SSC MTS MATHS QUIZ

Question 1:

Four goats are tied to each corner of a square plot of sides 18 metre with rope of 7 metre long each. Find the ungrazed area?

$180 \mathrm{~cm}^{2}$

$150 \mathrm{~cm}^{2}$

$170 \mathrm{~cm}^{2}$

$210 \mathrm{~cm}^{2}$

Question 2:

A Circular pavement was to be built around a square park of side $16 \mathrm{~m}$. The maximum width of pavement is $6 \mathrm{~m}$. Calculate the cost of cementing the pavement at Rs. 15 per $\mathrm{m}^{2}$.

Rs. 4750

Rs. 4380

Rs.5475

Rs. 5400

Question 3:

The diameter of the base of right circular cone is 10cm and its height is 12cm . What is the total surface area of cone ?

84π

90π

70π

65π

Question 4:

Find the total surface area of a cone, If its slant height is $21 \mathrm{~m}$ and diameter of its base is $24 \mathrm{~m}$. $\left[\right.$Assume $\left.\pi=\frac{22}{7}\right]$?

$1230.57 \mathrm{~m}^{2}$

$1244.57 \mathrm{~m}^{2}$

$1326 \cdot 67 \mathrm{~m}^{2}$

$1340.73 \mathrm{~m}^{2}$

Question 5:

A cylindrical pillar is $50 \mathrm{~cm}$ in diameter and $3.5 \mathrm{~m}$ in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. $12.50$ per $\mathrm{m}^{2}$. [Assume $\left.\pi=\frac{22}{7}\right]$

Rs.$68.75$

Rs.$78.32$

Rs.$62.36$

Rs.$72.34$

Question 6:

The diameter of a roller is $84 \mathrm{~cm}$ and its length is $120 \mathrm{~cm}$. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground . [Assume $\left.\pi=\frac{22}{7}\right]$

$1680 \mathrm{~m}^{2}$

$1782 \mathrm{~m}^{2}$

$1530 \mathrm{~m}^{2}$

$1584 \mathrm{~m}^{2}$

Question 7:

It is required to make a closed cylindrical tank of height $1 \mathrm{~m}$ and base diameter $140 \mathrm{~cm}$ from a metal sheet. How many square meters of the sheet are required for the same? [Assume $\left.\pi=\frac{22}{7}\right]$

$3.42 \mathrm{~m}^{2}$

$5.67 \mathrm{~m}^{2}$

$7.48 \mathrm{~m}^{2}$

$6.24 \mathrm{~m}^{2}$

Question 8:

The length, breadth and height of a room are $5 \mathrm{~m}, 4 \mathrm{~m}$ and $3 \mathrm{~m}$ respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs $7.50$ per $\mathrm{m}^{2}$.

460 Rs.

480 Rs.

560 Rs.

555 Rs.

Question 9:

The sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is $540 \mathrm{~cm}$. Find its area?

$8000 \mathrm{~cm}^{2}$

$9000 \mathrm{~cm}^{2}$

$12000 \mathrm{~cm}^{2}$

$10000 \mathrm{~cm}^{2}$

Question 10:

The angles of quadrilateral are in the ratio $3: 5: 9: 13$. Find the smallest angles of the quadrilateral.

$27^{\circ}$

$54^{\circ}$

$36^{\circ}$

$30^{\circ}$

Question 11:

The circumference of the base of a cylinder is $88 \mathrm{~cm}$ and its height is $15 \mathrm{~cm}$. Find its curved surface area and total surface area.

$2552 \mathrm{~cm}^{2}$

$2545 \mathrm{~cm}^{2}$

$2595 \mathrm{~cm}^{2}$

$2652 \mathrm{~cm}^{2}$

Question 12:

In an equilateral $\triangle \mathrm{ABC}$, the medians $\mathrm{AD}, \mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$, if the area of quadrilateral $\mathrm{AEGF}$ is $192 \sqrt{3} \mathrm{~cm}^{2}$, then find the length of $A D$ (in $\mathrm{cm}$ ).

$24 \sqrt{3}$

$14 \sqrt{3}$

$18 \sqrt{3}$

$12 \sqrt{3}$

Question 13:

A solid sphere of radius $2 \mathrm{~cm}$ is melted to convert in to a wire of length is $100 \mathrm{~cm}$. The radius of the wire.

$0.24 \mathrm{~cm}$

$0.27 \mathrm{~cm}$

$0.48 \mathrm{~cm}$

$0.33 \mathrm{~cm}$

Question 14:

The area of two similar triangles $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are 25 and 36 sq. unit. what is the ratio of their corresponding perimeter ?

$5: 6$

$25: 26$

$36: 42$

$6: 5$

Question 15:

The three different face diagonals of a cuboid are 39,40 and 41 respectively. Find the diagonal of the cuboid.

49

48

42

46

Question 16:

The area of a right angle triangle is 2520 $\mathrm{cm}^{2}$ and its hypotenuse is $106 \mathrm{~cm}$. Then find the perimeter.

250

252

156

224

Question 17:

A circular pavement was to be built around a square park of side is $12 \mathrm{~cm}$. The maximum width of pavement is $4 \mathrm{~m}$. calculate the cost of cementing the pavement at Rs. 16 per $\mathrm{m}^{2}$.

Rs.$2724 \cdot 48$

Rs.$2224 \cdot 50$

Rs.$2924 \cdot 45$

Rs.$2624 \cdot 49$

Question 18:

If the difference between the circumference and diameter of a circcle is $120 \mathrm{~cm}$ then the radius of the circle must be.

$28 \mathrm{~cm}$

$32 \mathrm{~cm}$

$14 \mathrm{~cm}$

$21 \mathrm{~cm}$

Question 19:

The edges of a rectangular box area in ratio $2: 3: 4$ and its surface area is $832 \mathrm{~cm}^{2}$ then find volume of the box .

$1520 \mathrm{~cm}^{3}$

$1505 \mathrm{~cm}^{3}$

$1496 \mathrm{~cm}^{3}$

$1536 \mathrm{~cm}^{3}$

Question 20:

A wire when bent in the form of a square enclosed a region of area $112.36 \mathrm{~cm}^{2}$. If the same wire is bent into the form of a circle, then the area of the circle is.

$124.36 \mathrm{~cm}^{2}$

$156.38 \mathrm{~cm}^{2}$

$142.70 \mathrm{~cm}^{2}$

$120.30 \mathrm{~cm}^{2}$

Question 21:

In an equilateral $\triangle A B C$, the madians $\mathrm{A} \mathrm{D}$, $\mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$. if the area of triangle AGE is $12 \sqrt{3} \mathrm{~cm}^{2}$, then find the lentght of AD.

$12 \sqrt{2}$

$8 \sqrt{2}$

$10 \sqrt{2}$

$6 \sqrt{2}$

Question 22:

In an euqilateral $\triangle A B C$, the medians, $\mathrm{AD}$, $\mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$. If the area of quardrilateral AEGF is $86 \sqrt{3} \mathrm{~cm}^{2}$, then find the length of $A D$ in $(\mathrm{cm})$.

$4 \sqrt{258} \mathrm{~cm}$

$2 \sqrt{258} \mathrm{~cm}$

$6 \sqrt{253} \mathrm{~cm}$

$2 \sqrt{257} \mathrm{~cm}$

Question 23:

The length, breadth and height of a room are $5 \mathrm{~m}, 4 \mathrm{~m}$ and $3 \mathrm{~m}$ respectively. Find the cost(in rupees) of white-washing the walls of the room and the ceiling at the rate of Rs $7.50$ per $\mathrm{m}^{2}$.

500

230

555

268

Question 24:

The paint in a certain container is sufficient to paint an area equal to $9.375 \mathrm{~m}^{2}$. How many bricks of dimensions $22.5 \mathrm{~cm} \times 10 \mathrm{~cm} \times 7.5 \mathrm{~cm}$ can be painted out of this container?

150

100

280

170

Question 25:

It is required to make a closed cylindrical tank of height 1m and base diameter 140 cm from a metal sheet. How many square meters of the sheet is required for the same?

6.72

7.98

6.5

7.48

Question 26:

The diameter of a roller is $84 \mathrm{~cm}$ and its length is $120 \mathrm{~cm}$. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^{2}$ ? [Assume $\pi=\frac{22}{7}$ ]

1,650

1,584

1,824

1,534

Question 27:

The curved surface area of a right circular cylinder is $4.4 \mathrm{~m}^{2}$. If the radius of the base of the cylinder is $0.7 \mathrm{~m}$, find its height. [Assume $\pi=\frac{22}{7}$ ]

5 m

4 m

7 m

1 m

Question 28:

Find the total surface area of a cone, if its slant height is 21m and diameter of its base is 24m.

$1258 \mathrm{~m}^{2}$

$1248 \mathrm{~m}^{2}$

$1248.75 \mathrm{~m}^{2}$

$1244.57 \mathrm{~m}^{2}$

Question 29:

The slant height and base diameter of a conical tomb are $25 \mathrm{~m}$ and $14 \mathrm{m}$ respectively. Find the cost(in rupees) of white-washing its curved surface at the rate of Rs 210 per $100 \mathrm{~m}^{2}$.

1200

1172

1175

1155

Question 30:

A hemispherical bowl made of brass diameter $10.5 \mathrm{~cm}$. Find the cost(in rupees) of plating it on the inside at the rate of Rs. 16 per $100 \mathrm{~cm}$.

25.42

27.72

35.84

12.12

Question 31:

A matchbox measures 4cm × 2.5cm × 1.5cm. What will be the volume of a packet containing 12 such boxes?

$180 \mathrm{~cm}^{3}$

$208 \mathrm{~cm}^{3}$

$154 \mathrm{~cm}^{3}$

$192 \mathrm{~cm}^{3}$

Question 32:

The capacity of a cubical tank is 50,000 litres of water. Find the breadth of the tank, if its length and depth are 2.5m and 10m respectively.

2 m

5 m

8 m

12 m

Question 33:

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

20

25

40

30

Question 34:

Perimeter of rectangle is equal to the perimeter of square whose area is 900 cm² and length of rectangle is 20% more than the side of a square then find the area of rectangle?

$861 \mathrm{~cm}^{2}$

$862 \mathrm{~cm}^{2}$

$863 \mathrm{~cm}^{2}$

$864 \mathrm{~cm}^{2}$

Question 35:

If D.C.S of two lines are propartional to (2, $3,-6)$ and $(3,-4,5)$ then teh a cute angle between then is

$\cos ^{-1}\left(\frac{49}{36}\right)$

$\cos ^{-1}\left(\frac{18 \sqrt{2}}{35}\right)$

$90^{\circ}$

$\cos ^{-1}\left(\frac{18}{35}\right)$

Question 36:

If the lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are at right angle then $\mathrm{k}$ $=?$

$-10$

$\frac{10}{7}$

$\frac{-10}{7}$

$\frac{-7}{10}$

Question 37:

What is the angle between two planes $2 x-$ $y+z=4$ and $x+y+2 z=6$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

Question 38:

The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

$(1,0,7)$

$(-1,0,7)$

$(1,0,7)$

None of these

Question 39:

The angle between the lines $\frac{x+1}{3}=\frac{y-1}{4}=\frac{z-2}{2}$ and the plane $2 \mathrm{x}-3 \mathrm{y}$ $+z+4=0$ is:

$\cos ^{-1}\left(\frac{-4}{\sqrt{406}}\right)$

$\sin ^{-1}\left(\frac{-4}{\sqrt{406}}\right)$

$\sin ^{-1}\left(\frac{4}{\sqrt{406}}\right)$

None of these

Question 40:

Circumference of a circle is equal to the perimeter of a square. What is ratio of area of the circle and the area of the square?

1 : 1

7 : 11

14 : 11

11 : 14

Question 41:

Circumference of a circle is equal to the perimeter of a equilateral triangle. Radius of the circle is 21 cm. What is the area of the equilateral triangle approximately in cm²?

837

838

839

840

Question 42:

In a rectangle, the length is $3 \mathrm{~cm}$ more than its breadth and the area of rectangle is $180 \mathrm{~cm}^{2}$. If a square is made by taking the breadth of rectangle as its side. Then find the perimeter of square.

$50 \mathrm{~cm}$

$41 \mathrm{~cm}$

$48 \mathrm{~cm}$

$44 \mathrm{~cm}$

Question 43:

Perimeter of a square $A$ is $60 \sqrt{2} \mathrm{~cm}$. What is the area of square B whose side is equal to the diagonal of square A? (in $\mathrm{cm}^{2}$ )

450

$240 \sqrt{2}$

900

3600

Question 44:

Length of a rectangle is increased by $15 \%$ and its breadth is decreased by $20 \%$, what will be the percentage change in its perimeter?

Decrease by $8 \%$

Decrease by $5 \%$

No change

Increase by $8 \%$

Question 45:

What is the maximum number of spherical balls, each $5 \mathrm{~cm}$ in diameter which can be made from a spherical ball of $45 \mathrm{~cm}$ radius?

729

5632

6032

841

Question 46:

Area of a given circle is $2464 \mathrm{~m}^{2}$. Perimeter of a rectangle is same as perimeter of circle. Find the diagonal (in $\mathrm{m}$ ) of the rectangle if length of rectangle is $20 \%$ more than the breadth of the rectangle.

$8 \sqrt{65}$

$8 \sqrt{61}$

$8 \sqrt{57}$

$4 \sqrt{65}$

Question 47:

Length of the rectangular field is $50 \%$ more than the breadth of the field. What will be the cost of fencing the field whose area is $726 \mathrm{sq} . \mathrm{m}$ and the cost of fencing is Rs. 8.5 per meter ? (in rupees).

935

890

845

865

Question 48:

A spherical cannon ball of radius 24 cm is melted and casted into two cylinders of equal size and shape having base radius 16 cm. Find the height of each cylinder?

36 cm

18 cm

32 cm

20 cm

Question 49:

A path of width 1.5 m is to be built around a rectangular park of length 12 m and breadth 9 m. Find the area of the rectangular path.

$72 \mathrm{~m}^{2}$

$60 \mathrm{~m}^{2}$

$75 \mathrm{~m}^{2}$

$80 \mathrm{~m}^{2}$

Question 50:

The diameter of a circle is doubled. By how much does the area increase?

2 times

4 times

8 times

16 times

Question 51:

The ratio of the length and breadth of a rectangle is $6: 5$ and its area is $6,750 \mathrm{~cm}^{2}$. Find the ratio of the breadth to the area of the rectangle.

$1: 80$

$1: 84$

$1: 100$

$1: 90$

Question 52:

What is the cost of leveling a triangular piece of land whose sides are $72 \mathrm{~m}$, $30 \mathrm{~m}$ and $78 \mathrm{~m}$ respectively at the rate of 20 paise per square metre?

Rs. 200

Rs. 210

Rs. 220

Rs. 216

Question 53:

A parallelogram PQRS whose sides are of lengths $8 \mathrm{~cm}$ and $12 \mathrm{~cm}$, has a diagonal of length $10 \mathrm{~cm}$. The length of the second diagonal is approximately:

$17.5 \mathrm{~cm}$

$18 \mathrm{~cm}$

$17 \mathrm{~cm}$

$17.8 \mathrm{~cm}$

Question 54:

The height and slant height of a right circular cone are $24 \mathrm{~cm}$ and $25 \mathrm{~cm}$ respectively. Considering the value of $\pi$ as $\frac{22}{7}$, find the curved surface area of the cone.

$572 \mathrm{~cm}^{2}$

$528 \mathrm{~cm}^{2}$

$539 \mathrm{~cm}^{2}$

$550 \mathrm{~cm}^{2}$

Question 55:

The ratio of length and breadth of a rectangle is $3: 1$. If its perimeter is $96 \mathrm{~m}$, then what will be the length of the rectangle?

$48 \mathrm{~m}$

$24 \mathrm{~m}$

$36 \mathrm{~m}$

$12 \mathrm{~m}$

Question 56:

A sphere of radius $9 \mathrm{~cm}$ is moulded to form a cylinder of radius $3 \mathrm{~cm}$. Find the height of the cylinder.

$54 \mathrm{~cm}$

$108 \mathrm{~cm}$

$162 \mathrm{~cm}$

$216 \mathrm{~cm}$

Question 57:

The length of one side of a rhombus and one of the two diagonals is $6 \mathrm{~cm}$. The area of a rhombus is......... $\mathbf{c m}^{2}$.

18

$9 \sqrt{3}$

$27 \sqrt{3}$

$18 \sqrt{3}$

Question 58:

The sum of the lengths of the sides of a cube is $3 / 5$ of the perimeter of the square. If the numerical value of the volume of a cube is equal to the numerical value of the area of the square, then the perimeter of the square is

500 unit

300 unit

360 unit

480 unit

Question 59:

The number of diagonals in a polygon of 27 sides is:

324

320

322

325

Question 60:

In $\triangle \mathrm{ABC}$, if $\angle \mathrm{A}=90^{\circ}, \mathrm{a}=25$ cm, $\mathrm{b}=7$ cm, then What will be the value of $\tan \mathrm{B}$?

$\frac{24}{7}$

$\frac{24}{25}$

$\frac{7}{25}$

$\frac{7}{24}$

Question 61:

The volume (in cubic $\mathrm{cm}$ ) of a right circular cylinder with radius $2 \mathrm{~cm}$ and height $2\mathrm{~m}$ is: (take $\pi=\frac{22}{7}$ )

$\frac{175}{7}$

$\frac{176}{21}$

$\frac{17600}{7}$

176

Question 62:

The surface area (in $\mathrm{sq. cm}$ ) of a sphere with radius $2 \mathrm{~cm}$ is: ( Take $\pi=\frac{22}{7}$ )

$\frac{352}{7}$

$\frac{350}{21}$

$\frac{352}{21}$

$\frac{350}{7}$

Question 63:

The ratio between the length and breadth of a rectangular room is $3: 2$. If only length is increased by $5 \mathrm{~m}$. The new area of room is $4000 \mathrm{~m}^{2}$. What is the breadth of a rectangular room is.

25

50

40

60

Question 64:

A room 9 meter long, 7 meter breadth and 3 $\mathrm{m}$ height has two windows $1 \frac{1}{2} \mathrm{~m} \times 1 \mathrm{~m}$ and a door $2 \mathrm{~m} \times 1 \frac{1}{2} \mathrm{~m}$. Find the cost of papering the wall with paper $50 \mathrm{~cm}$ wide at 25 paise meter.

Rs. 45

Rs. 50

Rs. 60

Rs. 75

Question 65:

The area of a circular field is equal to the area of a rectangular field. The ratio of length and breadth of the rectangular field is 17:13 respectively and the perimeter is 120 meters. What is the diameter of the circular field?

$2 \sqrt{\frac{3086}{11}}$

$2 \sqrt{\frac{3094}{11}}$

$\sqrt{\frac{3094}{11}}$

None of these

Question 66:

The perimeter of a semi-circular field is $72 \mathrm{~cm}$, find its radius.

$14 \mathrm{~cm}$

$7 \mathrm{~cm}$

$21 \mathrm{~cm}$

$28 \mathrm{~cm}$

Question 67:

Two spheres each of $15 \mathrm{~m}$ radius is melted down and recast into a cone with a height equal to the radius it's base. Find the height of the cone.

15$\mathrm{m}^{3}$

20$\mathrm{m}^{3}$

45$\mathrm{m}^{3}$

30$\mathrm{m}^{3}$

Question 68:

If the length and perimeter of a rectangle are in the ratio $1: 3$ and the area of rectangle is $338 \mathrm{~cm}^{2}$, then the breadth (in $\mathrm{cm}$ ) of the rectangle is:

11

12

13

14

Question 69:

Ratio of sides of a triangle is $17: 8: 15$, If perimeter is $96 \mathrm{~cm}$ then find the area of triangle.

$329.6 \mathrm{~cm}^{2}$

$324.6 \mathrm{~cm}^{2}$

$336.6 \mathrm{~cm}^{2}$

$345.6 \mathrm{~cm}^{2}$

Question 70:

Two equal circle intersect at $\mathrm{A}$ and $\mathrm{B}$. $\mathrm{C}$ and $\mathrm{D}$ are the centres of circles. If $\mathrm{ABCD}$ is a square of side $4 \mathrm{~cm}$, then find the area of shaded region (in $\mathrm{cm}^{2}$ )

$4 \pi-1$

$4 \pi-4$

$8 \pi-8$

$8 \pi-16$

Question 71:

Find the area of a square whose diagonal is half of 12 cm.

18 sq. cm

64 sq. cm

36sq . cm

72 sq. cm

Question 72:

The height of a cone is $45 \mathrm{~cm}$ and perimeter of its base is $176 \mathrm{~cm}$. What is the curved surface area of the cone? (take $\pi=\frac{22}{7}$ )

$4559 \mathrm{~cm}^{2}$

$4664 \mathrm{~cm}^{2}$

$4881 \mathrm{~cm}^{2}$

$4224 \mathrm{~cm}^{2}$,

Question 73:

A metallic hollow hemispherical bowl is made up of copper. The total copper used in making the bowl is $5022 \pi \mathrm{cm}^{3}$. The bowl can hold $1152 \pi \mathrm{cm}^{3}$ water. What is the thickness (in $\mathrm{cm}$ ) of bowl and the total surface area (in $\mathrm{cm}^{2}$ ) of the hemispherical bowl?

$8$ cm, $1116 \pi$ cm²

$12$ cm, $3819 \pi$ cm²

$9$ cm, $1467 \pi$ cm²

$9$ cm, $1469 \pi$ cm²

Question 74:

A hollow cylinder is made up of steal. The difference in its outer and inner CSA is 132 $\mathrm{cm}^{2}$. Height of cylinder is $21 \mathrm{~cm}$ and sum of its inner and outer radius is also $21 \mathrm{~cm}$. Then find the TSA of the hollow cylinder (in $\mathrm{cm}^{2}$ )

2904

2784

2524

3224

Question 75:

Area a of a isosceles trapezium is $312 \mathrm{~cm}^{2}$. If the parallel sides are in the ratio $8: 5$ and distance between them is $\left(\frac{3}{13}\right)$ th of the sum of its parallel sides, then the length of its diagonal (cm) is

$\sqrt{205}$

$2 \sqrt{41}$

$2 \sqrt{205}$

$4 \sqrt{205}$

Question 76:

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the 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. What is the curved surface area of the of conical surface?

$381.55 \mathrm{~m}^{2}$

$428.87 \mathrm{~m}^{2}$

$490.28 \mathrm{~m}^{2}$

$462 \mathrm{~m}^{2}$

Question 77:

A square whose Diagonal is $12 \sqrt{2} \mathrm{~cm}$ is made base of the pyramid. If height of the pyramid is $18 \mathrm{~cm}$, then what is the total surface area (in $\mathrm{cm}^{2}$ ) of the pyramid?

$72(\sqrt{3}+1)$

$144(\sqrt{10}+1)$

$144(\sqrt{10}+2)$

$72(\sqrt{10}+2)$

Question 78:

Water is flowing from a cylindrical pipe 8 $\mathrm{mm}$ in diameter at rate of 12 meter per minute. How long (time in seconds) will it take to fill up a conical vessel whose radius is $16 \mathrm{~cm}$ and height is $9 \mathrm{~cm}$.

$210 \mathrm{sec}$

$240 \mathrm{sec}$

$300 \mathrm{sec}$

$195 \mathrm{sec}$

Question 79:

If the edge of a cube be $10.5 \mathrm{~cm}$, then the volume of the cube is:

$1157.625 \mathrm{~cm}^{3}$

$1174.125 \mathrm{~cm}^{3}$

$1236.625 \mathrm{~cm}^{3}$

$1289.125 \mathrm{~cm}^{3}$

Question 80:

A wheel has a diameter of $84 \mathrm{~m}$. How many revolutions should it make to cover a distance of $792 \mathrm{~m}$ ? $\left(\pi=\frac{22}{7}\right)$

8

3

2

5

Question 81:

Find the cost of carpeting a room $13 \mathrm{~m}$ long and $9 \mathrm{~m}$ broad with a carpet $75 \mathrm{~cm}$ wide at the rate of Rs. $12.40$ per metre?

Rs. $1934.40$

Rs. $1265.43$

Rs. $1374.40$

Rs. $1005.21$

Question 82:

In an equilateral $\triangle \mathrm{ABC}$, the medians $\mathrm{AD}, \mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$, if the area of triangle $\mathrm{AGE}$ is $8 \sqrt{3} \mathrm{~cm}^{2}$, then find the length of $\mathrm{AD}$ (in $\mathrm{cm}$ ).

$8 \sqrt{3}$

$12$

$16$

$18$

Question 83:

One side of rectangular field is $15 \mathrm{~m}$ and one of its diagonals is $17 \mathrm{~m}$ find the area of the field?

$75 \mathrm{~m}^{2}$

$120 \mathrm{~m}^{2}$

$240 \mathrm{~m}^{2}$

$350 \mathrm{~m}^{2}$

Question 84:

If the diagonal of a cube is $\sqrt{363} \mathrm{~cm}$, then its volume is:

$363 \sqrt{3} \mathrm{~cm}^{3}$

$729 \mathrm{~cm}^{3}$

$1131 \sqrt{3} \mathrm{~cm}^{3}$

$1331 \mathrm{~cm}^{3}$

Question 85:

A wheel makes 12 revolutions per min. The angle in degree described by a spoke of the wheel in $1 \mathrm{~Sec}$ is.

$60^{\circ}$

$72^{\circ}$

$52^{\circ}$

$45^{\circ}$

Question 86:

If the edge of a cube be $2.4 \mathrm{~cm}$, then the volume of the cube

$13.824 \mathrm{~cm}^{3}$

$12.624 \mathrm{~cm}^{3}$

$13.324 \mathrm{~cm}^{3}$

$12.724 \mathrm{~cm}^{3}$

Question 87:

If the diagonal of a cube is $\sqrt{75} \mathrm{~cm}$, then its volume is:

$75 \mathrm{~cm}^{3}$

$64 \mathrm{~cm}^{3}$

$100 \mathrm{~cm}^{3}$

$125 \mathrm{~cm}^{3}$

Question 88:

The area of a rectangle is 240 m² and the perimeter is 46 m. What is the measure of the tallest pole to be placed in that area?

16

7

17

8

Question 89:

In an isosceles triangle $\mathrm{ABC}, \mathrm{AB}=\mathrm{AC}$ and $\mathrm{AD}$ is perpendicular to $\mathrm{BC}$ at $\mathrm{D}$. If $\mathrm{AD}=8 \sqrt{3} \mathrm{~cm}$ and perimeter of triangle ABC is $128 \mathrm{~cm}$, then the area of $\mathrm{ABC}$ is:

$244 \sqrt{3} \mathrm{~cm}^{2}$

$224 \sqrt{3} \mathrm{~cm}^{2}$

$264 \sqrt{3} \mathrm{~cm}^{2}$

$234 \sqrt{3} \mathrm{~cm}^{2}$

Question 90:

The areas of three adjacent faces of a cuboid are $44 \mathrm{~cm}^{2}, 132 \mathrm{~cm}^{2}$ and $75 \mathrm{~cm}^{2}$. The volume of the cuboid is:

$624 \mathrm{~cm}^{3}$

$640 \mathrm{~cm}^{3}$

$650 \mathrm{~cm}^{3}$

$660 \mathrm{~cm}^{3}$

Question 91:

The circumference of the base of a conical tent is $66 \mathrm{~m}$. If the height of the tent is $36 \mathrm{~m}$, what is the area (in $\mathbf{m}^{2}$ ) of the canvas used in making the tent? (Take $\pi=\frac{22}{7}$ )

$1237.5\mathrm{~m}^{2}$

$1171.5\mathrm{~m}^{2}$

$1254\mathrm{~m}^{2}$

$1155\mathrm{~m}^{2}$

Question 92:

A cylindrical vessel of radius $30 \mathrm{~cm}$ and height $42 \mathrm{~cm}$ is full of water. Its contents are emptied into a rectangular tub of length $75 \mathrm{~cm}$ and breadth $44 \mathrm{~cm}$. The height (in $\mathbf{c m}$ ) to which the water rises in the tub is. (Take $\pi=\frac{22}{7}$ )

$36\mathrm{~cm}$

$30\mathrm{~cm}$

$40\mathrm{~cm}$

$45\mathrm{~cm}$

Question 93:

A rectangular grassy lawn measuring $40 \mathrm{~m}$ by $25 \mathrm{~m}$ is to be surrounded externally by a path which is $2 \mathrm{~m}$ wide. Calculate the cost of levelling the path at the rate of Rs $8.25$ per square metre.

Rs. 2277

Rs. 2247

Rs. 2287

Rs. 2267

Question 94:

The one-meter-wide path is built inside a square park of side $30 \mathrm{~m}$ along its sides. The remaining part of the park is covered by grass. If the total cost of covering by grass is Rs 1176, find the rate per square meter at which the park is covered by the grass.

Rs. $50$

Rs. $70$

Rs. $1.70$

Rs. $2.50$

Question 95:

From a rectangular sheet of tin, of size $100 \mathrm{~cm}$ by $80 \mathrm{~cm}$, are cut four squares of side $10 \mathrm{~cm}$ from each corner. Find the area of the remaining sheet.

$7600 \mathrm{~cm}^{2}$

$7820 \mathrm{~cm}^{2}$

$7800 \mathrm{~cm}^{2}$

$7620 \mathrm{~cm}^{2}$

Question 96:

The sides of a triangle are in the ratio $\frac{1}{4}: \frac{1}{3}: \frac{1}{5}$. If the perimeter of the triangle is 188 cm, then the length (in $\mathrm{cm}$ ) of the largest side is:

60

80

100

84

Question 97:

A wire is bent in the form of a rectangle whose perimeter is 40 cm. The same wire has been modified and made into another rectangle whose length is 1/3 rd more than the length of the initial rectangle and width is half of the width of the initial one. What will be the area of the second rectangle ?

$100 \mathrm{~cm} ^{2}$

$96 \mathrm{~cm} ^{2}$

$64 \mathrm{~cm} ^{2}$

$84 \mathrm{~cm} ^{2}$

Question 98:

Find the total surface area of a solid cylindrical tin of radius 14 cm and height 7 cm. (Take, $\pi$ = $\frac{22}{7}$)

1808 cm$^2$

1748 cm$^2$

1848 cm$^2$

1448 cm$^2$

Question 99:

The total surface area of a solid right circular cone is $6930 \mathrm{~cm}^2$. Its curved surface area is $\frac{4}{5}$ its total surface area. What is the diameter (in $\mathrm{cm}$ ) of the base of the cone? (Take $\pi=\frac{22}{7}$ )

14

42

21

56

Question 100:

The surface area of a solid cube is $726 \mathrm{~cm}^2$. It is melted and recast into a solid cylinder of radius $11 \mathrm{~cm}$. What is the height (in cm) of the cylinder? (Take $\left.\pi=\frac{22}{7}\right)$

3.5

5.5

1.9

2.5

Question 101:

A rectangular field is of the dimensions 20 m length and 10 m breadth. If the length is increased by 10% and the breadth is decreased by 20%, then the ratio of the old area to the new area will be:

22 : 25

3:2

25 : 22

4:5

Question 102:

The adjacent sides of a parallelogram are 10 cm and 15 cm. If the distance between the shorter sides is 6 cm, then what is the distance between its longer sides?

9 cm

4 cm

25 cm

18 cm

Question 103:

The sides of a triangular park are 60 m, 297 m and 303 m. Its area is equal to the area of a square-shaped garden. What is the perimeter (in m) of the garden?

$36 \sqrt{110}$

$18 \sqrt{110}$

$18 \sqrt{330}$

$9 \sqrt{330}$

Question 104:

The curved surface area of a right circular cone is $3185 \pi \mathrm{cm}^2$. If the radius of its base is $35 \mathrm{~cm}$, then its height (in cm) will be:

42

84

98

49

Question 105:

A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

2

6

5

4

Question 106:

The total surface area of a solid cube is $294 \mathrm{~cm}^2$. It is melted and recast into a right circular cylinder of radius $7 \mathrm{~cm}$. What is the height (in $\mathrm{cm}$, correct to one decimal place) of the cylinder? (Take $\pi=\frac{22}{7}$ )

4.5

2.2

1.8

3.1

Question 107:

The parallel sides of a trapezium are $27 \mathrm{~cm}$ and $13 \mathrm{~cm}$, respectively. If the distance between the parallel sides is $7 \mathrm{~cm}$, then its area in square meters is

1.4.0

$0.014$

140.0

14.0

Question 108:

The width of the path around a square field is $4.5 \mathrm{~m}$ and its area is $105.75$ $m^2$. Find the cost of fencing the field at the rate of ₹ 100 per metre.

₹ 550

₹ 600

₹ 275

₹ 400

Question 109:

For a rectangular box, what is the product of the areas of the 3 adjacent faces that meet at a point?

$length \times breadth \times height$

$length + breadth + height$

$length \times breadth + breadth \times height + length \times height$

$(\text { length } \times \text { breadth } \times \text { height })^{2}$

Question 110:

A solid piece of iron in the form of a cuboid of dimensions 24.5 cm × 16.5 cm × 12 cm, is melted to form a solid sphere.

What is the radius (in cm) of the sphere? (Use π = $\frac{22}{7}$)

10.5

12.5

11

8

Question 111:

The area of a triangular park whose sides are $120 \mathrm{~m}, 137.5 \mathrm{~m}$ and $182.5 \mathrm{~m}$, is equal to the area of a rectangular garden whose sides are in the ratio $30: 11$. The longer side of the rectangular garden is:

$165 \mathrm{~m}$

$150 \mathrm{~m}$

$168 \mathrm{~m}$

$120 \mathrm{~m}$

Question 112:

The diagonal of a square is$4 \sqrt{2} \mathrm{~cm}$. The diagonal of another square whose area is double that of the first square is :

$8 \sqrt{5}$

$8$

$2 \sqrt{10}$

$4$

Question 113:

During a rainy day, $4 \mathrm{~cm}$ of rain falls. The volume (in $\mathrm{m}^{3}$ ) of water that falls on $1.5$ hectares of ground is:

600

450

750

500

Question 114:

The perimeter of a rhombus is $148 \mathrm{~cm}$ and one of its diagonals is $70 \mathrm{~cm}$. Its area is equal to the area of a rectangle whose sides are in the ratio $7: 3$. The longer side of the rectangle is:

$7 \sqrt{10} \mathrm{~cm}$

$8 \sqrt{5} \mathrm{~cm}$

$4 \sqrt{5} \mathrm{~cm}$

$14 \sqrt{10} \mathrm{~cm}$

Question 115:

The curved surface area of a right circular cylinder is $1320 \mathrm{~cm}^{2}$ and the radius of its base is $10.5 \mathrm{~cm}$. The volume (in $\mathrm{cm}^{3}$ ) of the cylinder is: (Take $\pi=\frac{22}{7}$ )

6930

6908

6798

6732

Question 116:

Four cubes each of side $8 \mathrm{~cm}$, are placed together end to end in a row. What is the total surface area (in $\mathrm{cm}^2$ ) of the solid so formed?

1728

512

1152

1536

Question 117:

The area of the base of a right circular cone is $81 \pi \mathrm{cm}^2$ and its height is 18 $\mathrm{cm}$. Its slant height is:

$15 \sqrt{5} \mathrm{~cm}$

$9 \sqrt{5} \mathrm{~cm}$

$21 \mathrm{~cm}$

$24 \mathrm{~cm}$

Question 118:

The area of a square inscribed in a circle, whose diagonal is $16 \mathrm{~cm}$, is:

$64 \times \sqrt{2} \mathrm{~cm}^{2}$

$64 \mathrm{~cm}^{2}$

$256 \mathrm{~cm}^{2}$

$128 \mathrm{~cm}^{2}$

Question 119:

The curved surface area of a cone is $25 \sqrt{2} \pi \mathrm{cm}^{2}$. If the height of the cone is equal to the radius of its base, then what is the volume (in $\mathrm{cm}^{3}$ ) of the cone? (Use $\pi=\frac{22}{7}$ ) correct to two decimal places.

130 .95

140

124.85

132 .75

Question 120:

The radius of a sphere is $6 \mathrm{~cm}$. The sphere is melted and drawn into a wire of radius $0.4 \mathrm{~cm}$. The length of the wire (in m) is:

$18 \mathrm{~m}$

$15 \mathrm{~m}$

$14 \mathrm{~m}$

$16 \mathrm{~m}$

Question 121:

The area of a triangular field with sides $220 \mathrm{~m}, 231 \mathrm{~m}$ and $319 \mathrm{~m}$ is equal to 15 times the area of a circular field. What will be the diameter (in m) of the field?

$14 \sqrt{11}$

$7 \sqrt{7}$

$7 \sqrt{11}$

$14 \sqrt{7}$

Question 122:

Find the number of lead balls of diameter each $2 \mathrm{~cm}$ that can be made from a sphere of diameter $18 \mathrm{~cm}$.

$729$

$827$

$843$

$972$

Question 123:

The perimeter of an equilateral triangle is 36$\sqrt{3}$ cm. Find its height.

18 cm

9 cm

10 cm

6 cm

Question 124:

A solid metallic rectangular block of dimensions $112 \mathrm{~cm} \times 44 \mathrm{~cm} \times 25 \mathrm{~cm}$ is melted and recast into a cylinder of radius $35 \mathrm{~cm}$. The curved surface area (in $\mathrm{cm}^2$ ) of the cylinder is: (Take $\pi=\frac{22}{7}$ )

7260

6600

7040

6160

Question 125:

The inner circumference of a circular path enclosed between two concentric circles is $264 \mathrm{~m}$. The uniform width of the circular path is $3 \mathrm{~m}$. What is the area (in $m^2$, to the nearest whole number) of the path? (Take $\pi=\frac{22}{7}$ )

696

756

820

948

Question 126:

ABCD is a trapezium in which AD||BC, AB = 5 cm , BC = 11 cm and AD =7 cm. DA is produced to a point F such that AF = 3 cm and BF⊥DF. Then, area of the trapezium ABCD is :

34 cm$^2$

36 cm$^2$

40.5 cm$^2$

42.75 cm$^2$

Question 127:

Deepak used to walk ten rounds along a rectangular ground with length 150 cm and breadth 100 m. If he has to walk around a square shaped ground having area 0.01 km$^2$, then how many rounds he has to walk so that he can complete his regular routine of walking?

Approximately 10

Exactly 11

Exactly 12

Approximately 13

Question 128:

The radius of the base of a metallic cylindrical box is 17.5 cm. Its height is one meter. What is the capacity (in litres) of the box?(Take $\pi=\frac{22}{7}$)

90.5

95

96.25

99

Question 129:

If $\mathrm{E}, \mathrm{F}$ and $\mathrm{V}$ are respectively the number of edges, faces and vertices of a square pyramid, then the value of $(2 E-F+2 V)$ is:

21

22

19

18

Question 130:

Area of a triangle of sides 24 cm, 25 cm and 7 cm is equal to the area of a rectangle of length 14 cm. Then, perimeter of the rectangle is:

20 cm

18 cm

36 cm

40 cm

Question 131:

The area of a circular field is $616 \mathrm{~m}^2$. Then, cost of fencing the field at the rate of ₹ 5 per metre is ( Take $\pi=\frac{22}{7}$ )

₹660

₹440

₹330

₹420

Question 132:

Which of the following figures do not have the same number of lines of symmetry?

Isosceles triangle and kite

Rhombus and rectangle

Scalene triangle and parallelogram

Kite and rhombus

Question 133:

The perimeter of the base of a right circular cylinder is $44 \mathrm{~cm}$ and its height is $8 \mathrm{~cm}$. Then, volume of the cylinder is (Take $\pi=\frac{22}{7}$ )

$1212 \mathrm{~cm}^3$

$1232 \mathrm{~cm}^3$

$1412 \mathrm{~cm}^3$

$1432 \mathrm{~cm}^3$

Question 134:

If $F, V$ and $E$ are respectively the number of faces, vertices and edges of a pentagonal prism, then which of the following statements is not true?

$F+E-V=12$

$V+E-F=18$

$2 V+F-E=10$

$2 V+2 F-E=19$

Question 135:

Area of a rhombus is 240 cm$^2$. If one of its diagonals is of length 30 cm, then perimeter of the rhombus is

120 cm

136 cm

60 cm

68 cm

Question 136:

Length of a rectangular field is thrice its breadth. If perimeter of the field is $400 \mathrm{~m}$, then ( $2 \times$ length $+3 \times$ breadth) is equal to:

$550 \mathrm{~m}$

$450 \mathrm{~m}$

$500 \mathrm{~m}$

$650 \mathrm{~m}$

Question 137:

From a cube of side 8 cm, small cubes each of side 4 cm are cut. What is the difference between the total surface area of all the small cubes and that of the original cube?

No difference

384 cm$^2$

382 cm$^2$

372 cm$^2$

Question 138:

If the height of a right circular cone is $24 \mathrm{~m}$ and its slant height is $30 \mathrm{~m}$, then what is the area of its curved surface? (Use $\pi=\frac{22}{7}$ )

$1697.143 \mathrm{~m}^2$

$1377.423 \mathrm{~m}^2$

$1778.654 \mathrm{~m}^2$

$1267.435 \mathrm{~m}^2$

Question 139:

The area of the floor of a cubical room is 192 m². The length of the longest rod that can be kept in that room is

18 m

22 m

24 m

26 m

Question 140:

12 spherical balls of radius 10 cm are dropped in a bucket which is full of water up to the brim. The water flowed out is collected in a cylindrical jar of radius 20 cm. What is the height (in cm) of the water in the jar? (Take, π = 22/7)

45

32

40

18

Question 141:

Which of the following figures have linear symmetry but no rotational symmetry?

Equilateral triangle

Rectangle

Kite

Rhombus

Question 142:

Area of a triangle of sides 45 cm, 51 cm and 24 cm is equal to the area of a rectangle of length 30 cm. Then, perimeter of the rectangle is:

96 cm

48 cm

120 cm

60 cm

Question 143:

The area of a circular garden of diameter $9.8 \mathrm{~m}$ is $\mathrm{A}$. Then, value of $2 \mathrm{~A}+4.48 \mathrm{~m}^2$ is (use $\pi=\frac{22}{7}$ )

$154.50 \mathrm{~m}^2$

$155.40 \mathrm{~m}^2$

$154.48 m^2$

$155.44 \mathrm{~m}^2$

Question 144:

The diameter of a road roller of length $1 \mathrm{~m}$ is $84 \mathrm{~cm}$. It takes 750 complete revolutions to level a ground once. Then, area of the ground is- (use $\pi=\frac{22}{7}$ )

$1980 m^2$

$990 m^2$

$2180 m^2$

$1090 m^2$

Question 145:

The sum of the length, the breadth and the height of a cuboid is 18cm. If the length of its diagonal is 13 cm, then the total surface area of the cuboid is:

$154 \mathrm{~cm}^2$

$155 \mathrm{~cm}^2$

$150 \mathrm{~cm}^2$

$145 \mathrm{~cm}^2$

Question 146:

A spherical ball of radius 3 cm, is immersed in water contained in a vertical cylinder of radius 5 cm. Assuming the water covers the ball completely, what is the rise in the water level (in cm), up to two decimal places)?

1.75

1.44

2.25

3.14

Question 147:

In a pool of length $50 \mathrm{~m}$ and width $45 \mathrm{~m}, 90$ persons take a dip. If the average displacement of water by the persons is $1 \mathrm{~m}^3$, then how much will the water level rise?

12 cm

40 cm

4 cm

10 cm

Question 148:

A wire, which is in the form of a circle with radius $14 \mathrm{~cm}$, is bent to form a square. What is the length (in $\mathrm{cm}$ ) of the side of the square? ( Use $\pi=\frac{22}{7}$ )

20.8

24

21.5

22

Question 149:

The width of the path around a square field is $5.5 \mathrm{~m}$ and its area is $130.75$ $m^2$. Find the cost of fencing the field at the rate of ₹ 110 per metre.

Rs.185

Rs. 210

Rs.195

Rs. 225

Question 150:

The length and the breadth of a rectangle are made to increase and decrease, respectively, by 10% and 12%. What is the percentage increase or decrease in its area?

Decrease by 1.8%

Increase by 1.8%

Decrease by 3.2%

Increase by 2.8%

Question 151:

A 42 cm high bucket in the form of a frustum is full of water. Radii of its lower and upper ends are 15 cm and 21 cm, respectively. If water from this bucket is poured in a cylindrical drum, whose base radius is 18 cm, then what will be the height of water (in cm) in the drum?

32.50

36.50

42.38

41.28

Question 152:

The difference between the two perpendicular sides of a right-angled triangle is $71 \mathrm{~cm}$ and its area is $546 \mathrm{~cm}^2$. What is the perimeter (in cm) of the triangle?

$186$

$172$

$182$

$192$

Question 153:

What is the difference in the volume (in $\mathrm{cm}^3$ ) of a sphere of radius $21 \mathrm{~cm}$ and that of a cone of radius $7 \mathrm{~cm}$ and height $21 \mathrm{~cm} ?$ (Use $\pi=\frac{22}{7}$ )

$37730$

$35838$

$39730$

$36730$

Question 154:

If the volume of a Hemisphere is equal to that of a cylinder having the same radius, then find the ratio of the radius to the height of the cylinder.

2:3

1:2

3:4

3:2

Question 155:

A rectangular piece of paper is $22 \mathrm{~cm}$ long and $10 \mathrm{~cm}$ wide is rolled along its length and a cylinder is formed. Find the volume of the cylinder.(take $\pi=22 / 7$ )

$175 \mathrm{~cm}^3$

$75 \mathrm{~cm}^3$

$125 \mathrm{~cm}^3$

$275 \mathrm{~cm}^3$

Question 156:

A race track is in the shape of a ring whose inner and outer circumference are $440 \mathrm{~m}$ and $506 \mathrm{~m}$, respectively. What is the cost of levelling the track at 6/sq.m? $\left(\pi=\frac{22}{7}\right)$

29,799

24,832

19,866

18,966

Question 157:

A cuboid of mercury, measuring 40 cm $\times 20$ cm $\times 16$ cm, is melted to form spheres of diameter $10$ cm. How many balls will be made in this way? (in approximation)

20

28

24

35

Question 158:

Find the total surface area of a sphere whose radius is $63 \mathrm{~cm}$.

$49836 \mathrm{~m}^2$

$40895 \mathrm{~m}^2$

$59796 \mathrm{~m}^2$

$49896 \mathrm{~m}^2$

Question 159:

A solid sphere of radius $2 \mathrm{~cm}$ is melted to convert in to a wire of length is $100 \mathrm{~cm}$. The radius of the wire.

$ 0.44$ cm

$0.33$ cm

$0.53 $cm

$ 0.30 $cm

Question 160:

The sides of a triangle are in the ratio $2: 3: 4$ The perimeter of the triangle is $18 \mathrm{~cm}$. The area of the triangle is?

$3 \sqrt{15} \mathrm{~cm}^{2}$

$4 \sqrt{15} \mathrm{~cm}^{2}$

$3 \sqrt{18} \mathrm{~cm}^{2}$

$4 \sqrt{14} \mathrm{~cm}^{2}$

Question 161:

A circular cylindrical can (having horizontal base) with internal diameter $20 \mathrm{~cm}$ and height $30 \mathrm{~cm}$ contains water to a height of $5 \mathrm{~cm}$. How many metal spheres of radius $5 \mathrm{~cm}$ have to be placed in the can, so that the water just fills up the can?

12 cm

15cm

20cm

18cm

Question 162:

A solid cube of volume $46656 \mathrm{~cm}^3$ is cut into 8 cubes of equal volumes. What is the ratio of surface area of the original cube and the total surface areas of the smaller 8 cubes?

$1: 2$

$1: 3$

$2: 3$

$3: 4$

Question 163:

The length, breadth and height of a cuboid are in the ratio $1: 2: 3$. If its total surface area is $1100 \mathrm{~cm}^2$, then its volume (in $\mathrm{cm}^3$ ) is :

$750 \sqrt{2}$

750

1500

$1500 \sqrt{2}$

Question 164:

The diameter of the base of a right circular solid cylinder is $14 \mathrm{~cm}$ and its volume is $2002 \mathrm{~cm}^3$. The total surface area of the cylinder (in $\mathrm{cm}^2$ ) is $\left(\right.$ Take $\pi=\frac{22}{7}$ ).

440

660

880

1320

Question 165:

The ratio between the curved surface area and the total surface area of a right circular cylinder is 2 : 3. What is the ratio of radius and height of the cylinder?

1 : 2

2 : 1

2 : 3

3 : 2

Question 166:

What is the ratio of the area of an equilateral triangle of side 2a units to that of a square, whose diagonal is 2a units?

$\sqrt{3}: 1$

$\sqrt{3}: 4$

$\sqrt{3}: 2$

$\sqrt{3}: 8$

Question 167:

A copper sphere of diameter $18 \mathrm{~cm}$ is drawn into a wire of diameter $4 \mathrm{~mm}$. The length of the wire, in metre is:

$0.234$ m

$243$ m

$0.254$ m

$254$ m

Question 168:

A field is in the form of a rectangle of length $18 \mathrm{~m}$ and width $15 \mathrm{~m}$ deep, in a corner of the field a pit is dug of area $7.5 \times 6$ and $0.8 \mathrm{~m}$ deep and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is:

$12 \mathrm{~cm}$

$15 \mathrm{~cm}$

$16 \mathrm{~cm}$

$18 \mathrm{~cm}$

Question 169:

PQRS is a rectangle. The ratio of the sides PQ and $Q R$ is $4: 3$. If the length of the diagonal $\mathrm{PR}$ is $20 \mathrm{~cm}$, then what is the area (in $\mathrm{cm}^{2}$ ) of the rectangle?

208

172

156

192

Question 170:

A rectangular lawn of length $30 \mathrm{~m}$ and breadth $15 \mathrm{~m}$ is to be surrounded externally by a path which is $3 \mathrm{~m}$ wide. Find the cost of making the path at the rate of Rs.20 per $\mathrm{m}^{2}$.

Rs. $6720$

Rs. $8530$

Rs. $6120$

Rs. $5520$

Question 171:

A hollow cylinder is made up of steal. The difference in its outer and inner CSA is 132 $\mathrm{cm}^{2}$. Height of cylinder is $21 \mathrm{~cm}$ and sum of its inner and outer radius is also $21 \mathrm{~cm}$. Then find the TSA of the hollow cylinder (in $\mathrm{cm}^{2}$ )

2704

2956

2864

2904

Question 172:

How many small solid spheres of radius $5 \mathrm{~mm}$ can be made from a solid metallic cone of base radius $21 \mathrm{~cm}$ and height of $40 \mathrm{~cm}$?

$35280$

$35000$

$32000$

$25000$

Question 173:

What is the value of:

$8 \sqrt{3} \sin 30^{\circ} \tan 60^{\circ}-3 \cos 0^{\circ}+3 \sin ^{2} 45^{\circ}+2 \cos ^{2} 30 ?$

12

15

18

9

Question 174:

From the top of a platform 7m high, the angle of elevation of a tower $30^{\circ}$. If the tower was 47 m high, how far away from the tower was the platform positioned?

$15 \sqrt{3} \mathrm{~m}$

$40 \sqrt{3} \mathrm{~m}$

$44 \sqrt{3} \mathrm{~m}$

$40 \mathrm{~m}$

Question 175:

If $\sin (A-B)=\frac{\sqrt{3}}{2}$ and $\sec A=2,0^{\circ} \leq A \leq 90^{\circ}, 0^{\circ} \leq B \leq 90^{\circ}$ , then what is the measure of $\mathrm{B}$ ?

$60^{\circ}$

$0^{\circ}$

$30^{\circ}$

$90^{\circ}$

Question 176:

If $\tan ^2 A+2 \tan A-35=0$, Given that $0 < A < \frac{\pi}{2}$ what is the value of $(2 \cos A+5 \sin A)$ ?

$19 \sqrt{26}$

$15 \sqrt{26}$

$\frac{19}{\sqrt{26}}$

$\frac{27}{\sqrt{26}}$

Question 177:

If $\sec A=\frac{41}{40}$, given that $A<90^{\circ}$, What is the value of the following?

$\frac{82 \sin A+9 \cot A}{164 \cos A-80 \tan A}$

$\frac{58}{142}$

$\frac{54}{142}$

$\frac{74}{147}$

$\frac{56}{124}$

Question 178:

If $3 \sec ^2 \theta+\tan \theta-7=0.0^{\circ}<\theta<90^{\circ}$, then what is the value of $\left(\frac{2 \sin \theta-3 \cos \theta}{\operatorname{cosec} \theta+\sec \theta}\right) ?$

$\frac{1}{2}$

$\frac{-1}{4}$

$\frac{5}{2}$

$\frac{3}{2}$

Question 179:

If $\cot B=\frac{84}{13}$, what is the value of $\sin B$ ?

$\frac{13}{85}$

$\frac{85}{13}$

$\frac{84}{85}$

$\frac{85}{84}$

Question 180:

In a right $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{AC}-\mathrm{BC}=2, \mathrm{AB}=8$, Then $\sec \mathrm{A}+\cot \mathrm{C}$ ?

$\frac{361}{120}$

$\frac{475}{120}$

$\frac{275}{120}$

$\frac{377}{120}$

Question 181:

$\frac{\cos ^2 45^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to :

1/4

1/8

1/2

1/6

Question 182:

The value of $\frac{\sin 37^{\circ} \cos 53^{\circ} \cot 45^{\circ}+\cos 37^{\circ} \sin 53^{\circ} \tan 45^{\circ}}{4 \sin 45^{\circ} \cos 45^{\circ}}$ is:

2

1

$\frac{1}{2}$

0