Q1.If p/x+q/y=m and q/x+p/y=n then what is x/y is equal to?
(c)(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
Q4. If x=2^(1/3)+2^(–1/3), then the value of 2x^3–6x–5 is equal to
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
(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 ?
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)
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?
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?