Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
Хариулт
(D)
\(x: x \in R\)
3
Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.
Хариулт
(A)
1, 3
4
A binary operation * is defined on the set of real numbers, by \(a * b = \frac{a}{b} + \frac{b}{a}\). If \((\sqrt{x} + 1) * (\sqrt{x} - 1) = 4\), find the value of x.
Хариулт
(D)
3
5
If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
Хариулт
(D)
\(\frac{4\sqrt{10}}{5}\)
6
If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.
Хариулт
(D)
13
7
\(P = {1, 3, 5, 7, 9}, Q = {2, 4, 6, 8, 10, 12}, R = {2, 3, 5, 7, 11}\) are subsets of \(U = {1, 2, 3, ... , 12}\). Which of the following statements is true?
Хариулт
(C)
\((R \cap P) \subset (R \cap U)\)
8
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
Хариулт
(C)
\(a = 9b^{3}\)
9
If \(\alpha\) and \(\beta\) are the roots of \(2x^{2} - 5x + 6 = 0\), find the equation whose roots are \((\alpha + 1)\) and \((\beta + 1)\).
Хариулт
(B)
\(2x^{2} - 9x + 13 = 0\)
10
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.
Хариулт
(C)
\(\frac{1}{2(x - 2)} + \frac{5x}{2(x- 2)^{2}}\)
11
If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n.
Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\).
Хариулт
(A)
324
14
The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b.
Хариулт
(B)
a = -5, b = 14
15
If \(\begin{vmatrix} k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix} 2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0.
Хариулт
(C)
3
16
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
Хариулт
(C)
291
17
The first term of a Geometric Progression (GP) is \(\frac{3}{4}\), If the product of the second and third terms of the sequence is 972, find its common ratio.
Out of 70 schools, 42 of them can be attended by boys and 35 can be attended by girls. If a pupil is selected at random from these schools, find the probability that he/ she is from a mixed school.
Хариулт
(B)
\(\frac{1}{10}\)
31
The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below
Mathematics
3
4
2
1
Physics
4
3
1
2
Calculate the Spearmann's rank correlation coefficient.
Хариулт
(C)
0.6
32
Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).
Хариулт
(B)
\(3\sqrt{13}\)
33
What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together?
Хариулт
(D)
\(\frac{2}{3}\)
34
If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
Хариулт
(D)
\(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)
35
A body of mass 28g, initially at rest is acted upon by a force, F Newtons. If it attains a velocity of \(5.4ms^{-1}\) in 18 seconds, find the value of F.
