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Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find the relation between x and y.
A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} = (6 N, 180°)\). Find the magnitude of the resultant force.
The ages, in years, of 5 boys are 5, 6, 6, 8 and 10. Calculate, correct to one decimal place, the standard deviation of their ages.
Three defective bulbs got mixed up with seven good ones. If two bulbs are selected at random, what is the probability that both are good?
Express the force F = (8 N, 150°) in the form (a i + b j) where a and b are constants.
A force F acts on a body of mass 12kg increases its speed from 5 m/s to 35 m/s in 5 seconds. Find the value of F.
Two balls are drawn, from a bag containing 3 red, 4 white and 5 black identical balls. Find the probability that they are all of the same colour.
Eight football clubs are to play in a league on home and away basis. How many matches are possible?
If the mean of -1, 0, 9, 3, k, 5 is 2, where k is a constant, find the median of the set of numbers.
Evaluate \(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\).
Simplify \(2\log_{3} 8 - 3\log_{3} 2\)
Calculate, correct to the nearest degree, the angle between the vectors \(\begin{pmatrix} 13 \\ 1 \end{pmatrix}\) and \(\begin{pmatrix} 1 \\ 4 \end{pmatrix}\).
Two fair dices, each numbered 1, 2, ..., 6, are tossed together. Find the probability that they both show even numbers.
The position vectors of A and B are (2i + j) and (-i + 4j) respectively; find |AB|.
Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{3}{4}\) respectively. Find the probability that exactly 2 of them hit the target.
The velocity \(v ms^{-1}\) of a particle moving in a straight line is given by \(v = 3t^{2} - 2t + 1\) at time t secs. Find the acceleration of the particle after 3 seconds.
A stone is projected vertically with a speed of 10 m/s from a point 8 metres above the ground. Find the maximum height reached. \([g = 10 ms^{-2}]\).
Which of the following is the semi- interquartile range of a distribution?