(np+mq)/(mp+nq)

(b)(np+mq)/(mp-nq)

(c)(np – mq)/(mp – nq)

(d)(np–mq)/(mp–nq)

**Q2.If the equation x² – px + q = 0 and x² + qx – p = 0 have a common root, then which one of the following is correct?**

(a) p – q = 0

(b) p + q – 2 = 0

(c) p + q – 1 = 0

(d) p – q – 1 = 0

**Q3.If √(3x^2–7x–30)–√(2x^2–7x–5)=x –5 has α & β as its roots, then the value of αβ is **

(a)–15

(b) –5

(c) 0

(d) 5

**Q4. If x=2^(1/3)+2^(–1/3), then the value of 2x^3–6x–5 is equal to **

(a) 0

(b) 1

(c) 2

(d) 3

**Q5. Three equal circles each of diameter d are drawn on a plane in such a way that each circle touches the other two circles. A big circle is drawn in such a manner that it touches each of the small circles internally. The area of the big circle is**

(a) πd^2

(b) πd^2 (2 –√3)^2

(c) (πd^2 (√3+1)^2)/2

(d) (πd^2 (√3+2)^2)/12

**Q6. In the figure given above, O is the centre of the circle. The line UTV is a tangent to the circle at T, ∠VTR = 52° and ∆PTR is an isosceles triangle such that TP = TR. What is ∠x + ∠y+∠z equal to ?**

(a) 175°

(b) 208°

(c) 218°

(d) 250°

**Q7.A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 m from the bottom of tower. After 5 s, the angle of depression becomes 30°. What is the approximate speed of the boat assuming that it is running in still water? **

(a) 31.5 km/hr

(b) 36.5 km/hr

(c) 38.5 km/hr

(d) 40.5 km/hr

**Q8. In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs. 8 per square metre.(in Rs) **

(a) 1100

(b) 1183

(c) 1232

(d) 1352

**Q9. Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir?**

(a) 20

(b) 30

(c) 40

(d) 50

**Q10. A round balloon of unit radius subtends an angle of 90° at the eye of an observer. What is the distance of the centre of the balloon from the eye of the observer?**

(a) 1/√2

(b) √2

(c) 2

(d) 1/2