
The area of a rhombus having one side 10 cm and one diagonal 12 cm is [SSC CGL Tier n, 2017]
A)
\[48\text{ }c{{m}^{2}}\] done
clear
B)
\[96\,\,c{{m}^{2}}\] done
clear
C)
\[144\text{ }c{{m}^{2}}\] done
clear
D)
\[192\text{ }c{{m}^{2}}\] done
clear
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The sum of the length and breadth of a rectangle is 6 cm. A square is constructed such that one of its sides is equal to a diagonal of the rectangle. If the ratio of areas of the square and rectangle is 5 : 2, the area of the square in \[c{{m}^{2}}\]is [SSC CGL Tier II, 2017]
A)
\[20\text{ }c{{m}^{2}}\] done
clear
B)
\[10\,c{{m}^{2}}\] done
clear
C)
\[\sqrt{5}\text{ }c{{m}^{2}}\] done
clear
D)
\[10\sqrt{2\,}c{{m}^{2}}\] done
clear
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The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circum circle and the incircle of the triangle is [SSC CGL Tier II, 2017]
A)
\[50\frac{1}{7}\,c{{m}^{2}}\] done
clear
B)
\[50\frac{2}{7}\,c{{m}^{2}}\] done
clear
C)
\[75\frac{1}{7}c{{m}^{2}}\] done
clear
D)
\[75\frac{2}{7}\,c{{m}^{2}}\] done
clear
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In trapezium ABCD, AB  CD and AB = 2CD. Its diagonals intersect at O. If the area of \[\Delta AOB=84\,c{{m}^{2}}\], then the area of \[\Delta COD\]is equal to [SSC CGL Tier II, 2015]
A)
\[72\text{ }c{{m}^{2}}\] done
clear
B)
\[42\,c{{m}^{2}}\] done
clear
C)
\[26\,c{{m}^{2}}\] done
clear
D)
\[21\,c{{m}^{2}}\] done
clear
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Quadrilateral ABCD is circumscribed about a circle. If the lengths of AB, BC, CD are 7 cm, 8.5 cm and 9.2 cm respectively, then the length (in cm) of DA is [SSC CGL Tier II, 2015]
A)
16.2 done
clear
B)
10.7 done
clear
C)
7.2 done
clear
D)
7.7 done
clear
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The area of an isosceles trapezium is \[176\text{ }c{{m}^{2}}\] and the height is 2/11th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is [SSC CGL Tier II, 2015]
A)
24 done
clear
B)
\[2\sqrt{137}\] done
clear
C)
\[\sqrt{137}\] done
clear
D)
28 done
clear
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The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. The area (in sq cm) of the rhombus is [SSC CGL Tier II, 2015]
A)
206 done
clear
B)
216 done
clear
C)
432 done
clear
D)
108 done
clear
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In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is \[(\sqrt{3}=1.732)\] [SSC CGL Tier II. 2014]
A)
98.55 sq cm done
clear
B)
100 sq cm done
clear
C)
101 sq cm done
clear
D)
95 sq cm done
clear
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Perimeter of a rhombus is 2p unit and sum of length of diagonals is m unit, then area of the rhombus is [SSC CGL Tier II, 2014]
A)
\[\frac{1}{4}{{m}^{2}}p\,\text{sq}\,\text{unit}\] done
clear
B)
\[\frac{1}{4}\,m{{p}^{2}}\,\text{sq}\,\text{unit}\] done
clear
C)
\[\frac{1}{4}({{m}^{2}}{{p}^{2}})\,\text{sq}\,\text{unit}\] done
clear
D)
\[\frac{1}{4}({{p}^{2}}{{m}^{2}})\,sq\,unit\] done
clear
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Two sides of a plot measuring 32 m and 24 m and the angle between them is a perfect right angle. the other two sides measure 25m each and the other three angles are not right angles. The area of the plot in m2 is [SSC CGL Tier II, 2014]
A)
768 done
clear
B)
534 done
clear
C)
696.5 done
clear
D)
684 done
clear
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A cost of cultivating a square field at a rate of Rs. 35 per hectare is Rs. 1215. The cost of putting a fence around it at the rate of 75 paise per metre would be
A)
Rs. 360 done
clear
B)
Rs. 810 done
clear
C)
Rs. 900 done
clear
D)
Rs. 1800 done
clear
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The area of a trapezium is \[384\,c{{m}^{2}}.\]If its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them, is 12 cm, the smaller of the parallel sides is
A)
20 cm done
clear
B)
24 cm done
clear
C)
30 cm done
clear
D)
36 cm done
clear
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The ratio of the number of sides of two regular polygons is 1 : 2. If each interior angle of the first polygon is \[120{}^\circ ,\] then the measure of each interior angle of the second polygon is
A)
\[140{}^\circ \] done
clear
B)
\[135{}^\circ \] done
clear
C)
\[150{}^\circ ~\] done
clear
D)
\[160{}^\circ \] done
clear
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A square is of area 200 sq m. A new square is formed in such a way that its side is equal to the length of the diagonal of the given square. Then, he area of the new square formed is
A)
\[200\sqrt{2}\text{ }sq\text{ }m\] done
clear
B)
\[400\sqrt{2\,}\,sq\,m\] done
clear
C)
\[400\,\,sq\,m\] done
clear
D)
\[800\,\,sq\,m\] done
clear
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If a regular polygon has each of its angles 3 equal to \[\frac{3}{5}\]times of 5 two right angles, then the number of sides is
A)
3 done
clear
B)
5 done
clear
C)
6 done
clear
D)
8 done
clear
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The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 6075 q m, What is its length?
A)
45 m done
clear
B)
75 m done
clear
C)
130 m done
clear
D)
135 m done
clear
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The cost of carpeting a room15 m long with a Carpet 75 cm wide at 90 paise/m is Rs. 108. The breadth of the room is
A)
6 m done
clear
B)
8 m done
clear
C)
9 m done
clear
D)
12 m done
clear
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If each side of a square is increased by 4 cm, then its area is increased by \[60\,c{{m}^{2}}.\] The side of the square is
A)
12 cm done
clear
B)
13 cm done
clear
C)
14 cm done
clear
D)
None of these done
clear
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The area of the largest circle that can be drawn inside a rectangle with sides 8 m by 7 m, is
A)
\[50\frac{2}{7}\,{{m}^{2}}\] done
clear
B)
\[38\frac{1}{8}\,{{m}^{2}}\] done
clear
C)
\[32\,{{m}^{2}}\] done
clear
D)
\[24\frac{1}{2}\,{{m}^{2}}\] done
clear
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A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6 : 5. The smaller side of the rectangle is
A)
30 cm done
clear
B)
60 cm done
clear
C)
72 cm done
clear
D)
132 cm done
clear
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A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle?
A)
\[88\text{ }c{{m}^{2}}\] done
clear
B)
\[154\text{ }c{{m}^{2}}\] done
clear
C)
\[616\,c{{m}^{2}}\] done
clear
D)
\[1250\text{ }c{{m}^{2}}\] done
clear
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If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by
A)
circle done
clear
B)
square done
clear
C)
equilateral triangle done
clear
D)
Both triangle and square done
clear
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The sides of a triangle are in the ratio \[\frac{1}{2}:\frac{1}{3} & :\frac{1}{4}.\]If the perimeter is 52 cm, then the length of the smallest side is
A)
9 cm done
clear
B)
10 cm done
clear
C)
11 cm done
clear
D)
12 cm done
clear
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If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area?
A)
No change done
clear
B)
8% decrease done
clear
C)
16% decrease done
clear
D)
16% increase done
clear
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The area of a right angled triangle is \[20\,c{{m}^{2}}\]and one of the sides containing the right angle is 4 cm. The altitude on the hypotenuse is
A)
\[\frac{41}{\sqrt{34}}\,cm\] done
clear
B)
\[\sqrt{\frac{41}{40}}\,cm\] done
clear
C)
\[\frac{29}{\sqrt{20}}\,cm\] done
clear
D)
\[\frac{20}{\sqrt{29}}\,cm\] done
clear
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The areas of two similar triangles are \[12\,c{{m}^{2}}\] and \[48\,c{{m}^{2}}.\]If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is
A)
0.525 cm done
clear
B)
4.2 cm done
clear
C)
4.41 cm done
clear
D)
8.4 cm done
clear
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The areas of a square and a rectangle are equal. If their perimeters are respectively \[{{p}_{1}}\]and \[{{p}_{2}}\] then which of the following is a true statement?
A)
\[{{p}_{1}}>{{p}_{2}}\] done
clear
B)
\[{{p}_{1}}\le {{p}_{2}}\] done
clear
C)
\[{{p}_{1}}<{{p}_{2}}\] done
clear
D)
\[{{p}_{1}}\ge {{p}_{2}}\] done
clear
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The area of a rhombus is \[144\,c{{m}^{2}}.\]If one of the diagonals is double the other, the lengths of its diagonals are
A)
6 cm, 12 cm done
clear
B)
12 cm, 24 cm done
clear
C)
16 cm, 32 cm done
clear
D)
18 cm, 36 cm done
clear
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A circular garden has a circumference of 440 m. There is a 7 m wide border inside the garden along its periphery. The area of the border is
A)
\[2918\,{{m}^{2}}\] done
clear
B)
\[2921\,{{m}^{2}}\] done
clear
C)
\[2924\,{{m}^{2}}\] done
clear
D)
\[2926\,{{m}^{2}}\] done
clear
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The area of a circle is increased by \[22\,c{{m}^{2}}\] when its radius is increased by 1 cm. The original radius of the circle is
A)
6 cm done
clear
B)
3.2 cm done
clear
C)
3 cm done
clear
D)
3.5 cm done
clear
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A square park has each side 100 m. At each corner of the park there is a flower bed in the form ofa quadrant of radius 14 m, as shown in the figure. The area of the remaining part of the park is
A)
\[9384\,{{m}^{2}}\] done
clear
B)
\[9290\,{{m}^{2}}\] done
clear
C)
\[9150\,{{m}^{2}}\] done
clear
D)
\[9050\,{{m}^{2}}\] done
clear
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In the given figure, OP = PQ = 14 cm and semicircles are drawn on OP, PQ and OQ as diameters. Then, the perimeter of the shaded area is
A)
88 cm done
clear
B)
176 cm done
clear
C)
264 cm done
clear
D)
352 cm done
clear
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In the adjoining figure, if the radius of each of the four outer circles is r, what is the radius of the inner circle?
A)
\[\frac{2r}{(\sqrt{2}+1)}\] done
clear
B)
\[\frac{r}{\sqrt{2}}\] done
clear
C)
\[(\sqrt{2}1)r\] done
clear
D)
\[\sqrt{2}r\] done
clear
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The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is
A)
500 done
clear
B)
600 done
clear
C)
700 done
clear
D)
800 done
clear
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The length of a rectangle is threefifth of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 8 cm?
A)
112.4 sq cm done
clear
B)
104.2 sq cm done
clear
C)
100.8 sq cm done
clear
D)
Cannot be determined done
clear
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The area of a square is threefifth the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square?
A)
60 cm done
clear
B)
80 cm done
clear
C)
44 cm done
clear
D)
None of these done
clear
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The length of a rectangle is 16 cm which is 2 cm more than the diameter of a circle. What is the area of the circle?
A)
112 sq cm done
clear
B)
176 sq cm done
clear
C)
161 sq cm done
clear
D)
None of these done
clear
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The area of a rectangle is equal to the area of a circle with circumference equal to 220 m. What is the length of the rectangle of its breadth is 50 m?
A)
56 m done
clear
B)
83 m done
clear
C)
77 m done
clear
D)
69 m done
clear
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The respective ratio of the length and breadth of a rectangular plot is 3 : 2. If the length of the plot is 40 m more than its breadth, what is the perimeter of the rectangular plot?
A)
200 m done
clear
B)
400 m done
clear
C)
500 m done
clear
D)
Cannot be determined done
clear
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A copper wire is bent in the form of square with an area of 121 cm2. If the same wire is bent in the form of a circle, the radius (in cm) of the circle is \[\left( \text{take}\pi \text{=}\frac{\text{22}}{\text{7}} \right)\]
A)
7 done
clear
B)
10 done
clear
C)
11 done
clear
D)
14 done
clear
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The length of a rectangle is equal to the 3/4th of the circumference of a circle. The width of this rectangle is 2/3rd of the radius of the circle. The circumference of the circle is 264 cm. The area of rectangle is
A)
\[4654\text{ }c{{m}^{2}}\] done
clear
B)
\[4488\text{ }c{{m}^{2}}\] done
clear
C)
\[5654\text{ }c{{m}^{2}}\] done
clear
D)
None of the above done
clear
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A lawn is in the form of a rectangle having its breadth and length in the ratio 3 : 4. The area of the lawn is \[\frac{1}{12}\]hectare. The 12 breadth of the lawn is
A)
25 m done
clear
B)
50 m done
clear
C)
75 m done
clear
D)
100 m done
clear
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The area of rectangle is thrice that of a square. The length of the rectangle is 20 cm and the Q breadth of the rectangle is \[\frac{3}{2}\] times that of the side of the square. The side of the square (in cm) is
A)
10 done
clear
B)
20 done
clear
C)
30 done
clear
D)
40 done
clear
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How many tiles, each \[4\,d{{m}^{2}},\]will be required to cover the floor of a room 8 m long and 6 m broad?
A)
200 done
clear
B)
260 done
clear
C)
280 done
clear
D)
300 done
clear
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The area of an equilateral triangle is \[9\sqrt{3}\,{{m}^{2}}\] The length (in m) of the median is
A)
\[2\sqrt{3}\] done
clear
B)
\[3\sqrt{3}\] done
clear
C)
\[3\sqrt{2}\] done
clear
D)
\[2\sqrt{3}\] done
clear
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The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?
A)
100 done
clear
B)
400 done
clear
C)
500 done
clear
D)
1000 done
clear
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The three perpendicular distances of three sides of an equilateral triangle from a point which lies inside that triangle are 6 cm, 9 cm and 12 cm, respectively. The perimeter of the triangle is
A)
\[42\sqrt{2}\,cm\] done
clear
B)
\[45\sqrt{3\,}\,cm\] done
clear
C)
\[52\sqrt{2}\,cm\] done
clear
D)
\[54\sqrt{3}\,cm\] done
clear
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The ratio of the areas of the circumcircle and the in circle of a square is
A)
2 : 1 done
clear
B)
1 : 2 done
clear
C)
\[\sqrt{2}:1\] done
clear
D)
\[1:\sqrt{2}\] done
clear
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