Mathematical Ability Test-5

The curve represented by the equations

x = 3(cos t + sin⁡ t)

y = 4(cos ⁡t − sin ⁡t) is:

The simplified value of (√3 + 1)(10 + √12)(√12 − 2)(5 − √3) is-

In a frequency distribution, if the mean and median are 10 and 9 respectively, then its mode is approximately:

A,B and C are three mutually exclusive and exhaustive events. P(A) = 2P(B) = 6P(C), Find P(B):

A, B, and C play cricket. If the ratio of the number of runs scored by A to that scored by B and the number of runs scored by B to that scored by C is 3:2. The total number of runs is 342. The number of runs scored by A was?

The number of terms which are free from radical signs in the expansion of 

A pipe can fill a tank with water in 20 hours but due to leakage at the tank in it's bottom, it takes 40 hours to fill the tank. In what time the leakage will empty the fully filled tank.

If in an ellipse minor axis is equal to 8 and the major axis is equal to 4 then its area is:

Ninad, Vikas, and Manav enter into a partnership. Ninad invests some amount at the beginning. Vikas invests double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs. 45,000 at the end of the year. What is Manav’s share in the profit?