CUET (UG) entrance exam Question Bank Solutions for Mathematics

Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?

The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is

The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is

The general solution of the differential equation `(ydx - xdy)/y` = 0

The general solution of the differential equation `x^xdy + (ye^x + 2x)  dx` = 0

Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`

What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2)  (-2 < y < 2)`

Find the equation of line which passes through the point (1, 2, 3) and is parallel to the vector `3hati + 2hatj - 2hatk`

Find the angle between the following pair of lines:- `(x - 2)/ = (y - 1)/5 = (z + 3)/(-3)` and `(x + 2)/(-1) = (y - 4)/8 = (z - 5)/4`

What will be the shortest distance between the lines, `vecr = (hati + 2hatj + hatk) + lambda(hati - hatj + hatk)` and `vecr = (2hati - hatj - hatk) + mu(2hati + hatj + 2hatk)`

Determine the distance from the origin to the plane in the following case x + y + z = 1

Distance between the planes :- 

`2x + 3y + 4z = 4` and `4x + 6y + 8z = 12` is

The planes `2x - y + 4z` = 5 and `5x - 2.5y + 10z` = 6

Find the shortest distance between the lines, `vecr = 6hati + 2hatj + 2hatk + lambda(hati - 2hatj + 2hatk)` and `vecr = - 4hati - hatk + mu(3hati - 2hatj - 2hatk)`

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.

The comer point of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let x = Px + qx where P, q > 0 condition on P and Q so that the maximum of z occurs at both (3, 4) and (0, 5) is

Minimise z = – 3x + 4y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0 What will be the minimum value of z ?

Any point in the feasible region that gives the optional value (maximum or minimum) of the objective function is called:-

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?