A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) - y\(^2\) + xy, where x, \(\in\) R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
Răspuns
(D)
1 + \(\sqrt{6}\)
2
Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)
If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k.
Răspuns
(B)
- 22
9
Differentiate \(\frac{x}{x + 1}\) with respect to x.
Răspuns
(D)
\(\frac{1}{(x + 1)^2}\)
10
Given that 2x + 3y - 10 = 0 and 3x = 2y - 11, calculate the value of (x - y).
Răspuns
(D)
- 5
11
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
Răspuns
(A)
N = X\(^{\frac{v}{p}}\) - M
12
Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
Răspuns
(C)
\(\frac{5}{4}\)
13
Given that P = {x : 1 \(\geq\) x \(\geq\) 6} and Q = {x : 2 < x < 10}. Where x are integers, find n(p \(\cap\) Q)
Răspuns
(A)
4
14
If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
Răspuns
(C)
\(\frac{3}{5}\)
15
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
Răspuns
(B)
9
16
Calculate the probability that the product of two numbers selected at random with replacement from the set {-5,-2,4, 8} is positive
Răspuns
(B)
\(\frac{1}{2}\)
17
Find the angle between i + 5j and 5i - J
Răspuns
(D)
90\(^o\)
18
Given that F = 3i - 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.
Răspuns
(C)
p=10, q=- 7
19
A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms\(^{-2}\)]
Răspuns
(A)
2.9.seconds
20
In which of the following series can be the formula S = \(\frac{a}{1 - r}\) where a is the first term and r is the common ratio, be used to find the sum of all the terms?
Răspuns
(D)
128 + 64 + 32 + 16 + ...
21
If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x.
Răspuns
(C)
- 0.01
22
Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...
Răspuns
(C)
(8 - 3n)y + 1
23
A circle with centre (5,-4) passes through the point (5, 0). Find its equation.
Răspuns
(C)
x\(^2\) + y\(^2\) - 10x + 8y + 25 =0
24
Calculate, correct to two decimal places, the area enclosed by the line 3x - 5y + 4 = 0 and the axes.
Răspuns
(C)
0.53 square units
25
In how many ways can the letters of the word MEMBER be arranged?
Răspuns
(C)
180
26
Which of the following is not an equation of a circle?
Răspuns
(D)
x\(^2\) - y\(^2\) + 3x - 5y = 2
27
A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.
Răspuns
(C)
15
28
In what interval is the function f : x -> 2x - x\(^2\) increasing?
Răspuns
(C)
x > 1
29
A force of 230N acts in its direction 065\(^o\). Find its horizontal component.
Răspuns
(D)
97.2
30
Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\))
Răspuns
(C)
\(\frac{2}{3}\)
31
A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?
Răspuns
(C)
60
32
The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.
Răspuns
(A)
0.58
33
A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.
Răspuns
(C)
\(\frac{5}{36}\)
34
The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.
Răspuns
(D)
225
35
P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ.
