Directions(1-5): Volume and Surface Area
1. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A. 75 cu. m B. 750 cu. m C. 7500 cu. m D. 75000 cu. m

Answer : Option B
Explanation: 1 hectare = 10,000 [latex]{m}^{2}[/latex] = 60 Depth = [latex]\frac{5}{100}[/latex]m = [latex]\frac{1}{20}[/latex]m ∴ Volume = (Area x Depth) = 15000 x [latex]\frac{1}{20}[/latex][latex]{m}^{3}[/latex] = 750 [latex]{m}^{3}[/latex]
2. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A. 720 B. 900 C. 1200 D. 1800

Answer : Option C
Explanation: 2(15 + 12) x h = 2(15 x 12) ⇒ h = [latex]\frac{180}{27}[/latex]m = [latex]\frac{20}{3}[/latex]m ∴ Volume = [15 x 12 x [latex]\frac{20}{3}[/latex]][latex]{m}^{3}[/latex] = 1200[latex]{m}^{3}[/latex]
3. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A. 84 B. 90 C. 168 D. 336

Answer : Option A
Explanation: Let the length of the wire be h. Radius = [latex]\frac{1}{2}[/latex]mm = [latex]\frac{1}{20}[/latex]cm ⇒[latex]\frac{22}{7}[/latex] x [latex]\frac{1}{20}[/latex] x [latex]\frac{1}{20}[/latex] x h = 66 ⇒[latex]\frac{66 × 20 × 20 × 7}{22}[/latex] = 8400 cm = 84 m.
4. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

A. 12 kg B. 60 kg C. 72 kg D. 96 kg

Answer : Option B
Explanation: Volume of water displaced = (3 x 2 x 0.01)[latex]{m}^{3}[/latex] = 0.06 [latex]{m}^{3}[/latex] ∴ Mass of man = Volume of water displaced x Density of water = (0.06 x 1000) kg = 60 kg.
5. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 [latex]{m}^{3}[/latex], then the rise in the water level in the tank will be:

A. 20 cm B. 25 cm C. 35 cm D. 50 cm

Answer : Option B
Explanation: Total volume of water displaced = (4 x 50) [latex]{m}^{3}[/latex] = 200 [latex]{m}^{3}[/latex] ∴ Rise in water level = [latex]\frac{200}{40 × 20}[/latex]m = 0.25 m = 25 cm

Directions(1-5): Fractions 1. The fraction 101 [latex]\frac{27}{100000}[/latex]

A. .01027 B. .10127 C. 101.00027 D. 101.000027

Answer : Option C
Explanation: 101 [latex]\frac{27}{100000}[/latex] = 101 + [latex]\frac{27}{100000}[/latex] = 101 + .00027 = 101.00027
2. [latex]\frac{5 × 1.6 - 2 × 1.4 }{1.3}[/latex] = ?

A. 0.4 B. 1.2 C. 1.4 D. 4

Answer : Option D
Explanation: Given Expression = [latex]\frac{8 - 2.8}{1.3}[/latex] [latex]\frac{5.2}{1.3}[/latex] = [latex]\frac{52}{13}[/latex] = 4
3. How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?

A. 5 B. 6 C. 7 D. None of these

Answer : Option B
Explanation: Sum of decimal places = 7. Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
4. 0.04 x 0.0162 is equal to:

A. 6.48 x [latex]{10}^{-3}[/latex] B. 6.48 x [latex]{10}^{-4}[/latex] C. 6.48 x [latex]{10}^{-5}[/latex] D. 6.48 x [latex]{10}^{-6}[/latex]

Answer : Option B
Explanation: 4 x 162 = 648. Sum of decimal places = 6. So, 0.04 x 0.0162 = 0.000648 = 6.48 x [latex]{10}^{-4}[/latex]
5. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?

A. 2010 B. 2011 C. 2012 D. 2013

Answer : Option B
Explanation: Suppose commodity X will cost 40 paise more than Y after z years. Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40 ⇒ 0.25z = 0.40 + 2.10 ⇒z = [latex]\frac{2.50}{0.25}[/latex] = [latex]\frac{250}{20}[/latex] = 10 ∴ x will cost 40 paise more than Y 10 years after 2001 i.e., 2011

Directions(1-5): Probability 1. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. [latex]\frac{3}{4}[/latex] B. [latex]\frac{4}{7}[/latex] C. [latex]\frac{1}{8}[/latex] D. [latex]\frac{3}{7}[/latex]

Answer : Option B
Explanation: Let number of balls = (6 + 8) = 14. A number of white balls = 8. P (drawing a white ball) = [latex]\frac{8}{14}[/latex] = [latex]\frac{4}{7}[/latex]
2. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A. [latex]\frac{1}{13}[/latex] B. [latex]\frac{3}{13}[/latex] C. [latex]\frac{1}{4}[/latex] D. [latex]\frac{9}{52}[/latex]

Answer : Option B
Explanation: Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = [latex]\frac{12}{52}[/latex] ∴ = [latex]\frac{3}{13}[/latex]
Directions(1-5): Mensuration 3. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is :

A. 30 cm B. 60 cm C. 72 cm D. 132 cm

Answer : Option B
Explanation: circumference = [latex]\frac{2*22}{7*42}[/latex] = 264 cm length of rectangle sides are 6x, 5x. then circumference is 2*(6x+5x) = 264, x = 12 smaller side of rectangle = 5x = 60 cm
4. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and the breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm2. Therefore, the length of the rectangle is :

A. 20 cm B. 30 cm C. 40 cm D. 50 cm

Answer : Option C
Explanation: b=x and l= 2x then (2x-5)(x+)-x*2x= 75 2[latex]{x}^{2}[/latex] + 5x-25-2[latex]{x}^{2}[/latex] = 75 x = 20 length = 40 cm
Directions(1-5): Averages 5. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A. 17 kg B. 20 kg C. 26 kg D. 31 kg

Answer : Option D
Explanation: Let A, B, C represent their respective weights. Then, we have: A + B + C = (45 x 3) = 135 .... (i) A + B = (40 x 2) = 80 .... (ii) B + C = (43 x 2) = 86 ....(iii) Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv) Subtracting (i) from (iv), we get : B = 31. B's weight = 31 kg.