SSC CGL Tier-2 25-October-2015 Maths

A boat moves downstream at the rate of 1 km in $$ 7\frac{1}{2} $$  minutes and upstream at the rate of 5 km an hour, What is the speed (in km/hour) of the boat in the still water?

The greatest number among $$ 3^{50}, 4^{40}, 5^{30},  6^{20}$$ is

Give that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3: 2. The ratio of their corresponding bases is

If $$ \sec \theta - \tan \theta = \frac{1}{\sqrt{3}} $$ then value of $$ \sec\theta \tan \theta$$ is

A man sells an article at 5% above its cost price.\f he had bough tit at 5% less than what he had paid for it and sold it at 2 less, he would have gained 10%. The cost price of the article is

The value of $$ \frac{(0.67 \times 0.67 \times0.67)  \times (0.33 \times 0.33 \times 0.33)}{(0.67 \times 0.67) \div (0.67 \times 0.33) \div (0.33 \times 0.33)} $$

If a +b =1, find the value of $$ a^3 + b^3  -  ab - (a^2  - b^2)^2 $$

AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between them is 3 cm, then the diameter of the circle is

Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is

Three science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and CG is 81. Then the average score of classes A, B and C is.