quantitative aptitude

Sin⁶ + cos⁶ is equal to? (a)          1 – 3sin² cos² θ (b)          1 – 3sin cos θ (c)           1+3sin² cos² θ (d)          1 Sol: Let a = sin² θ b = cos² θ. a³ + b³ = (a + b)³ – 3ab(a + b) sin6 θ+sin6 θ=1-3 sin2 θ cos 2 θ

A vessel of 115 litres is filled with milk and water. 70% of milk and 40% of water is taken out of the vessel it is found that the vessel is vacated by 52%. Find the difference between initial quantity of milk and water in litres? (a) 20 (b) 23 (c) 46 (d) 18 Sol:

What is the average of all the one digit, two digit and three digit natural numbers? (a)          300 (b)          500 (c)           1000 (d)          1250 Sol: Sum of all one digit, two digit & three digit natural numbers. 1 + 2 + 3 + ………………+999.

A manufacture of patent medicines gives 2 dozen extra bottles of the medicine for every order of 15 dozens a discount of 25% is also offered to the trader on one market price is a bottle is marked Rs. 119. Find the price at which a dozen bottle is manufactured if there is no loss

The range of the data 17, 21, 10, 4, 3, 33, 19, 7 is? (a) 6 (b) 12 (c) 16 (d) 30 Sol: Range = (Highest – Lowest) value = 33-3 =30

cos2θ-2sin2θ+2/sin2θ=1 , then what is the value of sin2+ 5cos+ tan2 . Sol: Cos² – 2sin² + 2 = sin² θ Cos² – sin² – 2sin² + 2 = 0. 1 – 2sin² – 2sin² + 2 = 0. 3 – 4sin² = 0 Sin θ= √3/2 θ =60 ° Put θ=60 °

Two inlet pipes can fill a cistern in 10 and 12 hours respectively and an outlet pipe can empty 80 gallons of water Per hour. All the three pipes working together can fill the empty cistern in 20 hours. What is the capacity (in gallons) of the tank? (a)          360 (b)          300 (c)           600 (d)         

X+Y+Z=1 and x3+y3+z3=4 then ? (a)0 (b)1 (c)-3 (d)-2 Sol: Put x = 0 y + z = 1, y³ + z³ = 4 (y + z)³ = 1 y³ + z³ + 3yz(y + z) = 1 4 + 3yz = 1 yz = -1 ATQ

If discount is equals to 1/5 of M.R.P and loss is half that discount then find the loss percent  Sol: MRP = 10 Discount = 2 SP = 8 = MRP – discount Loss = 1{half than discount} CP = 9

If the vertical height of a right circular cone is 28cm, and volume is 19712/3 cm3, then its curved surface area is? Sol: h = 28 cm.