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