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If \((2x^{2} - x - 3)\) is a factor of \(f(x) = 2x^{3} - 5x^{2} - x + 6\), find the other factor
If P = \({n^{2} + 1: n = 0,2,3}\) and Q = \({n + 1: n = 2,3,5}\), find P\(\cap\) Q.
Given that \(f(x) = 2x^{2} - 3\) and \(g(x) = x + 1\) where \(x \in R\). Find g o f(x).
The velocity, V, of a particle after t seconds, is \(V = 3t^{2} + 2t - 1\). Find the acceleration of the particle after 2 seconds.
Find the magnitude and direction of the vector \(p = (5i - 12j)\)
Solve \(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
A force (10i + 4j)N acts on a body of mass 2kg which is at rest. Find the velocity after 3 seconds.
Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the result of tossing a fair die 150 times, find the mode.
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining a 5.
Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a - \frac{1}{4}b)\).
A fair die is tossed twice. What is its smple size?
In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.
A curve is given by \(y = 5 - x - 2x^{2}\). Find the equation of its line of symmetry.
Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.
The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.
There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys
Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)
Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)
If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).