Maths

A survey on a sample of 50 new cars being sold at a local auto dealer was conducted to see which of the three popular options – E1 engine, E2 engine and E3 engines were already installed. Following were the observation of the survey:

I. 30 had E1 engine

II. 4 had E1 engine and E3 engine but no E2 engine

III. 24 had E2 engine

IV. 12 had E1 engine and E2 engine but no E3 engine

V. 22 had E3 engine

VI. 8 had E2 engine and E3 engine

VII. 6 had all three options

What is the number of cars that had none of the options?

If P + Q + R + S = 1540 and 2P = 3Q = 4R = 5S, then what will be the difference between the values of R and S?

The figure shows a cylindrical tube with a hemispherical bottom of radius 1 cm. if its length is 7 cm, find the capacity of the tube.

Given px² + qx + r = 0, pick out the incorrect statement from the following:

I. Roots are equal if q² = 4pr

II. Roots are equal but opposite in sign if q = 0

III. One root is reciprocal of the other if p = r          

IV. Roots are complex if q² > 4pr

The nature of roots of equation $x^2-2\sqrt[]{5}x+3=0$ is as follows

400 students were supposed to go to a camp for 100 days. After 20 days, 40% of the students left the camp. If the camp had food for all of them for 100 days, for how many more days will the food last than what was initially planned?

Two metals A and B are to be used for making two different alloys. There are only 506 kg of A and 322 kg of B. If the ratio by weight of A to B in the first alloy is 5 : 3 and that in the second is 4 : 7, find what weight of each alloy must be produced so that no metal will be left over.

Two people start from opposite ends A and B of a corridor and move towards B and A respectively. When they meet for the first time, the respective distances covered by them is in the ratio 3 : 5 and one of them has covered 30 metres more than the other. If the speed of the person from A is 6 m/s, when will the person from B reach the end A after meeting with person from A?

Three solid metal spheres of radii 3 cm, 4 cm, 5 cm respectively, are melted together. The metal is recast as a single solid sphere. Find the percentage reduction in the area of surface resulting from this.

In a geometric progression, product of 11th term, 18th term and 20th term is equal to the product of 28th term and 5th term. Which of the following is necessarily true about that geometric progression?