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