(a) 2^7

(b) 0

(c) 1

(d) 2

**Q2.A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, the ratio of radius and height is **

(a) 1∶2

(b) 1∶3

(c) 2 : 3

(d) 3 : 4

**Q3.A sector is formed by opening out a cone of base radius 8 cm and height 6 cm. Then the radius of the sector is (in cm) **

(a) 4

(b) 8

(c) 10

(d) 6

**ANS(c);**

Radius of sector = Slant height of cone

=√(h^2+r^2 )=√(6^2+8^2 )=√(36+64)

=√100=10 cm

** Q4.The perimeter of a rectangle having area equal to 144 cm^2 and sides in the ratio 4 : 9 is **

(a) 52 cm

(b) 56 cm

(c) 60 cm

(d) 64 cm

**ANS(a); **

Area of rectangle =l×b

144=4x×9x

x=2

So, Perimeter of rectangle =2(l+b) =2(9x+4x)

=2×13×2 =52 cm

** Q5. A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. Find the area of the field. **

(a) 45 sq m

(b) 35 sq m

(c) 60 sq m

(d) 30 sq m

**ANS(c);**

Distance travelled by A in 15 sec. =(52×15)/60=13 m

Diagonal of field = 13 m

l^2+b^2=169 …………….(i)

Distance travelled by B in 15 sec. =(68×15)/60=17 m

l+b=17 m …………..(ii)

from (i) & (ii) —

Area = lb=((l+b)^2-(l^2+b^2 ))/2

lb=60 sq. m.

**Q6.The breadth of a rectangle is 25 m. The total cost of putting a grass bed on this field was Rs. 12375, at the rate of Rs. 15 per sq m. What is the length of the rectangular field? **

(a) 27 m

(b) 30 m

(c) 33 m

(d) 32 m

**ANS(c);**

Area of rectangular field =12375/15

= 825 sq. m

A.T.Q. —

(L×B)=825

L×25=825

L=33 m

**Q7. A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is**

(a) 2.5√3 cm

(b) 5√3 cm

(c) 10√3 cm

(d) None of these

**ANS(d); **

Circumradius =2/3×height

Height =(10×3)/2=15 cm

So, length of perpendicular drawn from center =15-10=5 cm

**Q8.What is the total area of three equilateral triangles inscribed in a semi-circle of radius 2cm? **

(a) 12 cm^2

(b) (3√3)/4 cm^2

(c) (9√3)/4 cm^2

(d) 3√3 cm^2

** Q9. What is the area of the larger segment of circle formed by a chord of, length 5 cm subtending an angle of 90° at the centre? **

(a) 25/4 (π/2+1)cm^2

(b) 25/4 (π/2-1)cm^2

(c) 25/4 (3π/2+1)cm^2

(d) 25/4 (3π/2-1)cm^2

**Q10. Find the length of a rope by which a cow must be tethered in order that may be able to graze an area of 154 sq m. **

(a) 7 m

(b) 8 m

(c) 12 m

(d) 13 m

**ANS(a);**

Length of rope = Radius of circle

A.T.Q.—

πr^2=154

r=7 m