**Q1. Three cubes each of edge 3 cm long are placed together as shown in the adjoining Figure. Find the surface area of the cuboid so formed:**

(a) 182 sq. cm

(b) 162 sq. cm

(c) 126 sq. cm

(d) None of these

**Q2. Two solid right cones of equal heights are of radii r1 and r2 are melted and made to form a solid sphere of radius R. Then the height of the cone is:**

(a) (4R^2)/(r1^2+r2^2 )

(b) 4R/(r1+r2 )

(c) (4R^3)/(r1^2+r2^2 )

(d) R^2/(r1^2+r2^2 )

**Q3. What is the height of the cone which is formed by joining the two ends of a sector of circle with radius r and angle 60° :**

(a) √35/6 r

(b) √25/6 r

(c) r^2/√3

(d) 35/6 r

**Q4. 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 remainder 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

**Q5. Perimeter of a rhombus is 2p unit and sum of length of diagonals is m unit, then area of the rhombus is**

(a) 1/4 m^2 p sq. unit

(b) 1/4 mp^2 sq. unit

(c) 1/4(m^2-p^2) sq. unit

(d) 1/4(m^2+p^2) sq. unit

**Q6. Three circles of diameter 10 cm each are bound together by a rubber band as shown in the figure.**

**The length of the rubber band (in cm) if it is stretched is**

(a) 30

(b) 30 + 10 ?

(c) 10 ?

(d) 60 + 20 ?

**Q7. 1/4 [√3 cos23°-sin23°]=**

(a) cos 43°

(b) cos 70°

(c) cos 53°

(d) 1/2 cos 53°

**Q8. Value of sec^2 θ-(sin^2 θ-2 sin^4 θ)/(2 cos^4 θ-cos^2 θ)**

(a) 1

(b) 2

(c)-1

(d) 0

**Q10. A polygon has 54 diagonals. The number of sides in the polygon is:**

(a) 7

(b) 9

(c) 12

(d) None of these

**Solutions**

S1. Ans.(c)

Sol.

Length of cuboid = 9 cm

Height of cuboid = 3 cm

Breadth of cuboid = 3 cm

Surface area = 2(9 × 3 + 3 × 3 + 3 × 9)

= 126

S2. Ans.(c)

Sol. 4/3 πR^3=1/3 πr1^2 h+1/3 πr2^2 h

=π/3 (4R^3 )= πh/3 (r1^2+r2^2 )

=4R^3=h(r1^2+r2^2)

h=(4R^3)/(r1^2+r2^2 )

S3. Ans.(a)

Sol.

r = l

radius of sector = Slant height of cone

and Perimeter of cone = Arc of sector

2πrθ/(360°)=2πR (R is radius of cone)

(2πr60°)/(360°)=2πR

=R=r/6

=l^2=h^2+R^2

=r^2=h^2+(r^2/36)

(35r^2)/36=h^2,h=(r√35)/6

S4. Ans.(a)

Sol.

Volume = lbh

= 32 × 7 × 4

= 896 cm^3

S5. Ans.(c)

Sol. d1+d2=m

Perimeter of rhombus = 2√(d1^2+d2^2 )

2p=2√(d1^2+d2^2 )

p^2=d1^2+d2^2 …(i)

d1+d2=m square the both sides

(d1+d2 )^2=m^2

d1^2+d2^2+2d1 d2=m^2

p^2+2d1×d2=m^2

2d1×d2=m^2-p^2

d1×d2=(m^2-p^2)/2

Area = 1/2 d1×d2

1/2 d1×d2=1/4(m^2-p^2) sq. unit

S6. Ans.(b)

Sol. The length of rubber band = d (h + ?)

h = number of circles

= 10 (3 + ?) = 30 + 10?

S7. Ans.(d)

Sol. 1/4 [√3 cos23°-sin23°]

=1/2 [√3/2 cos23°-1/2 sin23°]

=1/2 [cos30°cos23°-sin30°sin23°]

=cos(A+B)=cosA cosB-sinA sinB

=1/2 cos(30°+23°)

=1/2 cos53°

S10. Ans.(c)

Sol. n(n-3)/2=54

n(n – 3) = 108

n^2-3n-108=0

n^2-12n+9n-108=0

n(n – 12) + 9 (n – 12)

n – 12 = 0

n = 12