## Mensuration Part 7: Advance math series 2000 most important questions.

Mensuration Part 7: Advance math series 2000 most important questions

**Q762.** **The ratio of land to water on the whole of the earth is 1: 2, and it is2: 3 on the northern hemisphere. The ratio of and to water on the southern hemisphere is:**

(a) 11: 4

(b) 4: 11

(c) 15: 4

(d) 4: 15

**Q763. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is:**

(a) 40%

(b) 42%

(c) 44%

(d) 46%

**Q764. A cube of edge 5 cm is cut into cubes each of edge of 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:**** **

(a) 1: 125

(b) 1: 5

(c) 1: 625

(d) 1: 25

**Q765. The perimeter of a rhombus is 40 m and its height is 5m. Its area is:**

(a) 60 m^{2}

(b) 50 m^{2}

(c) 45 m^{2}

(d) 55 m^{2}

**Q766.** **If D and E are the mid-points of the sides AB and AC respectively of the ****ABC in the figure given here, the shaded region of the triangle is what per cent of the whole triangular region?**

(a) 50%

(b) 25%

(c) 75%

(d) 60%

**Q767.** **The length of the perpendiculars drawn from any point in the interior of an equilateral triangle to the respective sides are p1, p2 and p3. The length of each side of the triangle is**

(a) 2/√3 (p_{1} + p_{2} + p_{3})

(b) 1/3 (p_{1} + p_{2} + p_{3})

(c) 1/√3 (p_{1} + p_{2} + p_{3})

(d) 4/√3 (p_{1} + p_{2} + p_{3})

**Q768.** **The length of a rectangle is decreased by 10% and its breadth is increased by 10%. By what per cent is its area changed?**

(a) 0%

(b) 1%

(c) 5%

(d) 100%

**Q769.** **A hollow cylindrical tube 20 cm long, is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume of iron used in making the tube is (p = 22/7****)**

(a) 1760 cu.cm.

(b) 880 cu. Cm.

(c) 440 cu. cm

(d) 220 cu. Cm.

**Q770. The diameter of the iron ball used for the shot-put game is 14cm. It is melted and then a solid cylinder of height 2 1/3**** cm is made. What will be the diameter of the base of the cylinder?**

(a) 14 cm

(b) 28 cm

(c) 14/3 cm

(d) 28/3 cm

**Q771. The area of the greatest circle, which can be inscribed in a square whose perimeter is 120 cm, is:**

(a) 22/7 X (15)^{2 }cm^{2}

(b) 22/7 X (7/2)^{3 }cm^{2}

(c) 22/7 X (15/2)^{2 }cm^{2}

(d) 22/7 X (9/2)^{2 }cm^{2}

**Q772. Diameter of a wheel is 3 cm. The wheel revolves 28 times in a minute. To cover 5.280 km distance, the wheel will take (taking π = 22/7) **

(a) 10 minutes

(b) 20 minutes

(c) 30 minutes

(d) 40 minutes

**Q773. If the diagonals of two squares are in the ratio of 2: 5, their areas will be in the ratio of**

(a) √2 : √5

(b) 2: 5

(c) 4 : 25

(d) 4 : 5

**Q774. The ratio of the outer and the inner perimeters of a circular path is 23: 22. If the path is 5 metres wide, the diameter of the inner circle is:**

(a) 110m

(b) 55m

(c) 120m

(d) 60m

**Q775. If both the radius and height of a right circular cone are increased by 20%, its volume will be increased by**

(a) 20%

(b) 40%

(c) 60%

(d) 72.8%

**Q776. The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is**

(a) 27 m

(b) 19 m

(c) 17 m

(d) 13 m

**Q777. The circum-radius of an equilateral triangle is 8 cm. The in radius of the triangle is**

(a) 3.25 cm

(b) 3.50 cm

(c) 4 cm

(d) 4.25 cm

**Q778. The difference between the length and breadth of a rectangle is 23m. If its perimeter is 206 m, then its area is**

(a) 1520 m^{2}

(b) 2420 m^{2}

(c) 2480 m^{2}

(d) 2520 m^{2}

**Q779. The radius of a circular wheel is 1.75 m. The number of revolutions that it will make in travelling 11 km., is**

(a) 1000

(b) 10,000

(c) 100

(d) 10

**Q780. A circular wire of diameter 42 cm is folded in the shape of a rectangle whose sides are in the ratio 6: 5. Find the area enclosed by the rectangle. (taking **** π = 22/7)**

(a) 540 cm^{2}

(b) 1080 cm^{2}

(c) 2160 cm^{2}

(d) 4320 cm^{2}

**Q781. A sphere of radius 2 cm is put into water contained in a cylinder of base-radius 4 cm. if the sphere is completely immersed in the water, the water level in the cylinder rises by**

(a) 1/3 cm

(b) 1/2 cm

(c) 2/3 cm

(d) 2 cm

**Q782. The perimeter of a rhombus is 40 cm. If one of the diagonals be 12 cm long, what is the length of the other diagonal?**

**Q783. Each of the height and base-radius of a cone is increased by 100%.Thepercentae increase in the volume of the cone is**

(a) 700%

(b) 400%

(c) 300%

(d) 100%

**Q784. Four equal circles each of radius ‘a’ units touch one another. The area enclosed between then **

**(π = 22/7)****, in square units, is**

(a) 3a^{2}

(b) 6a^{2}/7

(c) 41a^{2}/7

(d) a^{2}/7

**Q785. if the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by**

(a) 0%

(b) 25%

(c) 62.5%

(d) 75%

**Q786. The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeter of the** **rhombus is:**

(a) 80 cm

(b) 72 cm

(c) 68 cm

(d) 64 cm

**Q787. A took 15 sec, to cross a rectangular field diagonally walking at the rate of 52m/min. and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. The area of the field is:**

(a) 30 m^{2}

(b) 40 m^{2}

(c) 50 m^{2 }

(d) 60 m^{2}

**Q788. The perimeter of two squares are 24 cm and 32 cm. The perimeter (in cm) of a third square equal in area to the sum of the areas of these squares is:**

(a) 45

(b) 40

(c) 32

(d) 48

**Q789. The side of a triangle are 3 cm, 4 cm and 5 cm. The area (in cm2) of the triangle formed by joining the mid points of this triangle is:**

(a) 6

(b) 3

(c) 3/2

(d) 3/4

**Q790. If the height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the given cone to that of the second cone will be**

(a) 2: 1

(b) 1: 8

(c) 1: 2

(d) 8: 1

**Q791. Three circles of radius 3.5 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is**

(a) 1.975 cm^{2}

(b) 1.967 cm^{2}

(c) 19.67 cm^{2}

(d) 21.21 cm^{2}

**Q792. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 sq. cm. The circumference of each plate is (Taking π = 22/7)**

(a) 22 cm

(b) 44 cm

(d) 66 cm

(d) 68 cm

**Q793. The diagonals of a rhombus are 24 cm and 10 cm. The perimeter of the rhombus (in cm) is:**

(a) 68

(b) 65

(c) 54

(d) 52

**Q794. The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2** **cm.**

(a) 7 cm

(b) 9 cm

(c) 11 cm

(d) 16 cm

**Q795. A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is:**

(a) 25 min

(b) 20 min

(c) 50 min

(d) 100 min

**Q796. From a point in the interior of an equilateral triangle the perpendicular distances of the sides are √3 ****cm, 2 √3**** cm and 5√3**** cm. The perimeter (in cm) of the triangle is**

(a) 64

(b) 32

(c) 48

(d) 24

**Q797. The height of a conical tank is 60 cm and the diameter of its base is 64 cm. The cost of painting it from outside at the rate of Rs. 35 per sq. m. is:**

(a) Rs. 52.00 approx

(b) Rs. 39.20 approx

(c) Rs. 35.20 approx.

(d) Rs. 23.94 approx.

**Q798. The area (in m2) of the square which has the same perimeter as a rectangle whose length is 48 m and is 3 times its breadth is:**

(a) 1000

(b) 1024

(c) 1600

(d) 1042

**Q799. Three solid spheres of a metal whose radii are 1 cm, 6 cm and 8 cm are melted to form an other solid sphere. The radius of this new sphere is**

(a) 10.5 cm

(b) 9.5 cm

(c) 10 cm

(d) 9 cm

**Q800. A solid metallic spherical ball of diameter 6 cm is melted and recasted into a cone with diameter of the base as 12 cm. The height of the cone is**

(a) 6 cm

(b) 2 cm

(c) 4 cm

(d) 3 cm

**Q801. The length, breadth and height of a room is 5 m, 4 m, and 3 m respectively. Find the length of the largest bamboo that can be kept inside the room.**

(a) 5 m

(b) 60 m

(c) 7 m

(d) 5**√**2 m

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