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