Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.
16. If the radius of a circle increases by x units, its circumference increases by
A. 2?x units
B. 2?r units
C. 2?(r+x) units
D. 2? units
Answer
Explanation:
Let the radius of circle is r
New radius =(r+x) units
New circumference =2?(r+x)units
Original circumference =2?x units
17. If the diagonal and the area of a rectangle are 13 m and 60 m2, what is the length of the rectangle?
A. 13m
B. 5m
C. 12m
D. 10m
Answer
Explanation:
Let,
Length of rectangle L
Breadth of rectangle as B
Diagonal of the rectangle =(L²+B²)0.5= 13
L²+B² = 169
18. A rectangular sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of the diameter of the base to the breadth of the paper?
A. 1:π
B. 2:π
C. π:1
D. π:2
Answer
Explanation:
Height of the cylinder = Length of the paper
Circumference of its base = Breadth of the paper
2 π r = b
Diameter d = 2r = b/π
19. If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
A. 25 % Decrease
B. 50% increase
C. 25 % Increase
D. 50 % Decrease
Answer
Explanation:
Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000
Length of the rectangle is halved=New length
=Original length/2=100/2=50
Breadth is tripled
New breadth= Original breadth×3=100×3=300
New area = 50 × 300 = 15000
Increase in area = New Area – Original Area
= 15000 – 10000= 5000
Percentage of Increase in area
= (Increase in Area/Original Area)×100
=(5000/10000)×100=50%
20. The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs.800 per sq. meter?
A. 12000
B. Rs.16500.
C. Rs.19500
D. 18000
Answer
Explanation:
Area = 5.5 × 3.75 sq. meter.
Cost for 1 sq. meter. = Rs.800
Hence total cost = 5.5 × 3.75 × 800
= 5.5 × 3000
= Rs.16500
21. The area of a parallelogram is 72 cm2 and its altitude is twice the corresponding base. What is the length of the base?
A. 8 cm
B. 12 cm
C. 7 cm
D. 6 cm
Answer
Explanation:
Area of a parallelogram, A = bh
Where, b is the base and h is the height of the parallelogram
Let the base = x cm.
Then the height = 2x cm (? altitude is twice the base)
Area = x × 2x = 2x2
But the area is given as 72 cm2
2x2= 72
x2= 36
x = 6 cm
22. A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 7 cm x 6 cm. The maximum number of boxes that can be carried in the wooden box, is:
A. 1200000
B. 9800000
C. 7500000
D. 1000000
Answer
Explanation:
Number = (800*700*600)/8*7*6 = 1000000
23. A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.
A. 20
B. 40
C. 30
D. 10
Answer
Explanation:
Volume of the block = (6 x 12 x 15) cm3 = 1080cm3
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.
Volume of this cube = (3 x 3 x 3) cm3= 27cm3
Number of cubes= 1020/87
40 cm3
24. The perimeter of a square is 48 cm. The area of rectangle is 4 cm less than the area of square. If the length of the rectangle is 14 cm, then its perimeter is:
A. 24 cm
B. 48 cm
C. 50 cm
D. 54 cm
Answer
Explanation:
Side of the square= 12 cm.
Area of the rectangle= [(12*12)-4] cm2 = 140 cm2
Now, area= 140 cm2, length= 14 cm
Therefore, breadth= area/length= 140/14= 10cm
Hence perimeter= 2(l+B.= 2(14+10)= 48 cm
25. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
A. 2 : 1
B. 3 : 2
C. 25 : 18
D. 27 : 20
Answer
Explanation:
Volume of the large cube = (33 + 43 + 53) = 216 cm3.
Let the edge of the large cube be a.
So, a3 = 216
a = 6 cm.
Required ratio = 6 x (32 + 42 + 52) = 50 = 25 : 18.
x 62 36
26. The difference of the areas of two squares drawn on two line segments of different length is 32 sq. cm. Find the length of the greater line segment if one line is longer than the other by 2 cm.
A. 7 cm
B. 9 cm
C. 11 cm
D. 16 cm
Answer
Explanation:
Let the lengths of the line segments be x and (x+2) cm.
Then, (x+2)2-x2=32
x2+4x+4-x2=32
4x=28
x=7
Therefore, length longer line segment=(7+2)= 9 cm
27. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A. 49 m2
B. 50 m2
C. 53.5 m2
D. 55 m2
Answer
Explanation:
Area of the wet surface = [2(lb + bh + lh) – lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
28. The length of longest pole that can be placed on the floor of a room is 10 m and the length of the longest pole that can be placed in the room is 10 m. The height of the room is :
A. 6 m
B. 7.5 m
C. 8 m
D. 10 m
Answer
Explanation:
No explanation
29. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
A. 90 cm
B. 1 dm
C. 1 m
D. 1.1 cm
Answer
Explanation:
Let the thickness of the bottom be x cm.
Then,
[(330 – 10) x (260 – 10) x (110 – x)] = 8000 x 1000
(320 x 250) x (110 – x) = 8000 x 1000
(110 – x) = (8000 x 1000)/(320 x 250) = 100
x = 10 cm = 1 dm.
30. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the rise in level of the field will be :
A. 0.299 cm
B. 0.29 cm
C. 2.98 cm
D. 4.15 cm
Answer
Explanation:
No explanation
