CUET (UG) entrance exam Question Bank Solutions

Function given by f(x) = sin x is strictly increasing in.

Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.

The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is

The degree of differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin((dy)/(dx)) + 1` = 0 is:

The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is

Find the cartesian equation of the line which passes ·through the point (– 2, 4, – 5) and parallel to the line given by.

`(x + 3)/3 = (y - 4)/5 = (z + 8)/6`

A linear function z = ax + by, where a and b are constants, which has to be maximised or minimised according to a set of given condition is called a:-

Maximised value of z in z = 3x + 4y, subject to constraints : x + y ≤ 4, x ≥ 0. y ≥ 0

One kind of cake requires 200 g of flour and 25 g of fat, and another kind of cake require 100 g of flour and 50 kg fat. Find the mamximum number of cake which can be made from 5 kg of flour and l kg of fat assuming that there is no shortage of the other ingradients used in making the cakes.

If z = 200x + 500y  .....(i)

Subject to the constraints:

x + 2y ≥ 10  .......(ii)

3x + 4y ≤ 24  ......(iii)

x, 0, y ≥ 0  ......(iv)

At which point minimum value of Z is attained.

A factory makes tennis rackets and cricket bats. A tennis racte takes 1.5 hour of a machine time and 3 hours of craftman's time in its making white a cricket bat takes 3 hours of machine time and 1 hour of craftman's time. In a day the factory has the availability of not more than 42 hours of machine time and 24 hours of craftman time. Then what number of rackets and lot must be made if the factory is to work at full capacity?

A manufacturer produces nuts and bolts. It takes 1 hours of work on machine. A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hours on machine B to produce a packages of bolts. He earns a profit of Rs. 17.50 per packages on nuts and Rs. 7.00 per packages on bolts. How many packages of each should be produced each day so as to maximise his profit if he operates his machine for at the most 12 hours a day?

If 'A' and 'B' are events such that `P(A/B) = P(B/A)` then:-

The probability that a student is not swimmer is `1/5`, Then he probability that out of five students, for are swimmers is

If 'A' and 'B' are two events, such that P(A)0 and P(B/A) = 1 then.

If P(A/B) > P(A), then which of the following is correct:-

If A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then.

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, then what will be the value of P(E/F) and P(F/E).

Compute P(A/B) If P(B) = 0.5, P(A ∩ B) = 0.32

What will be the value of P(A ∪ B) it 2P(A) = P(B) = `5/13` and P(A/B) = `?/5`