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 (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
отговор
(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.
отговор
(B)
- 22
9
Differentiate \(\frac{x}{x + 1}\) with respect to x.
отговор
(D)
\(\frac{1}{(x + 1)^2}\)
10
Given that 2x + 3y - 10 = 0 and 3x = 2y - 11, calculate the value of (x - y).
отговор
(D)
- 5
11
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
отговор
(A)
N = X\(^{\frac{v}{p}}\) - M
12
Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
отговор
(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)
отговор
(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).
отговор
(C)
\(\frac{3}{5}\)
15
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
отговор
(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
отговор
(B)
\(\frac{1}{2}\)
17
Find the angle between i + 5j and 5i - J
отговор
(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.
отговор
(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\(^{-2}\)]
отговор
(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?
отговор
(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.
отговор
(C)
- 0.01
22
Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...
отговор
(C)
(8 - 3n)y + 1
23
A circle with centre (5,-4) passes through the point (5, 0). Find its equation.
отговор
(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.
отговор
(C)
0.53 square units
25
In how many ways can the letters of the word MEMBER be arranged?
отговор
(C)
180
26
Which of the following is not an equation of a circle?
отговор
(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.
отговор
(C)
15
28
In what interval is the function f : x -> 2x - x\(^2\) increasing?
отговор
(C)
x > 1
29
A force of 230N acts in its direction 065\(^o\). Find its horizontal component.
отговор
(D)
97.2
30
Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\))
отговор
(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?
отговор
(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.
отговор
(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.
отговор
(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.
отговор
(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.
