**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 𝜋 = 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 108𝜋cm^2. The volume of the hemisphere is **

(a) 72𝜋 cm^3

(b) 144𝜋 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

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