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Find the value of the constant k for which \(a = 4 i - k j\) and \(b = 3 i + 8 j\) are perpendicular.
If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?
A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?
Express \(r = (12, 210°)\) in the form \(a i + b j\).
| Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| No of students | 5 | 7 | 9 | 6 | 3 | 6 | 4 |
The table above shows the distribution of marks by some candidates in a test. If a student is selected at random, what is the probability that she scored at least 6 marks?
| Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| No of students | 5 | 7 | 9 | 6 | 3 | 6 | 4 |
The table above shows the distribution of marks by some candidates in a test. Find, correct to one decimal place, the mean of the distribution.
| Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| No of students | 5 | 7 | 9 | 6 | 3 | 6 | 4 |
The table above shows the distribution of marks by some candidates in a test. What is the median score?
Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the resultant force.
The probability of Jide, Atu and Obu solving a given problem are \(\frac{1}{12}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) respectively. Calculate the probability that only one solves the problem.
Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).
If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).
Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).