CUET (UG) entrance exam Question Bank Solutions for Mathematics

The function f(x) = x² – sin x + 5 is continuous at x =

What is the values of' 'k' so that the function 'f' is continuous at the indicated point

For what value of `k` the following function is continuous at the indicated point

`f(x) = {{:(kx^2",", if x ≤ 2),(3",", if x > 2):}` at x = 2

For what value of `k` the following function is continuous at the indicated point

`f(x) = {{:(kx + 1",", if x ≤ pi),(cos x",", if x > pi):}` at = `pi`

Find the values of `a` and ` b` such that the function by:

`f(x) = {{:(5",", if  x ≤ 2),(ax + b",", if 2 < x < 10),(21",", if x ≥ 10):}`

is a continuous function.

Which of the following graph represent the strictly increasing function.

Let x₀ be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x₀ –  h, ro + h) containing x₀. Then which of the following statement is/ are true for the above statement.

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`

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.

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 P(A) = `1/2`, P(B) = 0, then `P(A/B)` is

If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then

Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to

The value of the integral `int_(-1)^2 [x]  dx` is