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Maths Quiz for KVS and CTET Exams

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 cos⁡23°-sin⁡23°]=
(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 cos⁡23°-sin⁡23°]
=1/2 [√3/2 cos⁡23°-1/2 sin⁡23°]
=1/2 [cos⁡30°cos⁡23°-sin⁡30°sin⁡23°]
=cos⁡(A+B)=cos⁡A cos⁡B-sin⁡A sin⁡B
=1/2  cos⁡(30°+23°)
=1/2  cos⁡53°

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
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