CUET (UG) entrance exam Question Bank Solutions

The coordinates of the foot of the perpendicular drawn from the point A(1, 0, 3) to the join of the points B(4, 7, 1) and C(3, 5, 3) are

Find the values of 'K' if area of triangle is 4 square units and vertices are (k, 0), (4, 0), (0, 2).

What will the equation of line joining (1, 2) and (3, 6) using determinants

If the area of triangle is 35 square units with vertices (2, – 6), (5, 4) and (k, 4) then k is

If Δ = `|(1, 2, 3),(2, -1, 0),(3, 4, 5)|`, then `|(1, 6, 3),(4, -6, 0),(3, 12, 5)|` is

Let y = `f(x)` be the equation of a curve. Then the equation of tangent at (x_o, y_o) is :- 

The point on the curve `x^2 = 2y` which is nearest to the point (0, 5) is

For all real values of `x`, the minimum value of `(1 - x + x^2)/(1 + x + x^2)`

The maximum value of `[x(x - 1) + 1]^(2/3), 0 ≤ x ≤ 1` is

In a bank principal increases at the rate of r% per year find the value of r of Rs.100 double itself in 10 years `(log e^2 = 0.6931)`

In a bank, principal increases at the rate of 5% per year. An amount of Rs.1000 is deposited with this bank, how much will it worth after 10 years `(e^(0.5) = 1.648)`

Find the vector component of the vector with initial point (2, 1) and terminal point (–5, 7).

The equation of the circle passing through the foci of the ellipse `x^2/16 + y^2/9` = 1 and having centre at (0, 3) is

The domain of the function defined by f(x) = log_x 10 is

Which of the following graph represents the extreme value:-

If θ f(x) = `int_0^x t sin t  dt` then `f^1(x)` is

Find the equations of the planes that passes through three points (1, 1, – 1), (6, 4, – 5),(– 4, – 2, 3)

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:-

Suppose that two cards are drawn at random x from a deck of cards. Let x be the number of aces obtained. Then value of E(x) is

Which of the following is a homogeneous differential equation?