CUET (UG) entrance exam Question Bank Solutions

Which of the following is magnitude of vectors. `veca = hati + hatj + hatk`

What is the product of  `(3veca * 5vecb) * (2veca + 7vecb)`

Find the vector equation of a plane which is at a distance of 7 units from the origin and which is normal to the vector `3hati + 5hatj - 6hatk`

What will be the cartesian equation of the following plane. `vecr * (hati + hatj - hatk)` = 2

In the following cases find the c9ordinates of foot of perpendicular from the origin `2x + 3y + 4z - 12` = 0

Find the vector and cartesian equations of the planes that passes through (1, 0, – 2) and the normal to the plane is `hati + hatj - hatk`

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)

If f(x) = ax² + 6x + 5 attains its maximum value at x = 1, then the value of a is

If the horizontal and vertical components of a force are negative, then that force is acting in between

The minimum value of `1/x log x` in the interval `[2, oo]` is

The function f(x) = [x], where [x] =greater integer of x, is

Let A be the foot of the perpendicular from focus P of hyperbola `x^2/a^2 - y^2/b^2 = 1` on the line bx – ay = 0 and let C be the centre of hyperbola. Then the area of the rectangle whose sides are equal to that of PA and CA is, 

Range of projectile will be maximum when angle of projectile is

The function `f(x) = x^3 - 6x^2 + 9x + 25` has

The maximum area of a right angled triangle with hypotenuse h is:

The method of splitting a single force into two perpendicular components along x-axis and y-axis is called as ______.

The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.

A unit vector perpendicular to the plane ABC, where A, B and C are respectively the points (3, –1, 2), (1, –1, –3) and (4, –3, 1), is