Given the functions f·g: ℝ → ℝ, where f(x) = x² - 1 and g(x) = 2x + 1.

(g·f)(2) is:

If logₓ y = 2 and xy= 125,

then the values of x and y are respectively.

The vertical asymptotes of the curve

y = 1 / (x-2)(x+3) are:

When the polynomial p(x) = ax³ + 5x² + 2x - 8 is divided by (x -1), the remainder is -3.

So a is:

The set of values of x for which

[ (x+1)² + 3 ] / [ (x+3)(x-2) ] < 0 is:

A function f: ℝ → ℝ is defined by:

f(x) = 4β + 4x, if x < 1 and f(x) = 4x - β² - 4 if x >1.

If f(x) has a limit at x = 1, the value of:

Let p and q be statements. The compound statement ⊕ on the table could

Given the lines:

L₁: r = 3i - 2j + 4k + ∂(4i + 2j - 3k) 

L₂: r = i + 3j + k + δ(8i + 4j - 6k) 

L₃: r = 2i + 6j + 2k + β(i - 4j + 4k) 

L₄: r = 4i + 12j + 4k - μ(i + 3j + k). 

Which pair of lines are parallel?

A relation R defined on a non-empty set S is called a partial order if R is:

If ∑^∞_(r=1) m / 2^(r-1) = 10, then m is:

The first order differential equation obtained from the function

y = Ax + Inx is:

The shaded region represents

A function f: ℝ → ℝ is given by:

f(x) = (x+6) / x² - 2x - 15.

The domain of f is:

A curve is defined parametrically by x = 2t, y = 2/t.

The Cartesian equation of the curve is:

If r = i + 2j + 2k, s = -2i +3j + k,

then r x s is:

Given that f(θ) = sin θ - √3 cos θ.

Expressing f(θ) in the form R sin(θ - α) where R > 0 and α an acute angle, we obtain f(θ) is:

If f(x) = x² + kx - 3 has a root in the interval [1, 2] then the range of k is:

Given that the sum and product of roots of the equation

2x² - 2x + q = 0 are equal, the value of q is:

The sum of the first n terms of an arithmetic progression is n(2n+3).

The nth term of the progression is:

| (-5+10i) / (1+2i) |

The line L has equation r = 5i - 8j + k + ∂(i + 3j + 2k) and the plane π has equation 2x + 2y - z = 5.

The sine of the acute angle between the line and the plane is:

What is the result of d(3x + 2)⁴ /dx :

The equation of the circle which passes through the origin and the points (2, 0) and (0, -4) is:

The area of the finite region bound by the curve y = 2x - 1/x and the lines x = 1 and x = 3 is:

If a root of the equation x² + 2x + 1 = 0 is also a root of the equation x³ - 2x² + 6x + k = 0, the value of the constant k is:

A periodic function f, of period 4, is defined by

f(x) = x², 0 ≤ x < 2 and

f(x) = x + 2, 2 ≤ x < 4.

Then f(9) is:

Two functions f·g: ℝ → ℝ are such that

f(x) = 2x - 1 and (f·g)(x) = x - 2.

Then g(x) is:

The equation of the tangent to the curve,

y = 3x(2 - x²) at the point (1, 3) is:

Simplifying

(sin 5x - sin x) / (sin 4x - sin 2x) gives:

The number of arrangements of the word ARREARS is:

In the expansion of √(3+x), the range of values of x for which the complete expansion is valid is:

Evaluating 1 + 1/3 + 1/9 + 1/27 + … gives:

lim_x→∞( (4x² - 1) / (2x² + 1) ) is:

∫⁴₁ ((x+3) / x) dx is:

If the matrix M is as shown, then its determinant is:

The position vector of a particle at time t seconds is r, where r = [ (t² + 1)i + t³j ] m.

The vel of the particle when t = 2 is:

The extension a force of 20N produces in a spring of natural length 5 m whose modulus of is 150 N is:

The velocity of a particle A relative to another B is (7i + 5j) m/s.

Given that the velocity of A is (8i + 6j) m/s.

The velocity of B is:

Given that A and B are events with P(A) = 1/4 and P(A∪B) = 1/3 and P(A∩B) = 1/12. P(A|B) is:

A small sphere of mass 0.6 kg is moving on a horizontal table with a speed of 10 m/s when it collides with a fixed smooth wall perpendicular to the table surface. It rebounds with a speed of 15/2 m/s.

The coefficient of restitution between the sphere and the wall is:

Three particles of masses 5kg, 3 kg and m kg lie on the y-axis at the points (0, 4), (0, 2) and (0, 5) respectively.

The centre of mass of the system is at the point (0, 4).

The value of m is:

A car wheel of radius 1/2 m is moving at a speed of 10/3 m/s.

Its angular speed in rad/s is:

A car accelerates uniformly from a velocity of 10 m/s to 60 m/s in 6 seconds on a straight road.

The distance it covered is:

A box contains ten green and six white marbles.

A marble is chosen at random, its colour noted and it is not replaced.

This process is repeated once.

The probability that the marbles chosen are of the same colour is:

The engine of a car of mass 1,200 kg works at a constant rate of 69 kW up a road inclined at an angle sin⁻¹ (1/6) to the horizontal.

Given that the non-gravitational resistance to the motion of the car is 300 N and taking g as 10 m/s², the maximum speed of the car is:

The work done by a force F (i - 2j - 4k) N which moves its point of application from a point A with position vector r_A = (3i - 4j) m to another point B with position vector r_B = (-i - 6k) m is:

A particle decelerating to rest has its speed v m/s at time t seconds given by: v = 6t - ½ t².

The deceleration of the particle when v = 10 is:.

A particle of mass of 14 kg rests on a smooth horizontal table. It is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to a particle of mass 6 kg which hangs freely.

Given that the acceleration of the system 3 m/s² when it is released from rests, the force exerted by the string on the pulley is:

A smooth sphere A of mass 6 kg travelling at 4 m/s travelling at 2 m/s in the opposite direction.

Given that the speed of B after impact is 2 m/s.

The kinetic energy of A impact is: