Q1. Suppose the angle of elevation of the top of a tree at a point E due East of the tree is 60° and that at a point F due West of the tree is 30°. If the distance between the points E and F is 160 ft, then what is the height of the tree?
(a) 40√3 ft
(b) 60 ft
(c) 40/√3 ft
(d) 23 ft
Q2. From a tower 125 metres high the angle of depression of two objects, which are in horizontal line through the base of the tower are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the objects is
(a) 125√3 m
(b) 125(√3-1) m
(c) 125 / (√3-1) m
(d) 125 (√3+1) m
Q3. A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
(a) 91.64 metres
(b) 90.46 metres
(c) 89.64 metres
(d) 93.64 metres
Q4. A wheel revolves 24 times in 10 seconds. How many time does it take in revolving an angle of 110 rad?
(a) 5 sec
(b) 7.3 sec
(c) 10 sec
(d) None of these
Q5. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is
(a) 1520 m^2
(b) 2420 m^2
(c) 2480 m^2
(d) 2520 m^2
Q6. If the area of a triangle with base 12 cm is equal to the area of square with side 12 cm. the altitude of the triangle will be
(a) 12 cm
(b) 24 cm
(c) 18 cm
(d) 36 cm
Q7. A 7m wide road runs outside around a circular park, whose circumference is 176m. the area of the road is : (use ? = 22/7)
(a) 1386 m^2
(b) 1472 m^2
(c) 1512 m^2
(d) 1760 m^2
Q8. The perimeter of a triangle is 40 cm and its area is 60 cm^2. If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is
(a) 4
(b) 6
(c) 8
(d) 15
Q9. The height of an equilateral triangle is 15 cm. the area of the triangle is
(a) 50√3 sq. cm
(b) 70√3 sq. cm
(c) 75√3 sq. cm
(d) 150√3 sq. cm
Q10. A rectangular sheet of metal is 40 cm by 15 cm. equal squares of side 4 cm are cut off at the corners and the reminder is folded up to form an open rectangular box The volume of the box is
(a) 896 cm^3
(b) 986 cm^3
(c) 600 cm^3
(d) 916 cm^3
Q11. A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made?
(a) 25
(b) 75
(c) 50
(d) 125
Q12. The total surface area of a solid hemisphere is 108?cm^2. The volume of the hemisphere is
(a) 72? cm^3
(b) 144? cm^3
(c) 108√6 cm^3
(d) 54√6 cm^3
Q13. A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:
(a) 25%
(b) 30%
(c) 50%
(d) 75%
Q14. A sphere is cut into two hemispheres. One of them is used as a bowl. It takes 8 bowlfuls to fill a conical vessel of height 12 cm and radius 6 cm. The radius of the sphere (in centimeter) will be
(a) 3
(b) 2
(c) 4
(d) 6
Q15. If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to
(a) 1/4th of the hemisphere
(b) radius of the hemisphere
(c) 1/2 of the radius of the hemisphere
(d) 1/6th of the radius of the hemisphere
