CUET (UG) entrance exam Question Bank Solutions for Mathematics

Form the point of intersection (P) of lines given by x₂ – y² – 2x + 2y = 0, points A, B, C, Dare taken on the lines at a distance of `2sqrt(2)` units to form a quadrilateral whose area is A₁ and the area of the quadrilateral formed by joining the circumcentres of ΔPAB, ΔPBC, ΔPCD, ΔPDA is A₂, then `A_1/A_2` equals

The equation of the curve passing through the point `(0, pi/4)` whose differential equation is sin x cos y dx + cos x sin y dy = 0, is

The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4  dx` is

`int (cos^2x)/(sin x + cos x)^2  dx` is equal to

The probability of obtaining an even prime number on each die when a pair of dice is rolled is

Two events 'A' and 'B' are said to be independent if

If P(A) = `3/5` and P(B) = `1/5`, find P(A ∩ B), If A and B are independent events.

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Let A and B be independent events P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)

The speed of a stream is 3 km/hr. A boat goes 24 km and comes back to the starting point in 6 hours. What is the speed (in km/hr) of the boat in still water?

The solution of the differential equation `(dx)/(dy) + Px = Q` where P and Q are constants or functions of y, is given by

The existence of unique solution of the system of linear equations x + y + z = a, 5x – y + bz = 10, 2x + 3y – z = 6 depends on 

If α, β are different values of x satisfying the equation a cos x + b sinα x = c, where a, b and c are constants, then `tan ((alpha + beta)/2)` is

The solution of the differential equation `(dy)/(dx) = 1 + x + y + xy` when y = 0 at x = – 1 is

The value of λ, such that the following system of equations has no solution, is

`2x - y - 2z = - 5`

`x - 2y + z = 2`

`x + y + lambdaz = 3`

`int cos(log x)  dx = F(x) + C` where C is arbitrary constant. Here F(x) =

A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is

In system of equations, if inverse of matrix of coefficients A is multiplied by right side constant B vector then resultant will be?

The number of values of k for which the linear equations 4x + ky + 2z = 0, kx + 4y + z = 0 and 2x + 2y + z = 0 possess a non-zero solution is

If the system of equations x + λy + 2 = 0, λx + y – 2 = 0, λx + λy + 3 = 0 is consistent, then