CUET (UG) entrance exam Question Bank Solutions for Mathematics

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?

Probability that 'A' speaks truth is `4/5`. A coin is taked. A reports that head appears. the probability that actually there was head is

If 'A' and 'B' are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is true :-

Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

A ball is thrown upward at a speed of 28 meter per second. What is the speed of ball one second before reaching maximum height? (Given that g= 10 meter per second²)

Range of projectile will be maximum when angle of projectile is

Find the equation of the curve at every point of which the tangent line has a slope of 2x:

The area above the x-axis and under the curve `y = sqrt(1/x - 1)` for `1/2 ≤ x ≤ 1` is: