If \(log_{y}\frac{1}{8}\) = 3, find the value of y.
Answer
(C)
\(\frac{1}{2}\)
2
A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).
Answer
(B)
\(\frac{-4\sqrt{3}}{3}\)
3
Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)
Answer
(B)
\(1+ \frac{1}{2}\sqrt{3}\)
4
If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.
Answer
(D)
\(\pm6\)
5
Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)
Answer
(C)
(\(\frac{2}{3}, \frac{-4}{3}\))
6
The function f: x \(\to \sqrt{4 - 2x}\) is defined on the set of real numbers R. Find the domain of f.
Answer
(B)
\(x \leq 2\)
7
Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).
Answer
(A)
-5
8
Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.
Answer
(D)
-22
9
Find the coefficient of \(x^{4}\) in the expansion of \((1-2x)^{6}\).
Answer
(C)
240
10
Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,...
Answer
(B)
46
11
How many ways can 6 students be seated around a circular table?
Answer
(C)
120
12
If \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\), find the value of k.
Answer
(C)
0.8
13
Express cos150° in surd form.
Answer
(B)
\(-\frac{\sqrt{3}}{2}\)
14
A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.
Answer
(D)
2x+3y=4
15
\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).
Answer
(C)
\(\frac{3}{2}\)
16
\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)
There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys
Answer
(C)
6006
25
The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.
Answer
(D)
36
26
Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.
Answer
(A)
10x+1
27
A curve is given by \(y = 5 - x - 2x^{2}\). Find the equation of its line of symmetry.
Answer
(B)
\(x = \frac{-1}{4}\)
28
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.
Answer
(B)
\(225 - \frac{3x}{2}\)
29
A fair die is tossed twice. What is its smple size?
Answer
(C)
36
30
Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a - \frac{1}{4}b)\).
