Maths

A, B and C can alone do a work in 15 days, 20 days and 30 days, respectively. They work together for some time after which C leaves. A total of Rs. 18000 is paid for the work and B gets Rs. 6000 more than C. For how many days did A work?

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

For which of the following values of a and b, f(x) = a – x² + 1 and g(x) = x² + b + 3 and f(2) g(1) < 0 holds true.

How many zeroes will be there at the end of the number N, if N = 100! + 200!?

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?