 # SSC CGL Advance Math Series Exam Tier-II Part-13

SSC CGL Advance Math Series Exam Tier-II Part -13

SSC CGL Advance Math Series Exam Tier-II Part-13

Q1002. The radius of a circle is increased by 1%. How much does the area of the circle increase?

(a) 1%                               (b) 1.1%                             (c) 2%                                    (d) 2.01%

Q1003. The circumference of a circle is 100 cm. The measure of a side of the square inscribed in this circle is

(a) 25√2π cm                  (b)  50√2/πcm                          (c) 50√2π cm                     (d)25√2 /π cm

Q1004. In a cylindrical vessel of diameter 24 cm filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Then the increase in height of water level is:

(a) 1.5 cm                        (b) 2 cm                             (c) 3 cm                                    (d) 4.2 cm

Q1005. The floor of a corridor is 100m long and 3m wide. Cost of covering the floor with carpet 50 cm wide at the rate of Rs. 15 per m is

(a) Rs. 4500                     (b) Rs. 9000                      (c) Rs. 7500                         (d) Rs. 1900

Q1006. The diameters of two cylinders, whose volumes are equal, are in the ratio 3 : 2. Their heights will be in the ratio

(a) 4 : 9                              (b) 5 : 6                              (c) 5 : 8                                  (d) 8 : 9

Q1007. A 7 m wide road runs outside around a circular park, whose circumference is 176 m. The area of the road is: [use π = 22/7]

(a) 1386 m2                       (b) 1472 m2                      (c) 1512 m2                          (d) 1760 m2

Q1008. A cube and a sphere have equal surface areas. The ratio of their volumes is

(a) π : 6                         (b) √π  :  √6                      (c) √6 :√π                                 (d) 6 : π

Q1009. If a chord of length 16 cm is at a distance of 15 cm from the centre of the circle, then the length of the chord of the same circle which is at a distance of 8 cm from the centre is equal to

(a) 10 cm                         (b) 20 cm                           (c) 30 cm                              (d) 40 cm

Q1010. If each of the length and breadth of a rectangle is increased by 50%, by what percent does its area increase?

(a) 125                             (b) 100                               (c) 55                                   (d) 50 Q1011. A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is

(a) 896 cm3                      (b) 986 cm3                         (c) 600 cm3                          (d) 916 cm3

Q1012. The surface areas of two spheres are in the ratio 4 : 9. Their volumes will be in the ratio

(a) 2 : 3                           (b) 4 : 9                              (d) 8 : 27                            (d) 64 : 729

Q1013. if the measures of one side and one diagonal of a rhombus are 10 cm and 16 cm respectively, then its area in cm2 is:

(a) 60                         (b) 64                                  (c) 96                                 (d) 100

Q1014. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water (in litres) will fall into the sea in a minute?

(a) 4,00,000              (b) 40,00,000                      (c) 40,000                      (d) 4,000

Q1015. If a triangle with base 8 cm has the same area as a circle with radius 8 cm, then the corresponding altitude (in cm) of the triangle is

(a) 12                    (b) 20                              (c) 16                                 (d) 32

Q1016. If the height of a cone is increased by 100% then its volume is increased by:

(a) 100%                  (b) 200%                            (c) 300%                          (d) 400%

Q1017. The size of a rectangular piece of paper is 100 cmrolling the paper along its length. The volume of the cylinder is  (

(a) 4400 cm3                    (b) 15400 cm3                     (c) 35000 cm3                     (d) 144 cm3

Q1018. The circumference of a circle is 11 cm and the angle of a sector of the circle is 60. The area of the sector is(use π = 22/7)

(a) 1 29/48 cm2                 (b) 2 29/48 cm2                   (c) 1 27/48 cm2                  (d) 2 27/48 cm2

Q1019. The length and breadth of a rectangle are increased by 20% and 25% respectively. The increase in the area of the resulting rectangle will be:

(a) 60%                         (b) 50%                              (c) 40%                              (d) 30%

Q1020. The measures (in cm) of sides of a right angled triangle are given by consecutive integers. Its area (in cm2) is

(a) 9                                  (b) 8                                    (c) 5                                       (d) 6

Q1021. A solid metallic cone is melted and recast into a solid cylinder of the same base as that of the cone. If the height of the cylinder is 7 cm, the height of the cone was

(a) 20 cm                         (b) 21 cm                           (c) 28 cm                              (d) 24 cm

Q1022. The total surface area of a solid hemisphere is 108 cm2. The volume of the hemisphere is

(a) 72 cm3                      (b) 144 cm3                     (c) 108 cm3                    (d) 54 cm3

Q1023. The radius of the base and height of a right circular cone are in the ratio 5 : 12. If the volume of the cone is 314 cm3, the slant height (in cm) of the cone will be

(a) 12                     (b) 13                                  (c) 15                               (d) 17

Q1024. Each side of an equilateral triangle is 6 cm. Find its area.

(a) 9√3 sq. cm.                    (b) 6√3 sq.cm                (c) 4√3 sq. cm.                                   (d) 8√3  sq. cm.

Q1025. Lengths of the perpendiculars from a point in the interior of an equilateral triangle on its sides are 3 cm, 4 cm and 5 cm. Area of the triangle is

(a) 48 cm2                        (b) 54 cm2                   (c) 72 cm2                      (d) 80 cm2

Q1026. If the length of the diagonal of a cube is 8 cm, then its surface area is

(a) 192cm2                    (b) 512 cm2                       (c) 768 cm2                          (d) 384 cm2

Q1027. From four corners of a square sheet of side 4 cm, four pieces, each in the shape of arc of a circle with radius 2 cm, are cut out. The area of the remaining portion is:

(a) (8 –π)sq. cm.                                                             (b) (16 – 4π) sq.cm.

(c) (16 – 8π)sq. cm.                                                         (d) (4 – 2π) sq. cm.

Q1028. Each interior angle of a regular polygon is 18 more than eight times an exterior angle. The number of sides of the polygon is

(a) 10                            (b) 15                                    (c) 20                                     (d) 25

Q1029. The length of each side of an equilateral triangle is 14 cm. The area of the incircle, in cm2, is

(a) 450                            (b) 308                                  (c) 154                                   (d) 77

Q1030. A solid wooden toy is in the shape of a right circular cone shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy (nearly).

(a) 104 cm3                       (b) 162 cm3                       (c) 427 cm3                          (d) 266 cm3

Q1031. Three circles of diameter 10 cm each, are bound together by a rubber band, as shown in the figure. The length of the rubber band, in cm, if it is stretched as shown, is

(a) 30                           (b) 30 + 10π                     (c) 10π                              (d) 60 + 20π

Q1032. The area of a circle inscribed in a square of area 2m2 is

(a) π/4 m2                             (b) π/2 m2                                        (c)π m2                                 (d) 2πm2

Q1033. An equilateral triangle is drawn on the diagonal of a square. The of the area of the triangle to that of the square is

(a) √3 : 2                                (b) √2 : √3                       (c) 2 :√3                               (d) 1 :√2

Q1034. If the numerical value of the perimeter of an equilateral triangle is  times the area of it, then the length of each side of the triangle is

(a) 2 unit                        (b) 3 unit                           (c) 4 unit                              (d) 6 unit

Q1035. The perimeters of two squares are 40 cm and 24 cm. The perimeter of a third square whose area is equal to the difference of the areas of these squares, is

(a) 34 cm                             (b) 32 cm                             (c) 38 cm                              (d) 30 cm

Q1036. cylinder, having double the volume but the same height as that of the first cylinder must be equal to

(a) r/√2                         (b) 2r                                  (c) r√2                                  (d)√2r

Q1037. A right circular cylinder, a hemisphere and a right circular cone stand on the same base and have the same height. The ratio of their volumes is

(a) 3 : 6 : 1                         (b) 3 : 4 : 1                         (c) 3 : 2 : 1                            (d) 4 : 3 : 1

Q1038. The ratio of the areas of two isosceles triangles having the same vertical angle (i.e. angle between equal sides) is 1 : 4. The ratio of their heights is

(a) 1 : 4                              (b) 2 : 5                              (c) 1 : 2                                  (d) 3 : 4

Q1039. If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm2 respectively. Then the maximum length of a stick that can be placed inside the box is

(a) 5√2 cm                         (b) 5 cm                                (c) 6 cm                                                (d) 2√5 cm

Q1040. The radius of the in-circle of a triangle is 2cm. If the area of the triangle is 6 cm2, then its perimeter is

(a) 2 cm                                   (b) 3 cm                                (c) 6 cm                                     (d) 9 cm

Q1041. The base of a solid right prism is a triangle whose sides are 9 cm, 12 cm, and 15 cm. The height of the prism is 5 cm. Then, the total surface area of the prism is

(a) 180 cm2                          (b) 234 cm2                         (c) 288 cm2                          (d) 270 cm2

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