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question_answer1)
Length and breadth of a rectangle are 3.2 m and 150 cm. Then the area is
A)
48sq cm done
clear
B)
4.8 cm done
clear
C)
4.8 sq m done
clear
D)
48cm done
clear
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question_answer2)
The length and breadth of a rectangular plot are 900 m and 700 m respectively. If three rounds offence is fixed around the field at the cost of Rs.8 per meter, the total amount spent is
A)
Rs.768 done
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B)
Rs.7680 done
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C)
Rs.76,800 done
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D)
Rs.768,000 done
clear
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question_answer3)
Area of the shaded figure is
A)
2400 sq m done
clear
B)
48 sq m done
clear
C)
50 sq m done
clear
D)
98 sq m done
clear
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question_answer4)
A playground which is 250 m long and 20 m broad is to be fenced with wire. How much wire is needed?
A)
270m done
clear
B)
230m done
clear
C)
540m done
clear
D)
None of these done
clear
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question_answer5)
The distance covered by a farmer around a field of 120 m, length and 80m width is............... m.
A)
200 done
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B)
300 done
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C)
400 done
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D)
500 done
clear
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question_answer6)
If the length and breadth of a rectangle are doubled then its perimeter is
A)
Tripled done
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B)
doubled done
clear
C)
Made half done
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D)
none of these done
clear
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question_answer7)
The length of a rectangle is \[28\pi sq.units\] of its breadth. If its perimeter is 132m, its area will be............
A)
\[1,080\,{{m}^{2}}\] done
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B)
\[640\,{{m}^{2}}\] done
clear
C)
\[1,620\,\,{{m}^{2}}\] done
clear
D)
\[2,160\,{{m}^{2}}\] done
clear
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question_answer8)
The difference between the length and breadth of a rectangle is 23 m. If the perimeter is 206 m, then the area is
A)
\[88sq.units\] done
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B)
\[88\pi sq.units\] done
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C)
\[48\pi sq.units\] done
clear
D)
None of these done
clear
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question_answer9)
The length and breadth of a rectangular hall are 0.4 m and 30 cm respectively. The distance between two opposite comers of the hall is
A)
34.16m done
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B)
50m done
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C)
34.16cm done
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D)
50cm done
clear
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question_answer10)
In a trapezium whose parallel sides measure 24 cm and 15 cm and the distance between them is 10 cm. Find the area of trapezium.
A)
\[1:\sqrt{3}\] done
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B)
\[50%\] done
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C)
\[100%\] done
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D)
\[125%\] done
clear
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question_answer11)
If ABCD is a parallelogram, then the ratio of the areas of parallelogram ABCD and \[150%\] is
A)
1:2 done
clear
B)
2:1 done
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C)
cannot be determined done
clear
D)
None of these done
clear
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question_answer12)
The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10 cm and its altitude is 8 cm. Its area is
A)
\[\sqrt{3}:1\] done
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B)
\[\sqrt{2}:1\] done
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C)
\[\sqrt{5}:2\] done
clear
D)
\[2:\sqrt{5}\] done
clear
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question_answer13)
The length of diagonal of a square whose area is \[37\frac{1}{2}%\] is
A)
130m done
clear
B)
\[60%\] done
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C)
169m done
clear
D)
144m done
clear
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question_answer14)
The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Its area is
A)
\[75%\] done
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B)
\[120%\] done
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C)
\[8m\times 6m\] done
clear
D)
\[\frac{5}{2}(9+5\sqrt{3})sq.cm\] done
clear
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question_answer15)
The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to largest side is
A)
\[\frac{5}{2}(13+5\sqrt{3})sq.cm\] done
clear
B)
\[\frac{5}{2}(8+5\sqrt{3})sq.cm\] done
clear
C)
\[\frac{5}{2}(10+5\sqrt{3})sq.cm\] done
clear
D)
30cm done
clear
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question_answer16)
If the altitude of an equilateral triangle is \[4m\times 2m\]cm, its area is
A)
\[625c{{m}^{2}}\] done
clear
B)
\[125c{{m}^{2}}\] done
clear
C)
\[150c{{m}^{2}}\] done
clear
D)
\[100c{{m}^{2}}\] done
clear
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question_answer17)
The ratio between the length and the perimeter of a rectangular plot is 1 : 3 and the ratio between the breadth and perimeter of that plot is 1 : 6. What is the ratio between the length and area of that plot?
A)
2:1 done
clear
B)
1:6 done
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C)
1:8 done
clear
D)
Data inadequate done
clear
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question_answer18)
The circumference of a circle is 44 m, then the area of the circle is
A)
\[77{{m}^{2}}\] done
clear
B)
\[1232c{{m}^{3}}\] done
clear
C)
\[=4\times 500m=2km\] done
clear
D)
\[2\sqrt{3}c{{m}^{2}}\] done
clear
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question_answer19)
The area of a circle is\[2\sqrt{2}c{{m}^{2}}\], then the diameter is
A)
56m done
clear
B)
154m done
clear
C)
176m done
clear
D)
None of these done
clear
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question_answer20)
The difference between circumference and radius of a circle is 37 m. The circumference of that circle is
A)
7m done
clear
B)
44m done
clear
C)
154m done
clear
D)
None of these done
clear
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question_answer21)
The area of the sector of a circle, whose radius is 6 m, when the angle at the centre is \[3\sqrt{3}c{{m}^{2}}\] is
A)
\[6\sqrt{2}c{{m}^{2}}\] done
clear
B)
\[6084.5{{m}^{2}}\] done
clear
C)
\[276.5{{m}^{2}}\] done
clear
D)
\[154{{m}^{2}}\] done
clear
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question_answer22)
If the circumference of a circle is \[44{{m}^{2}}\], then the diameter of the circle is
A)
\[2464{{m}^{2}}\] done
clear
B)
\[{{42}^{o}}\] done
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C)
\[13.2{{m}^{2}}\] done
clear
D)
30 unit done
clear
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question_answer23)
When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to
A)
area done
clear
B)
circumference done
clear
C)
\[14.2{{m}^{2}}\] done
clear
D)
4unit done
clear
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question_answer24)
If the ratio of circumference of two circles is 4:9, the ratio of their area is
A)
9:4 done
clear
B)
16:81 done
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C)
4:9 done
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D)
2:3 done
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question_answer25)
If the radii of two concentric circles are 15 cm and 13 cm, respectively, then the area of the circulating ring in sq. cm will be
A)
176 done
clear
B)
178 done
clear
C)
180 done
clear
D)
200 done
clear
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question_answer26)
A sector of \[13.4{{m}^{2}}\] cut out from a circle has an area of \[14.4{{m}^{2}}\]sq. cm. The radius of the circle is
A)
3cm done
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B)
2.5cm done
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C)
3.5cm done
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D)
3.6cm done
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question_answer27)
The radius of a sphere is increased by P%. Its surface area increase by
A)
\[\frac{30}{\pi }\] done
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B)
\[60\pi \] done
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C)
\[\frac{15}{\pi }\] done
clear
D)
\[\frac{30}{{{\pi }^{2}}}\] done
clear
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question_answer28)
The height and radius of a cone are 3 cm and 4 cm respectively. Its curved surface area must be is
A)
\[2\pi \] done
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B)
\[{{120}^{o}}\] done
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C)
\[9\frac{3}{7}\] done
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D)
\[P%\] done
clear
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question_answer29)
The ratio of the volume and surface area of a sphere of unit radius
A)
4:3 done
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B)
3:4 done
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C)
1:3 done
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D)
3:1 done
clear
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question_answer30)
The slant height of a cone is increased by P%. If radius remains same, the curved surface area is increased by
A)
P% done
clear
B)
\[{{P}^{2}}%\] done
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C)
2P% done
clear
D)
None of these done
clear
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question_answer31)
The volumes of two spheres are in the ratio 64:27. Find the difference of their surface areas, if the sum of their radii is 7 units.
A)
\[\left( 2P+\frac{{{P}^{2}}}{100} \right)%\] done
clear
B)
\[\frac{{{P}^{2}}}{2}%\] done
clear
C)
\[62\frac{6}{7}sq.cm\] done
clear
D)
\[57\frac{3}{4}sq.cm\] done
clear
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question_answer32)
The ratio of radii of two cylinders is \[6c{{m}^{2}}\]and heights are in the ratio 2:3. The ratio of their volumes is
A)
1:9 done
clear
B)
2:9 done
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C)
4:9 done
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D)
5:9 done
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question_answer33)
The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic metre, then the number of persons who can be accommodated in the hall are
A)
120 done
clear
B)
150 done
clear
C)
140 done
clear
D)
100 done
clear
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question_answer34)
Each side of a cube is increased by 50%. Then the surface area of the cube is increased by
A)
\[12c{{m}^{2}}\] done
clear
B)
\[{{P}^{2}}%\] done
clear
C)
\[28\pi sq.units\] done
clear
D)
\[88sq.units\] done
clear
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question_answer35)
The edge of a cute is 20 cm. How many small cubes of 5 cm edge can be formed from this cube?
A)
4 done
clear
B)
32 done
clear
C)
64 done
clear
D)
100 done
clear
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question_answer36)
Two cylinders of same volume have their heights in the ratio 1:3. Find the ratio of their radii.
A)
\[88\pi sq.units\] done
clear
B)
\[48\pi sq.units\] done
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C)
\[1:\sqrt{3}\] done
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D)
\[50%\] done
clear
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question_answer37)
The area of a rhombus, one side of which measures 20 cm and one diagonal 24 cm, is:
A)
256sq.cm done
clear
B)
384sq.cm done
clear
C)
512sq.cm done
clear
D)
480sq.cm done
clear
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question_answer38)
The cost of cultivating a square field at the rate of Rs.160 per hectare is Rs.1440. Find the cost of putting a fence around it at the rate of 75 paise per meter:
A)
Rs. 1200 done
clear
B)
Rs. 1800 done
clear
C)
Rs. 900 done
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D)
None of these done
clear
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question_answer39)
The length of a rectangle is increased by 60% By what percentage would the width have to be decreased to maintain the same area:
A)
\[100%\] done
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B)
\[125%\] done
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C)
\[150%\] done
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D)
\[\sqrt{3}:1\] done
clear
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question_answer40)
A room \[\sqrt{2}:1\] is to be carpeted by a carpet 2 m wide, the length of carpet required
A)
12m done
clear
B)
36m done
clear
C)
24m done
clear
D)
48m done
clear
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question_answer41)
The area of the trapezium ABCD is:
A)
\[\sqrt{5}:2\] done
clear
B)
\[2:\sqrt{5}\] done
clear
C)
\[37\frac{1}{2}%\] done
clear
D)
\[60%\] done
clear
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question_answer42)
One diagonal of a rhombus is 24 cm and its side is 13 cm. The area of the rhombus is:
A)
25sq.m done
clear
B)
312sq.m done
clear
C)
125sq.cm done
clear
D)
120sq.cm done
clear
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question_answer43)
Diagonal of a parallelogram are 6 cm and 8 cm, respectively and one side is 5 cm. The area of parallelogram is:
A)
48sq.cm done
clear
B)
30sq.cm done
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C)
24sq.cm done
clear
D)
40sq.cm done
clear
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question_answer44)
The ratio of areas of two squares if ratio of their diagonals 2:1.
A)
2:1 done
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B)
3:1 done
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C)
3:2 done
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D)
4:1 done
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question_answer45)
Each side of an equilateral triangle is increased by 1.5%. The percentage increase in its area is:
A)
3.02% done
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B)
3% done
clear
C)
4.5% done
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D)
5.7% done
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question_answer46)
If each of the dimensions of a rectangle is increased by 100%, its area is increased by:
A)
100% done
clear
B)
200% done
clear
C)
300% done
clear
D)
400% done
clear
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question_answer47)
A table cover \[75%\] is spread on a meeting table is .25 m of the cover hanging all around the table. The cost of polishing the table top at Rs.2.25 per square metre is:
A)
Rs. 8.89 done
clear
B)
Rs. 11.81 done
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C)
Rs. 8.59 done
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D)
none of these done
clear
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question_answer48)
The volume of a cube is 125 cm3. The surface area of cube is:
A)
\[120%\] done
clear
B)
\[8m\times 6m\] done
clear
C)
\[\frac{5}{2}(9+5\sqrt{3})sq.cm\] done
clear
D)
\[\frac{5}{2}(13+5\sqrt{3})sq.cm\] done
clear
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question_answer49)
The length of the longest rod that can be fit in a cubical room of 4 cm side is:
A)
8.66m done
clear
B)
5.196m done
clear
C)
6.928m done
clear
D)
7.264m done
clear
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question_answer50)
The ratio of total surface area to lateral surface area of a cylinder whose radius is 80 cm and height 20 cm is :
A)
2:1 done
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B)
3:1 done
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C)
4:1 done
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D)
5:1 done
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question_answer51)
A rectangular carpet has an area of \[120\text{ }{{m}^{2}}\]and a perimeter of 46 m. The length of its diagonal is:
A)
15m done
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B)
16m done
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C)
17m done
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D)
20m done
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question_answer52)
A man walked 20 m to cross a rectangular field diagonally If the length of the field is 16 m, the breadth of the field is:
A)
4m done
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B)
16m done
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C)
12m done
clear
D)
cannot be determined done
clear
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question_answer53)
If the ratio of the areas of two squares is 9 : 1 then the ratio of their perimeter is:
A)
9:1 done
clear
B)
3:4 done
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C)
3:1 done
clear
D)
1:3 done
clear
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question_answer54)
Area of four walls of a room is\[\frac{5}{2}(8+5\sqrt{3})sq.cm\]. The length and breadth of the room are 7.5 m and 3.5m, respectively. The height of the room is:
A)
7.7m done
clear
B)
3.5m done
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C)
6.77m done
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D)
5.4m done
clear
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question_answer55)
If a right circular cone of vertical height 24 cm has a volume of \[\frac{5}{2}(10+5\sqrt{3})sq.cm\], then the area of its curved surface is:
A)
\[4m\times 2m\] done
clear
B)
\[625c{{m}^{2}}\] done
clear
C)
\[125c{{m}^{2}}\] done
clear
D)
\[150c{{m}^{2}}\] done
clear
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question_answer56)
The radii of two cylinders are in the ratio of 2 : 3 and their heights in ratio of 5 : 3, their volumes will be:
A)
4:9 done
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B)
27:20 done
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C)
20:27 done
clear
D)
9:4 done
clear
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question_answer57)
A playground is in the form of a rectangle having semicircle on the shorter sides. Find its area when the length of the rectangular portion is 80 m and the breadth is 42 m.
A)
\[4746\,{{m}^{2}}\] done
clear
B)
\[77{{m}^{2}}\] done
clear
C)
\[1232c{{m}^{3}}\] done
clear
D)
\[1254c{{m}^{2}}\] done
clear
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question_answer58)
In the given figure, ABCD is a field in the form of a quadrilateral whose sides are indicated. If\[304c{{m}^{2}}\]. The area of field is:
A)
\[550c{{m}^{2}}\] done
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B)
\[154c{{m}^{2}}\] done
clear
C)
\[4746{{m}^{2}}\] done
clear
D)
\[4748{{m}^{2}}\] done
clear
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question_answer59)
A chord of a circle of radius 14 cm makes a right angle at the centre. The areas of the minor and the major segment of the circle are respectively:
A)
\[4050{{m}^{2}}\] done
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B)
\[5049{{m}^{2}}\] done
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C)
\[\angle DAB={{90}^{o}}\] done
clear
D)
None of these done
clear
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question_answer60)
The area of a triangle with two of its side equals 5.1 metres and the third side 4.6 metres is:
A)
10.47sq.m done
clear
B)
2.86sq.m done
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C)
10.45sq.m done
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D)
None of these done
clear
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question_answer61)
The area of a circle whose radius is \[306{{m}^{2}}\] is:
A)
\[307{{m}^{2}}\] done
clear
B)
\[308{{m}^{2}}\] done
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C)
\[309{{m}^{2}}\] done
clear
D)
not possible done
clear
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question_answer62)
Find the volume of the largest right circular cone that can be cut out of cube whose edge is 9 cm:
A)
\[56c{{m}^{2}}\text{ and }560c{{m}^{2}}\] done
clear
B)
\[560c{{m}^{2}}\text{ and }56c{{m}^{2}}\] done
clear
C)
\[56c{{m}^{2}}\text{ and 61}6c{{m}^{2}}\] done
clear
D)
\[{{r}^{2}}\] done
clear
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question_answer63)
How many bricks 20 cm by 10 cm will be needed to pave the floor of a room 25m long and 16m wide?
A)
18000 done
clear
B)
20000 done
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C)
22000 done
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D)
24000 done
clear
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question_answer64)
How long will it take for a boy to run around a square field of area 25 hectares at 10 km per hour?
A)
12min done
clear
B)
14min done
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C)
16min done
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D)
18min done
clear
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question_answer65)
The perimeter of a circular plot is equal to that of a square plot. What is the ratio of their respective areas?
A)
13:11 done
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B)
14:11 done
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C)
15:11 done
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D)
16:11 done
clear
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question_answer66)
Four circles of radius 1 cm each are placed in such a way on a plane paper that each touches the other. Find the area \[\pi {{r}^{2}}\] of the space left in between the four circles. \[2\pi {{r}^{4}}\]
A)
0.82 done
clear
B)
0.84 done
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C)
0.86 done
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D)
0.88 done
clear
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question_answer67)
Two cubes, each of edge 12 cm are joined end to end. Find the surface area of the resulting cuboid.
A)
\[\pi {{r}^{4}}\] done
clear
B)
\[190.93c{{m}^{3}}\] done
clear
C)
\[189.5c{{m}^{3}}\] done
clear
D)
\[181.25c{{m}^{3}}\] done
clear
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question_answer68)
If the radius of the base of a right circular cylinder is reduced by 50%, keeping the same height, what is the ratio of the volume of the reduced cylinder to that of the original?
A)
1:9 done
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B)
1:8 done
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C)
1:4 done
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D)
1:2 done
clear
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question_answer69)
Find the number of coins 1.5 cm in diameter and 0.2 cm thick melted from a right circular cylinder whose height is 8 cm and diameter 6 cm.
A)
620 done
clear
B)
640 done
clear
C)
660 done
clear
D)
680 done
clear
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question_answer70)
It needs 50 ml paint for painting a picture\[169c{{m}^{3}}\]. How much paint is needed to paint a similar picture\[{{(cm)}^{2}}\]?
A)
100 ml done
clear
B)
400 ml done
clear
C)
750 ml done
clear
D)
200 ml done
clear
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question_answer71)
A room is 15 metres long, 4 metres broad and 3 metres high. Find the cost of whitewashing its four walls at 50 P. per\[(\pi =3.14)\].
A)
Rs.60 done
clear
B)
Rs 57 done
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C)
Rs 55 done
clear
D)
Rs 52 done
clear
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question_answer72)
The inside circumference of a circular field is 1188 m. Aroid 7 m wide is constructed on the outside. Find its area.
A)
\[1450c{{m}^{2}}\] done
clear
B)
\[1440c{{m}^{2}}\] done
clear
C)
\[1420c{{m}^{2}}\] done
clear
D)
\[1410c{{m}^{2}}\] done
clear
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question_answer73)
If all the sides of a triangle be increased by 200 per cent, what is the corresponding increase in its area?
A)
300% done
clear
B)
400% done
clear
C)
600% done
clear
D)
800% done
clear
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question_answer74)
The edges of three iron cubes are 6 cm, 8 cm and 10 cm, respectively. A new cube was made by melting them. Find the edge of the new cube.
A)
8cm done
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B)
12cm done
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C)
14cm done
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D)
10cm done
clear
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question_answer75)
A hall is \[50cm\times 25cm.\]; the number of persons, who can be accommodated in it, each requiring \[100cm\times 50cm\] of air is
A)
2200 done
clear
B)
1100 done
clear
C)
2500 done
clear
D)
3300 done
clear
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question_answer76)
A conical flask of radius r and height h is full of water. It is emptied into another conical flask of radius xr. If this flask becomes fall, what is its height?
A)
\[{{m}^{2}}\] done
clear
B)
\[8070{{m}^{2}}\] done
clear
C)
\[8270{{m}^{2}}\] done
clear
D)
\[8370{{m}^{2}}\] done
clear
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question_answer77)
The surface area of a sphere is x. What is its volume?
A)
\[8470{{m}^{2}}\] done
clear
B)
\[100m\times 75m\times 22m\] done
clear
C)
\[50{{m}^{3}}\] done
clear
D)
\[3{{x}^{2}}h\] done
clear
View Solution play_arrow
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question_answer78)
The volumes of two spheres are in the ratio 64 : 27. Find the radius of the larger if the sum of their radii is 21 cm.
A)
9cm done
clear
B)
12cm done
clear
C)
15cm done
clear
D)
14cm done
clear
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question_answer79)
Area of the shaded region is
A)
96 sq.m done
clear
B)
15 sq.m done
clear
C)
81 sq.m done
clear
D)
111 sq. m done
clear
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question_answer80)
In the given fig. ABCD is a parallelogram. \[\frac{h}{{{x}^{2}}}\] and \[\frac{xh}{3}\],if \[\frac{3h}{x}\]\[\frac{4\pi x}{3}\]and \[\frac{x}{3}\sqrt{\frac{x}{4\pi }}\] Find DL
A)
\[{{(4\pi x)}^{3/2}}\] done
clear
B)
\[\frac{3\sqrt{2}}{\pi }{{x}^{3/2}}\] done
clear
C)
\[DL\bot AB\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer81)
A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by
A)
11:12 done
clear
B)
21:33 done
clear
C)
22:33 done
clear
D)
14:11 done
clear
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question_answer82)
The largest sphere is cut off from a cube of side 5 cm. The volume of the sphere will be:
A)
\[DM\bot BC\] done
clear
B)
\[AB=18cm,\] done
clear
C)
\[BC=12cm,\] done
clear
D)
\[DM=10cm,\] done
clear
View Solution play_arrow
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question_answer83)
A hollow spherical ball whose inner radius is 4 cm is fall of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is
A)
4cm done
clear
B)
\[6\frac{1}{2}cm\] done
clear
C)
8cm done
clear
D)
16cm done
clear
View Solution play_arrow
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question_answer84)
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
A)
\[6cm\] done
clear
B)
\[6\frac{2}{3}cm\] done
clear
C)
\[27\pi c{{m}^{3}}\] done
clear
D)
\[30\pi c{{m}^{3}}\] done
clear
View Solution play_arrow
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question_answer85)
The dimensions of the floor of a rectangular hall are \[108\pi c{{m}^{2}}\] m. The floor of the hall is to be tiled fully with \[\frac{125\pi }{6}c{{m}^{2}}\] rectangular tiles without breaking tiles to smaller size. The number of tiles required is:
A)
4800 done
clear
B)
2600 done
clear
C)
2500 done
clear
D)
2400 done
clear
View Solution play_arrow
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question_answer86)
A horse is tethered to a comer of a field which is in the shape of an equilateral triangle. If the length of the rope through which it is tied be 7m, then the area of the field over which it can graze is:
A)
49 sq.cm done
clear
B)
\[8\pi cm\] done
clear
C)
\[H=\frac{h}{{{x}^{2}}}.\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer87)
The length and breadth of a square are increased by 40% and 30% respectively. The area of resulting rectangle exceeds the area of the square by:
A)
42% done
clear
B)
62% done
clear
C)
82% done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer88)
A tin sheet is in the form of a rhombus whose side is 5 cm and one of its diagonals is 8 cm. Then the cost of painting the sheet at the rate of \[x=4\pi {{r}^{2}}\] on both of its sides is:
A)
Rs.84 done
clear
B)
Rs.140 done
clear
C)
Rs.168 done
clear
D)
none of these done
clear
View Solution play_arrow
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question_answer89)
A is a right circular cylinder on which a cone B is placed. The entire structure is melted and spheres are formed each having radius 1 cm. How many spheres can be formed?
A)
18 done
clear
B)
20 done
clear
C)
21 done
clear
D)
23 done
clear
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question_answer90)
A plot is in the form of a rectangle ABCD having semicircle on BC as shown in figure. The semicircle portion is grassy while the remaining plot is without grass. The area of the plot without grass where AB = 60 m and BC = 28 m is:
A)
\[\Rightarrow \] done
clear
B)
\[r=\sqrt{\frac{x}{4\pi }}\] done
clear
C)
\[\therefore \] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer91)
An athletic track 14m wide consists of two straight sections 130m long joining semicircular ends whose inner radius in 3.5m. The area of the shaded region is:
A)
\[=\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi \times {{\left( \frac{x}{4\pi } \right)}^{3/2}}\] done
clear
B)
\[=\frac{4}{3}\pi \times \frac{x}{4\pi }\sqrt{\frac{x}{4\pi }}=\frac{x}{3}\sqrt{\frac{x}{4\pi }.}\] done
clear
C)
\[\frac{\frac{4}{3}\pi {{r}^{3}}}{\frac{4}{3}\pi {{(21-r)}^{3}}}=\frac{64}{27}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer92)
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m, the height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. The area of the canvas required for the tent is:
A)
\[\Rightarrow \] done
clear
B)
\[\frac{r}{21-r}=\frac{4}{3}\] done
clear
C)
\[\Rightarrow \] done
clear
D)
\[3r=84-4r\] done
clear
View Solution play_arrow
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question_answer93)
Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.
A)
\[\Rightarrow \] done
clear
B)
\[r=12cm.\] done
clear
C)
\[(12\times 8-5\times 3)Sq.m\] done
clear
D)
\[96-15=81sqm\] done
clear
View Solution play_arrow
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question_answer94)
A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, what is the ratio of their base to their heights?
A)
3:4 done
clear
B)
5:4 done
clear
C)
6:7 done
clear
D)
9:8 done
clear
View Solution play_arrow
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question_answer95)
The circumference of a circle is 100 cm. What is the largest side of a square inscribed in the circle?
A)
\[AB\times DL=BC\times DM\] done
clear
B)
\[18\times DL=12\times 10\] done
clear
C)
\[DL=\frac{12\times 10}{18}=\frac{20}{3}=6\frac{2}{3}cm,\] done
clear
D)
\[=2\pi \times 42=84\pi cm.\] done
clear
View Solution play_arrow
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question_answer96)
If the length of a rectangle is increased by 50% and its breadth is decreased by 25%, what is the change percent in its area?
A)
12.5% increase done
clear
B)
10% increase done
clear
C)
25% increase done
clear
D)
20% increase done
clear
View Solution play_arrow
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question_answer97)
A water tank whose dimensions are 1.5 m, 0.75 m and 0.48 m is fall. Its contents are emptied into another empty tank whose base area is\[1\,{{m}^{2}}\]. How much the water level shall rise?
A)
64m done
clear
B)
0.54m done
clear
C)
5.4cm done
clear
D)
0.34cm done
clear
View Solution play_arrow
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question_answer98)
It is required to construct a conical circus tent of radius 21 m and 35m slant height. The width of the canvas cloth is 3 metres. What will be the length of the cloth which shall do the needful?
A)
700m done
clear
B)
1250m done
clear
C)
776.5m done
clear
D)
770m done
clear
View Solution play_arrow
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question_answer99)
A hollow sphere of internal and external radii respectively, 2cm and 4cm is melted into a solid cone of base radius 4 cm. Find the height of the cone.
A)
12cm done
clear
B)
7cm done
clear
C)
14cm done
clear
D)
21cm done
clear
View Solution play_arrow
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question_answer100)
Match column I with column II and select the correct answer using the code given below the columns:
Column I | Column II |
(A) In a circle with centre 0 and radius 5 cm, AB is a chord of length \[4x=84\pi \] cm. Then the area of sector AOB is........ \[x=21\pi \]. | (p) 154 |
(B) Area of a quadrant of a circle whose circumference is 44 cm, is......... \[=\pi {{(42)}^{2}}:{{(21\pi )}^{2}}\pi \times 42\times 42:21\times 21\times \pi \times \pi =4:\pi \]. | (q) 330 |
(C) A chord of a circle of radius 14 cm subtends a right angle at the centre. | (r) \[=4:\frac{22}{7}=14:11\] |
(D) The area of ring whose outer and inner radii are 19cm and 16cm, respectively is......... \[R=\frac{5}{2}cm.\] | (s) \[\therefore \] |
A)
\[A-(s),B-(r),C-(p),D-(q)\] done
clear
B)
\[=\frac{4}{3}\pi {{r}^{3}}\] done
clear
C)
\[=\frac{4}{3}\times \frac{22}{7}\times 64c{{m}^{3}}[r=4cm]\] done
clear
D)
\[=\frac{44\times 64}{21}c{{m}^{3}}.\] done
clear
View Solution play_arrow
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question_answer101)
DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): Area of the triangle having three sides 4 m, 6 m and 8 m is 135 sq. m. Reason (R): If a, b, c are the lengths of the sides of a triangle Area \[=\frac{1}{3}\pi {{r}^{2}}h=\frac{1}{3}\times \frac{22}{7}\times {{r}^{2}}\times 2=\frac{44{{r}^{2}}}{21}\] where \[\frac{44\times 64}{21}=\frac{44{{r}^{2}}}{21}\]
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true but R is not the correct explanation of A. done
clear
C)
A is true but R is false done
clear
D)
A is false but R is true. done
clear
View Solution play_arrow
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question_answer102)
DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): If the side of a rhombus is 10 cm and one diagonal is 16 cm, then area of the rhombus is \[{{r}^{2}}=64\]. Reason (R): Area of rhombus\[=2\times area\,of\,triangle.\]
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true but R is not the correct explanation of A. done
clear
C)
A is true but R is false done
clear
D)
A is false but R is true. done
clear
View Solution play_arrow
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question_answer103)
DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): The area of the sector of a circle with radius 4 cm and of angle \[r=8cm.\] Reason (R): Area of a sector of angle\[p{}^\circ \]of a circle with radius R is \[=(l+b)-\sqrt{{{l}^{2}}+{{b}^{2}}}=\frac{1}{2}\]
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true but R is not the correct explanation of A. done
clear
C)
A is true but R is false done
clear
D)
A is false but R is true. done
clear
View Solution play_arrow
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question_answer104)
DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): The circumference of a circle of diameter 14 cm is 44 cm. Reason (R): Circumference of the circle of radius\[307{{m}^{2}}\]
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true but R is not the correct explanation of A. done
clear
C)
A is true but R is false done
clear
D)
A is false but R is true. done
clear
View Solution play_arrow
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question_answer105)
DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): Volume of two spheres are in the ratio 64:27. Then the ratio of their surface areas are 16: 9. Reason (R): Volume of a sphere \[308{{m}^{2}}\] and surface area \[309{{m}^{2}}\]
A)
Both A and R are individually true and R is the correct explanation of A. done
clear
B)
Both A and R are individually true but R is not the correct explanation of A. done
clear
C)
A is true but R is false done
clear
D)
A is false but R is true. done
clear
View Solution play_arrow
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question_answer106)
DIRECTIONS: Read the following passages and answer the questions that follow. A well is a vertical open cylinder of radius 1.2 m and height 5 m. The well contains water to a depth of 3 m (use: \[56c{{m}^{2}}\text{ and }560c{{m}^{2}}\])
The total internal area of the curved surface of the well and the bottom of the well is
A)
\[560c{{m}^{2}}\text{ and }56c{{m}^{2}}\] done
clear
B)
\[56c{{m}^{2}}\text{ and 61}6c{{m}^{2}}\] done
clear
C)
\[{{r}^{2}}\] done
clear
D)
\[\pi {{r}^{2}}\] done
clear
View Solution play_arrow
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question_answer107)
DIRECTIONS: Read the following passages and answer the questions that follow. A well is a vertical open cylinder of radius 1.2 m and height 5 m. The well contains water to a depth of 3 m (use: \[56c{{m}^{2}}\text{ and }560c{{m}^{2}}\])
The volume of water in the well, is \[2\pi {{r}^{4}}\]
A)
13560 done
clear
B)
31560 done
clear
C)
53160 done
clear
D)
51360 done
clear
View Solution play_arrow
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question_answer108)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE ? 1 Wood is required to make a closed box of external length 1.2 m, breadth 90 cm and height 72 cm. The thickness of the walls of the box being 2 cm throughout. The Capacity of the box is
A)
\[\pi {{r}^{4}}\] done
clear
B)
\[190.93c{{m}^{3}}\] done
clear
C)
\[189.5c{{m}^{3}}\] done
clear
D)
\[181.25c{{m}^{3}}\] done
clear
View Solution play_arrow
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question_answer109)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE ? 1 Wood is required to make a closed box of external length 1.2 m, breadth 90 cm and height 72 cm. The thickness of the walls of the box being 2 cm throughout. The Volume of the wood used, is
A)
\[169c{{m}^{3}}\] done
clear
B)
\[{{(cm)}^{2}}\] done
clear
C)
\[(\pi =3.14)\] done
clear
D)
\[1450c{{m}^{2}}\] done
clear
View Solution play_arrow
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question_answer110)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE ? 1 Wood is required to make a closed box of external length 1.2 m, breadth 90 cm and height 72 cm. The thickness of the walls of the box being 2 cm throughout. The total cost of the wood at the rate of 20 paise per \[1440c{{m}^{2}}\] is
A)
9864.40 done
clear
B)
1968440 done
clear
C)
19486.40 done
clear
D)
19846.40 done
clear
View Solution play_arrow
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question_answer111)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE - 2 Area of the path enclosed between two concentric circles of radii R, r is \[1420c{{m}^{2}}\] and area of sector of a circle with sector angle \[1410c{{m}^{2}}\][r = radius of the circle] The areas of two concentric circles are 19 cm and 16 cm, respectively. Then the area of ring enclosed by these is
A)
\[50cm\times 25cm.\] done
clear
B)
\[100cm\times 50cm\] done
clear
C)
\[{{m}^{2}}\] done
clear
D)
\[8070{{m}^{2}}\] done
clear
View Solution play_arrow
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question_answer112)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE - 2 Area of the path enclosed between two concentric circles of radii R, r is \[1420c{{m}^{2}}\] and area of sector of a circle with sector angle \[1410c{{m}^{2}}\][r = radius of the circle] The areas of two concentric circles are \[8270{{m}^{2}}\] and \[8370{{m}^{2}}\]respectively Then the width of the ring is
A)
2.5 cm done
clear
B)
2.8cm done
clear
C)
3.5cm done
clear
D)
3.7cm done
clear
View Solution play_arrow
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question_answer113)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE - 2 Area of the path enclosed between two concentric circles of radii R, r is \[1420c{{m}^{2}}\] and area of sector of a circle with sector angle \[1410c{{m}^{2}}\][r = radius of the circle] The area of a sector of a circle with radius 7 cm and angle of the sector\[8470{{m}^{2}}\], is \[100m\times 75m\times 22m\]
A)
\[50{{m}^{3}}\] done
clear
B)
\[3{{x}^{2}}h\] done
clear
C)
\[\frac{h}{{{x}^{2}}}\] done
clear
D)
\[\frac{xh}{3}\] done
clear
View Solution play_arrow
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question_answer114)
DIRECTIONS: Read the following passages and answer the questions that follow. PASSAGE - 2 Area of the path enclosed between two concentric circles of radii R, r is \[1420c{{m}^{2}}\] and area of sector of a circle with sector angle \[1410c{{m}^{2}}\][r = radius of the circle] A group of workers engaged in plastering a wall completed half of the work on one day and quarter of the remaining in next day if still 45 sq mt. of the wall remained to be plastered, find the area of the wall.
A)
120 sq.cm done
clear
B)
90 sq. m done
clear
C)
120 sq. m done
clear
D)
90 sq.cm done
clear
View Solution play_arrow
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question_answer115)
Match column I with column II and select the correct answer using the code given below the columns:
Column-I | Column-II |
A. Area of equilateral triangle is | (p) \[\frac{x}{3}\sqrt{\frac{x}{4\pi }}\] (Product of sides containing right angles) |
B. Height of an equilateral triangle is | (q) \[{{(4\pi x)}^{3/2}}\] (Product of diagonals) |
C. Area of rhombus is | (r) \[\frac{3\sqrt{2}}{\pi }{{x}^{3/2}}\] |
D. Area of trapezium is | (s) \[DL\bot AB\] |
E. Area of right angled triangle is | (t) \[DM\bot BC\] |
A)
\[AB=18cm,\] done
clear
B)
\[BC=12cm,\] done
clear
C)
\[DM=10cm,\] done
clear
D)
\[A-(t),B-(s),C-(q)D-(r),E-(p)\] done
clear
View Solution play_arrow
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question_answer116)
Match column I with column II and select the correct answer using the code given below the columns:
Column-I | Column-II |
A. Volume of a cylinder is | (p) \[\frac{1}{3}\pi {{r}^{2}}h\] |
B. Volume of a cone is | (q) \[\frac{4}{3}\pi {{r}^{3}}\] |
C. Volume of a sphere is | (r) \[\sqrt{{{h}^{2}}+{{r}^{2}}}\] |
D. Slant height of a cone is | (s) \[\pi {{r}^{2}}h\] |
A)
\[A-(s),B-(p),C-(r),D-(q)\] done
clear
B)
\[\frac{125\pi }{6}c{{m}^{2}}\] done
clear
C)
\[8\pi cm\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow