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Q:

A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is

A) rs.58 B) rs.158
C) rs.258 D) rs.358
 
Answer & Explanation Answer: C) rs.258

Explanation:

area of cross roads = (55 x 4) + (35 x 4)- (4 x 4) = 344sq m

cost of graveling = 344 x  (75/100) = Rs. 258

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Q:

A took 15 seconds 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 68m/min. The area of the field is?

A) 50 B) 60
C) 70 D) 80
 
Answer & Explanation Answer: B) 60

Explanation:

length of the diagonal = 52 x (15/60) =13m 

sum of length and breadth = 68 x (15/60) = 17m

 

l2+b2=13 or l+b =17

area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169]

=1/2 x 120 = 60 sq.m

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Q:

A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?

A) 140 B) 150
C) 160 D) 170
 
Answer & Explanation Answer: A) 140

Explanation:

when folded along the breadth
we have 2(l/2 +b) = 34 or l+2b = 34...........(1)
when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2)
from 1 &2 we get l=14 and b=10
Area of the paper = 14*10 = 140 sq cm

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Q:

Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is

A) 12 B) 32
C) 42 D) 52
 
Answer & Explanation Answer: C) 42

Explanation:

required area = [14 x 14 - (4 x 1/4 x 22/7 x 7 x 7) ]sq.cm

= 196 - 154 = 42 sq.cm.

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Q:

A particle which is four times in mass and two times in charge that of proton is

A) helium atom B) an alpha particle
C) deuteron D) tritium
 
Answer & Explanation Answer: B) an alpha particle

Explanation:
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Q:

Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is

A) 1.967 B) 1.867
C) 1.767 D) 1.567
 
Answer & Explanation Answer: A) 1.967

Explanation:

required area = (area of an equilateral triangle of side 7 cm)- (3 * area of sector with à = 60 degrees and r = 3.5cm)
34*7*7-3*227*3.5*3.5*60360 sq cm

 

=34*49-11*0.5*3.5 sq cm

 

= 1.967 sq cm

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Q:

A semicircular shaped window has diameter of 63cm. Its perimeter equals

A) 162 B) 132
C) 142 D) 172
 
Answer & Explanation Answer: A) 162

Explanation:

perimeter of window = πr+2r 

= [(22/7) x (63/2) + 63] = 99+63 = 162 cm

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Q:

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

A) 10ft B) 20ft
C) 30ft D) 40ft
 
Answer & Explanation Answer: B) 20ft

Explanation:

let the radius of the pool be Rft

 

Radius of the pool including the wall = (R+4)ft

 

Area of the concrete wall = πR+42-R2=πR+4+RR+4-R = 8πR+2 sq feet

 

=> 8πR+2 = 1125πR2 =>11R2 =200R+2

 

Radius of the pool R = 20ft

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