Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
إجابة
(D)
\(x: x \in R\)
3
Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.
إجابة
(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.
إجابة
(D)
3
5
If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
إجابة
(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.
إجابة
(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?
إجابة
(C)
\((R \cap P) \subset (R \cap U)\)
8
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
إجابة
(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 \((\beta + 1)\).
إجابة
(B)
\(2x^{2} - 9x + 13 = 0\)
10
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.
إجابة
(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 \((x - \frac{3}{x^{2}})^{9}\).
إجابة
(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.
إجابة
(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.
إجابة
(C)
3
16
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
إجابة
(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.
إجابة
(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.
إجابة
(C)
0.6
32
Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).
إجابة
(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?
إجابة
(D)
\(\frac{2}{3}\)
34
If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
إجابة
(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.
