Maths

There are three glasses of equal capacity. The ratio of milk & water in the three is 2 : 5, 3 : 4, 4 : 5. The mixture of these three is put into a bucket. Find ratio of water to milk in the bucket.

A car running from point P₁ to point P₂ meets with an accident 50 km from point P₁, after which it travels with three- fifths of its original velocity and arrives 3 hours late at point P₂; if the accident had occurred 50 km further on, it would have been only 2 hours late. Find the distance from point P₁ to point P₂.

Two runners ride from A to B a distance of 55 km, and the first arrives 30 minutes before the second. They then ride from B to A, the first giving the second a start of 4 km and yet arrive 6 minutes before him. Find the speed of A.

There is a right circular cone of base radius 5 cm. This cone is cut into two portions by a plane parallel to its base such that the portion above the plane is a cone of base radius 3 cm and the portion below the plane has a height of 6 cm. Find the volume of the bottom solid.

A Banana seller sells x dozen Bananas. If he had sold 100 dozen Bananas more at 20 paise a dozen less or if he had sold 120 dozen less at 30 paise a dozen more, he would have received the same amount for his Bananas. How many dozens does he sell?

A shopkeeper buys 216 packets of biscuits at the rate of Rs. $\frac{x}{8}$ per pkt. He sells 8 dozen at the rate of Rs. 2.36 x per dozen and the rest at 16 $\left(\frac{x}{4}+1\right)$ paise each. What is the value of profit?

8 litres of wine are drawn from a cask and replaced by 8 litres of water. 8 litres of the mixture are next drawn and again replaced by 8 litres of water. If the ratio of wine to water in the cask is now 81 : 19, how much wine was in the cask at first? (There was no water in the cask at first.)

S1, S2 and S3 are three contestants for a race of 2,000 metres. If S1 can give S2 a start of 100 metres and S3 a start of 138 metrse, then of how many metres would S2 give a start to S3 in a similar race?

 If the shortest distance between the straight lines 3(x – 1) = 6(y – 2) = 2(z – 1) and 4(x – 2) = 2(y - $\lambda )$  = (z – 3), $\lambda \in R$ is $\frac{1}{\sqrt[]{38}},$  then the integral value of  is equal to:

(a) Let n denote the number of solutions of the equation z² +  where z is a complex number. Then the value of $\lambda$  is equal to:

Let the circle S : 36x² + 36y² – 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x – 2y = 4 and 2x – y = 5 lies inside the circle S, then: