# Quant Ability

What is the number of wax balls, each of radius 1 cm, that can be molded out of a sphere of radius 8 cm?

- 1024
- 768
- 512
- 256

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equal to?

- 0.001 cm
- 0.01 cm
- 0.1 cm
- 1.0 cm

The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is

- 327 π
- 307 π
- 293 π
- 273 π

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

- 3 : 2
- 1 : 2
- 2 : 1
- 2 : 3

If the height of a right circular cone is increased by 200%, and the radius of the base is reduced by 50%, then the volume of the cone

- remains unaltered
- decreases by 25%
- increases by 50%
- increases by 25%

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

- 4.5 cm
- 2.25 cm
- 2 cm
- 1.5 cm

10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs.5 per square metre?

- Rs.400
- Rs.440
- Rs.480
- Rs.500

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

- 12 cm
- 24 cm
- 30 cm
- 36 cm

A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs.25/- per square metre?

- Rs.800
- Rs.480
- Rs.400
- Rs.240

How many degrees are there in an angle which equals two-third of its complement?

- 60°
- 48°
- 45°
- 36°

In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?

- 26°
- 28°
- 38°
- 52°

ABC is an isosceles triangle such that AB = BC = 8 cm and ∠ABC = 90°. What is the length of the perpendicular drawn from B on AC?

- 4√2 cm
- 4 cm
- 2 cm
- 2√2 cm

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?

- r/4
- r/2
- √2r
- r

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to?

- 0
- 1
- 2
- 4

A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is

- 5√3 cm
- 5 cm
- 10√3 cm
- 10 cm

In the figure given, LM is parallel to QR. If LM divides the triangle PQR such that area of trapezium LMRQ is two times the area of triangle PLM, then what is PL/PQ equal to?

- 1/3
- 1/√2
- 1/√3
- 1/2

In histogram the width of the bars is proportional to

- number of classes
- class interval
- cumulative frequency
- frequency

What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?

- 30°
- 45°
- 60°
- 75°

If sin x + cos x = c, then sin^{6} x + cos^{6} x is equal to

- (1 + 6c
^{2}- 3c^{4})/16 - (1 + 6c
^{2}- 3c^{4})/4 - (1 + 6c
^{2}+ 3c^{4})/16 - (1 + 6c
^{2}+ 3c^{4})/4

The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?

- 48 m
- 49 m
- 50 m
- 51 m

If tan A + cot A = 4, then tan^{4} A + cot^{4} A is equal to

- 194
- 191
- 110
- 80

The value of cosec^{2} 67 + sec^{2} 57 - cot^{2} 33 - tan^{2} 23 is

- 2√2
- 2
- √2
- 0

If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?

- 1/3
- 1/2
- 3/4
- 2/3

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

- 48 m
- 30 m
- 25 m
- 24 m

In a certain school, the ratio of boys and girls is 7 : 5. If there are 2400 students in the school, then how many girls are there?

- 500
- 700
- 800
- 1000

Age of X is 6 times that of Y. After 4 years, X is 4 times elder to Y. What is the present age of Y?

- 4 yr
- 5 yr
- 6 yr
- 7 yr

Two numbers are in the ratio 3:5. If 9 is subtracted from each number, then they are in the ratio of 12:23. What is the second number?

- 44
- 55
- 66
- 77

A fruit-seller buys lemons at 2 for a rupee and sells them at 5 three rupees. What is his gain percent?

- 10%
- 15%
- 20%
- 25%

What is the number whose 20% is 30% of 40?

- 50
- 60
- 80
- 90

The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by

- 34.75%
- 32.25%
- 31%
- 30%

The price of an article is ₹ 25. After two successive cuts by the same percentage, the price becomes ₹ 20.25. If each time the cut was x%, then

- x = 9
- x = 10
- x = 11
- x = 11.5

If m% of m + n% of n = 2% of (m × n), then what percentage of m is n?

- 25%
- 50%
- 75%
- 100%

A man loses 20% of his money. After spending 25% of the remainder, he has ₹ 480 left. What is the amount of money he originally had?

- ₹ 600
- ₹ 720
- ₹ 800
- ₹ 840

An employee is required to contribute 10% of his pay to General Provident Fund. If he gets ₹13,500 as net pay in a month, then what is the monthly General Provident Fund contribution (assuming no other deductions)?

- ₹ 1215
- ₹ 1350
- ₹ 1500
- ₹ 1650

An automobile financer claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging the interest at the rate of 10%, the effective rate of interest becomes:

- 11%
- 10.75%
- 10.5%
- 10.25%

What is the compound interest on ₹1600 at 25% per annum of 2 year compounded annually

- ₹ 900
- ₹ 800
- ₹ 750
- ₹ 700

4 goats or 6 sheep can graze a field in 50 days. 2 goats and 9 sheep can graze a field in

- 100 days
- 75 days
- 50 days
- 25 days

A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together.

- 2 days
- 3 days
- 4 days
- 5 days

76 ladies complete a job in 33 days. Due to some reason some ladies did not join the work and therefore it was completed in 44 days. The number of ladies who did not report for the work is

- 17
- 18
- 19
- 20