objective Ques (108 results)
SSC CGL Mains 20241)
17.70
SSC CGL Mains 20242)The ratio between the length and the breadth of a rectangular park is 3 : 2, and the perimeter of the park is 120 m. Find the area (in m2) of the park.
864
SSC CGL Mains 20243)
1330
SSC CGL 20224)The area of a triangle is 96 cm2 and the ratio of its sides is 6 ∶ 8 ∶ 10. What is the perimeter of the triangle?
48 cm
SSC CGL 20225)The minute hand of a clock is 20 cm long. Find the area on the face of the clock swept by the minute hand between 8 a.m. and 8:45 a.m.
\({{6600} \over 7}\) cm2
SSC CGL 20226)A horse is grazing in a field. It is tied to a pole with a rope of length 6 m. The horse moves from point A to point B making an arch with an angle of 70°. Find the area of the sector grazed by the horse.
22 m
SSC CGL 20227)The area of two similar triangles are 324 cm2 and 289 cm2, respectively. What is the ratio of their corresponding altitudes?
\(\frac{18}{17}\)
SSC CGL 20228)How many spherical lead shots each of diameter 8.4 cm can be obtained from a rectangular solid of lead with dimension 88 cm, 63 cm, 42 cm,\((take \pi= \frac{22}{7} ) \)?
750
SSC CGL 20229)The perimeters of two similar ΔABC and ΔPQR are 48.4 cm and 12.1 cm, respectively. What is the ratio of the areas of ΔABC and ΔPQR?
16 ∶ 1
SSC CGL 202210)A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and the lower circular ends of the frustum are 21 m and 39 m, respectively, then find the area of the cloth (in m2) used to make the tent (ignoring the wastage).
(Use \(π = \frac{{22}}{7}\))
\(2107 \frac{{2}}{7}\)
SSC CGL 202211)The sides of a triangular field are 360 m, 480 m and 600 m. Its area is equal to the area of a square field. What is the side (in m) of the square field?
\(120 \sqrt{6}\)
SSC CGL 202212)The inner circumference of a circular path enclosed between two concentric circles is 264 m. The uniform width of the circular path is 3 m. What is the area (in m2, to the nearest whole number) of the path? (Take \(\pi=\frac{22}{7} \) )
820
SSC CGL 202213)The area of a carboard (in cm2) needed to make a closed box of size 20 cm × 10 cm × 8 cm will be:
880
SSC CGL 202214)What will be the total cost (in Rs.) of polishing the curved surface of a wooden cylinder at rate of Rs. 50 per m2, if its diameter is 70 cm and height is 6 m? (Take π = \(\frac{22}{7}\) )
660
SSC CGL 202215)If the length of a diagonal of a square is (a + b), then the area of the square is:
\(\frac{1}{2}\left( {{{\rm{a}}^2} + {{\rm{b}}^2}} \right) + {\rm{ab}}\)
SSC CGL 202216)The length and the breadth of a rectangle are made to increase and decrease, respectively, by 8% and 10%. What is the percentage increase or decrease in its area?
Decrease by 2.8%
SSC CGL 202217)The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
Rs. 550
SSC CPO 202018)The base of a triangle is equal to the perimeter of a square whose diagonal is \(9\sqrt 2\) cm, and its height is equal to the side of a square whose area is 144 cm2. The area of the triangle (in cm2) is:
216
SSC CPO 202019)The internal length, breadth and height of a cuboidal room are 12 m, 8 m and 10 m, respectively. The total cost (in Rs.) of whitewashing only all four walls of the room at the cost of Rs. 25 per m2, is:
Rs. 10,000
SSC CPO 202020)The perimeter of a square is half the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then what is the area (in m2) of the rectangle ?
384
SSC CPO 202021)The sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertex, circles of radius 4.2 cm are drawn. What is the area (in cm2) of the portion covered by the three sectors of the circle ? (π = 22/7)
27.72
SSC CPO 202022)One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area (in cm2) of rhombus ?
120
SSC CPO 202023)If each side of a square is decreased by 17%, then by what percentage does its area decrease ?
31.11%
SSC CPO 202024)A 64 cm wide path is made around a circular garden having a diameter of 10 metres. The area (in m2) of the path is closest to:
21
SSC CPO 202025)The internal measures of a cuboidal room are with length as 12 m, breadth as 8 m and height as 10 m. The total cost (in Rs.) of whitewashing all four walls of the room and also ceiling of the room, if the cost of white washing is Rs. 25 per m2, is:
12,400
SSC CPO 202026)The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of a square by 10 cm and the breadth is less than 5 cm. The perimeter (in cm) of the rectangle is:
50
SSC CPO 202027)The base of a triangle is equal to the perimeter of a square whose diagonal is \( 6\sqrt 2\) cm, and its height is equal to the side of a square whose area is 144 cm2. The area of the triangle (in cm2) is:
144
SSC CPO 202028)The two parallel sides of a trapezium are 17 cm and 15 cm, respectively. If the height of the trapezium is 6 cm, then its area (in m2) is:
0.0096 m2
SSC CPO 202029)The area of a field in the shape of a hexagon is 1944√3 m2. What will be the cost (in Rs.) of fencing it at the rate of Rs. 11.50 per metre?
Rs. 2,484
SSC CPO 202030)A rectangular lawn whose length is twice of its breadth is extended by having four semi-circular portions on its sides. What is the total area (in m2) of the lawn of the smaller side of the rectangle is 12 m? (Take π = 3.14)
853.2
SSC CPO 202031)If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:
10%
SSC CPO 202032)The two parallel sides of a trapezium are 27 cm and 13 cm, respectively. If the height of the trapezium is 7 cm, then what is its area in m2?
0.014
SSC CPO 202033)A rectangular lawn whose length is twice of its breadth is extended by having four semi-circular portions on its sides. What is the total cost (in Rs.) of levelling the entire lawn at the rate of Rs. 100 per square metre, if the smaller side of the rectangular lawn is 12 m? (Take π = 3.14)
85,320
SSC CPO 202034)If a wheel has diameter 42 cm, then how far does the wheel go (in metres) in 12 revolutions? (Take π = \(\frac {22} 7 \))
15.84
SSC CPO 202035)One side of a rhombus is 13 cm and one of its diagonals is 10 cm. What is the area of the rhombus (in cm2)?
120
SSC CPO 202036)If each side of a rectangle is decreased by 11%, then its area will decrease by:
20.79%
SSC CPO 202037)The perimeter of a square is the same as the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then the area (in m2) of the rectangle is:
96
SSC Selection Post Matric 202238)The area of a triangular plot, whose side are 100 m, 105 m and 145 m, is equal to a rectangular field, whose sides are in the ratio 7 : 10. The perimeter (in m) of the rectangular field is:
\(170 \sqrt3\)
SSC Selection Post Matric 202239)The length (in m) of the longest pole that can be fitted in a room of dimensions 24 m × 12 m × 3 m is:
27
SSC Selection Post Matric 202240)A park is in a shape of a rectangle with length 180 m and breadth 120 m. At the centre of the park, there is a circular lawn of circumference 502.4 m. The area of the park, excluding the area of lawn, in m2 is: (Take π = 3.14)
1504
SSC Selection Post Matric 202241)The area of triangular field with sides 48 m, 90 m and 102 m is equal to 3 times the area of rectangular plot whose sides are in the ratio 4 ∶ 5. The perimeter of the rectangular plot is:
108 m
SSC Selection Post Matric 202242)If the diameter of the base of a cone is 24 cm and its curved surface area is \(1395\frac{3}{7}\) cm2, then its volume (in cm3) is:
Take π =\(\frac{22}{7}\)
5280
SSC Selection Post Matric 202243)The lateral surface area of a cube is 576 cm2. What is its volume (in cm3) ?
1728
SSC Selection Post Matric 202244)What is the area (in sq.m) of a circular path of uniform width of 1.4 m surrounding a circular garden of diameter 126 m? (Take π = 22/7)
560.56
SSC Selection Post Matric 202245)The breadth of a rectangular field is 7.5 m shorter than its length. One-third of the breadth is equal to one-fourth of the length of the rectangle. What is the average (in m, to the nearest integer) of its length and breadth?
26
SSC Selection Post Matric 202246)A 70 cm wide path is made around a circular garden having a diameter of 14 meters. What is the area of the path (in m2)?
10.29 \(\pi\)
SSC Selection Post Matric 202247)If the length of the diagonal of a cube is 16√3 cm, what is its lateral surface area (in sq cm)?
1,024
SSC CHSL 202148)A rectangle with perimeter 50 cm has its sides in the ratio 1 ∶ 4. What is the perimeter of a square whose area is the same as that of the rectangle?
40 cm
SSC CHSL 202149)In Δ ABC, D and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm, AC = 5 cm and the area of trapezium ACED = 32 cm2, then what will be the area of Δ BDE?
18 cm2
SSC CHSL 202150)The area of the largest triangle that can be inscribed in a semi-circle of radius 6 cm is:
36 cm2
SSC CHSL 202151)The perimeter of a rectangle is 86 cm. The numbers representing its area and breadth are in the ratio of 9 ∶ 1, respectively. The breadth of the rectangle is:
34 cm
SSC CHSL 202152)If the radius of a circle is equal to a diagonal of a square whose area is 12 cm2, then the area of the circle is:
24 π cm2
SSC CHSL 202153)A square park has been divided into two rectangles of equal area. If the perimeter of each of these rectangles is 39 m, then what will be the perimeter of the square park?
52 m
SSC CHSL 202154)If the adjacent sides of a rectangle whose perimeter is 60 cm are in the ratio 3 ∶ 2, then what will be the area of the rectangle?
216 cm2
SSC CHSL 202155)The base of a triangle is equal to the perimeter of a square whose diagonal is \(7\sqrt 2 \ cm\) and its height is equal to the side of a square whose area is 169 cm2. The area (in cm2) of the triangle is:
182
SSC CHSL 202156)One side of a rectangular field is 39 m and its diagonal is 89 m. What is the area of the field?
3120 m2
SSC CHSL 202157)In a rectangular park having dimensions 60 m × 40 m, two circular flower beds with radius 7 m are developed. What is the area of the remaining portion of the park? (use \(\pi =\frac{22}{7}\) )
2092 m2
SSC CHSL 202158)In ΔABC, the length of BC is less than twice the length of AB by 2 cm. The length of AC exceeds the length of AB by 6 cm. The perimeter is 60 cm. The length (in cm) of the largest side of the triangle ABC is:
26
SSC CHSL 202159)What is the cost (in Rs.) of levelling a triangular park with sides 60 m, 112 m and 164 m at the rate of Rs. 10.50 per m2 ?
21,168
SSC CHSL 202160)The perimeters of two similar triangles ABC and PQR are 156 cm and 46.8 cm, respectively. If BC = 19.5 cm and QR = x cm, then the value of x is:
5.85 cm
SSC CHSL 202161)ABC is a right-angled triangle, right-angled at B. D is a point on AC such that AD = 12 cm and CD = 16 cm. If BD bisects ∠ABC , then the perimeter of ΔABC will be:
67.2 cm
SSC CHSL 202162)What is the perimeter (in cm) of an equilateral triangle whose height is 3.46 cm ? Take √3 = 1.73.
12
SSC CHSL 202163)One-quarter of a circular pizza of diameter 28 cm was removed from the whole pizza. What is the perimeter (in cm) of the remaining pizza? (Take π = 22/7)
94
SSC CHSL 202164)The inner and outer radii of two concentric circles are 6.7 cm and 9.5 cm, respectively. What is the difference between their circumferences (in cm) ? Take π = 22/7
17.6
SSC CHSL 202165)The length of the base of a triangle is 3 cm smaller than the length of its altitude. Its area is 104 cm2. What is the length of the base?
13 cm
SSC CHSL 202166)From a point P that is at a distance of 15 cm from centre O of a circle of radius 9 cm, in the same plane, a pair of tangents PQ and PR is drawn to the circle. The area of quadrilateral PQOR is:
108 cm2
SSC CHSL 202167)If the perimeter of a circle is 88 cm, then what is the area of the circle? (Take π = 22/7)
616 cm2
SSC CHSL 202168)The length of a rectangle is 10 cm more than the side of a square and its breadth is 8 cm less than the side of the square. If the areas if both the rectangle and square are equal, then what will be perimeter (in cm) of the rectangle?
164
SSC CHSL 202169)The perimeter of ΔABC and ΔDEF are 39.6 cm and 26.4 cm, respectively, and ΔABC ~ ΔDEF. What is the ratio of the areas of ΔABC and ΔDEF?
9 ∶ 4
SSC CHSL 202170)The area of a triangular field whose sides are 65 m, 72 m, and 97 m is equal to the area of a rectangular park whose sides are in the ratio of 5 ∶ 13. What is the perimeter (in m ) of the rectangular park?
216
SSC CHSL 202171)The lengths of three sides of a triangle are in the ratio 3 ∶ 4 ∶ 5. Among three sides, the difference between the largest side and the smallest side of this triangle is 3.6 cm. The area (in \(cm^2\)) of the triangle is:
19.44
SSC CHSL 202172)The area of a triangular field whose sides are 96m, 110m, and 146 m is equal to the area of a rectangular park whose sides are in the ratio 3 ∶ 2. What is the perimeter (in m) of the rectangular park?
40√ 55
SSC CHSL 202173)The diameter of a wheel is 1.33 m. What distance (in m, to the nearest whole number) will it travel in 380 revolutions?
(take π = 22/7)
1588
SSC CHSL 202174)The perimeter of an isosceles triangle is 91 cm and its base is \(1 \frac{1}{4}\) times each of its equal sides. What is the length (in cm) of its base?
35
SSC CHSL 202175)The length of the base of a right-angled triangle is 40 cm and its hypotenuse is 41 cm long. What is its area (in cm2) and perimeter (in cm), respectively?
180 and 90
SSC CHSL 202176)The area of a circle that is inscribed in a square of area \(17 \frac {9}{11} cm^2\) is :
14 cm2
SSC CHSL 202177)In ΔABC, medians BE and CF are perpendicular to each other and intersect at M. If BE = 9 cm and CF = 13 cm, then the area of ΔABC will be:
78 cm2
SSC CHSL 202178)If the area of a right-angled isosceles triangle is 676 cm2, then the length of its hypotenuse is:
52 cm
SSC CHSL 202179)Two circular football grounds of radius 42 m and 35 m are to be replaced with a bigger circular ground. What would be the radius of this new ground if the new ground has the same area as the sum of the two small grounds?
\(\sqrt{2989}\) m
SSC CHSL 202180)The perimeter of an isosceles triangle is 3.6 m and its base is 30 cm shorter than each of the equal sides. What is the area (in m2) of the triangle?
0.6
SSC CHSL 202181)The diameter of a semicircle is 5.6 m what is its perimeter (in m, correct to one decimal place)? ( Take \( \pi = \frac{{22}}{7}\) )
14.4
SSC CHSL 202182)The sum of the radii of two circles is 286 cm and the area between the concentric circle is 50336 cm2 what are the radii (in cm) of the two circles? Take \( \pi =\frac{{22}}{7}\)
115 and 171
SSC CHSL 202183)ΔABC ~ ΔPQR. The perimeters of ΔABC and ΔPQR are 72 cm and 43.2 cm, respectively. What is the ratio of the are area of ΔABC to the area of ΔPQR?
25 ∶ 9
SSC CHSL 202184)ΔABC ~ ΔEDF, Area ABC ∶ Area DEF = 49 ∶ 4. If AB, AC, BC are, respectively, 10 cm, 14 cm, 21 cm, then what is the length (in cm) of EF?
4
SSC CHSL 202185)The perimeter and the area of a rectangular sheet are 42 m and 108 m2, respectively. The length of the diagonal is:
15 m
SSC CHSL 202186)A wire is bent to form a square of area 169 cm2.If the same wire is bent to form a circle, then what is its area (in cm2, to the nearest whole number)?
Take [\(\pi = \frac{{22}}{7}\) ]
215
SSC CHSL 202187)What is the perimeter of a right-angled triangle whose sides (making 90°) are 20√3 cm and 15√3 cm?
60√3 cm
SSC CHSL 202188)The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:
840
SSC CHSL 202189)What is the area (in \(m^2\), up to 1 place of decimal) of an equilateral triangular field of side 8.5 m?
\(18.1\sqrt3\)
SSC CHSL 202190)Find the area (in cm2) and the diameter (in cm), respectively, of a circle whose circumference is 40π cm?
400 π and 40
SSC CHSL 202191)One diagonal of a rhombus is 8√3 cm. If the other diagonal is equal to its side, then the area (in \(cm^2\) ) of the rhombus is:
32√3
SSC CGL 202092)The diagonal of a square A is (a + b) units. What is the area (in square units) of the square drawn on the diagonal of square B whose area is twice the area of A?
\(2(a+b)^2\)
Area of square A = \( \frac{(diagonal)^2}{2} = \frac{(a + b)^2}{2}\) ;
Area of square B = \(2 \times area \space of \space square A = 2\times \frac{(a + b)^2}{2} = (a + b)^2\) ;
Side of B = a + b ;
Diagonal of B = \(\sqrt{2} side = \sqrt{2}(a+b)\) ;
Area (in square units) of the square drawn on the diagonal of square B = \((side)^2 = (\sqrt{2}(a+b))^2 = 2(a + b)^2\)
SSC CGL 202093)The perimeter of a square is 64 cm. Its area will be:
256 \(cm^2\)
Perimeter of square = 64 cm ; ⇒ 4 x Side = 64; ⇒ Side = 16 cm; Area of square = \((Side)^2=(16)^2 = 256 \space cm^2\)
SSC CGL 202094)A metallic sphere of diameter 40 cm is melted into smaller spheres of radius 0.5 cm each. How many such small balls can be made?
64,000
Number of smaller balls = \({Volume \space of\space bigger \space ball\over Volume\space of \space a\space smaller\space ball}\) = \({{4\over3}\pi R^3\over {4\over3}\pi r^3}=({20\over0.5})^3= 64000\)
SSC CGL 202095)A circular disc of area \(0.64\pi\space m^2\) rolls down a length of 1.408 km. The number of revolutions it makes is: (Take \(\pi ={22\over7}\))
280
Area = \(\pi r^2\);
\(\pi r^2= 0.64\pi\space m^2\);
r = 0.8 m;
Circumference of disc = \(2 \pi r = 2 \times (22/7) \times 0.8 = 5.02\) ;
Length = 1.408 km = 1408 m;
The number of revolutions = 1408/5.02 = 280
SSC CGL 202096)The inner and outer radius of a circular track are 29 m and 23 m respectively. The cost of leveling the track at Rs. 7 per sq. metre is :
Rs. 6,864
Radius of outer circle = 29 m;
Radius of inner circle = 23 m;
Area of the circular track = \(\pi (R^2-r^2)\);
Total cost of leveling the track = \({22\over7}(29^2-23^2)\times7\) = Rs. 6864
SSC CGL 202097)Two circles of radii 8 cm and 6 cm touch each other externally. The length of the direct common tangent is:
13.86 cm
The length of the direct common tangent = \(2\sqrt{r1.r2}\);
r1 = 8 cm;
r2 = 6 cm;
The length of the direct common tangent = \( 2\sqrt{8 \times 6} = 2\sqrt{48} = 2 \times 6.93 = 13.86 cm\)
SSC CGL 202098)The area of the four walls of a room having length 6 m, breadth 4 m and height 4 m, is:
80 sq. metre
l = 6m, b = 4m, h = 4m ; Area of four walls of a room = \(2\times h(l+b)=2\times4(6+4)\) = 80 sq. metre
SSC CGL 202099)The perimeter of an isosceles triangle is 50 cm.If the base is 18 cm, then find the length of the equal sides.
16 cm
Let Each equal side of isosceles triangle = x cm.
According to the question, x + x + 18 = 50; ⇒ x = 16 cm.
SSC CGL 2020100)If the perimeter of a certain rectangle is 50 units and its area is 150 sq. units, then how many units is the length of its shorter side?
10
Let, the length of rectangle= x units; Its width = y units; According to the question, 2(x+y) = 50;
x + y = 25 ---(1) ; and, xy = 150___(2); \((x-y)^2=(x+y)^2-4xy\) \(=(25)^2-4\times150=25\); ⇒ \(x-y=\sqrt{25} =5\)____(3);
By equation (1) - (3) we have; x + y - x + y = 25 - 5 = 20; So y = 10 units
SSC CGL 2020101)Find the area and circumference of a circle if the radius is 14 cm.(Take \(\pi= {22\over7}\))
Area = \(616 \)\(cm^2\); circumference = 88 cm
Radius of circle = 14 cm. ;
Area of circle = \(\pi r^2={22\over7}\times{(14)^2}= 616 cm^2\);;
Circumference of circle = \(2\pi r = 2\times{22\over7}\times 14 = 88 cm\)
SSC CGL 2020102)What is the area of a triangle whose sides are 3 cm, 5 cm and 4 cm?
\(6\) \(cm^2\)
By triplet 3-4-5, the triangle will be right angle triangle so,
5 will be hypotenuse.
Area of triangle = \({1\over2}\times base\times height\) = \({1\over2}\times3\times4 = 6 \) \(cm^2\)
SSC CGL 2020103)The perimeter of a square plot is the same as that of a rectangular plot with sides 35 m and 15 m. The side of the square plot is:
25 metre
The perimeter of a rectangular plot = 2(length + breadth) = 2(35 + 15) = 100 m;
The perimeter of a square plot = perimeter of a rectangular plot;
The perimeter of a square plot = 100 m;
100 = 4 side;
side = 100/4 = 25 m
SSC CGL 2020104)A wheel covers a distance of 1,100 cm in one round. The radius of the wheel is :
175 cm
A wheel covers a distance of 1,100 cm in one round so,
Perimeter of wheel = 1100 cm;
\(2\pi r\) = 1100;
r = \(550\times\frac{7}{22}\) = 175 cm;
Diameter = 2r = 2 175 = 350 cm
SSC CGL 2019105)A field roller, in the shape of a cylinder, has a diameter of 1 m and length of \(1\frac{1}{4}\) m. If the speed at which the roller rolls is 14 revolutions per minute, then the maximum area (in square m ) that it can roll in 1 hour is: (Take \(\pi={22\over7}\) )
3300
Area covered in single revolution = \(2 \pi rh\) ;
Area covered in 1 hour = \({2\times {22\over 7} \times {1\over 2} \times {5\over 4} \times 14 \times 60} = 3300 cm^2\)
SSC CGL 2019106)In a trapezium ABCD, \(DC \parallel AB \), AB = 12 cm and DC = 7.2 cm. What is the length of the line segment joining the midpoints of its diagonals?
2.4 cm
By the property, EF = \(\frac{AB - CD}{2} = \frac{12 - 7.2}{2} = \frac{4.8}{2} \)= 2.4 cm
SSC CGL 2019107)In \(\triangle ABC\), D and E are the points on sides AB and BC respectively such that DE||AC . If AD : DB = 5 : 3, then what is the ratio of the area of \(\triangle BDE\) to that of the trapezium ACED?
9 : 55
\(\triangle ABC ~ \triangle DEB;\)
(\because DE is parallel to AC);
\(\angle B\) is a common angle.
So, ratio area of the \( \triangle BDE : \triangle ABC \);
\((3)^2 : (3 + 5)^2\) = 9 : 64;
Area of trapezium ACED = area of the \(\triangle ABC - \triangle BDE \)= 64 - 9 = 55;
Ratio of the area of\( \triangle BDE\) to that of the trapezium ACED = 9 : 55
SSC CGL 2020108)What is the area of a sector of a circle of radius 14 cm and central angle 45 degree? take \(\pi = {22 \over 7} \)
77 sqcm
Area of Sector = \(x = \pi r^2 .{\theta \over 360 } = 77 cm^2\)