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