Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},...\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term.
Trả lời
(C)
\(81\sqrt{2}\)
5
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.
A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.
Trả lời
(D)
-4
16
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.
Trả lời
(B)
5.50
17
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
Trả lời
(A)
8.25
18
If r denotes the correlation coefficient between two variables, which of the following is always true?
Trả lời
(D)
\(-1 \leq r \leq 1\)
19
A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)
Trả lời
(A)
3.0 seconds
20
Differentiate \(\frac{x}{x + 1}\) with respect to x.
Trả lời
(B)
\(\frac{1}{(x + 1)^{2}}\)
21
Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.
Trả lời
(A)
\(5\sqrt{3} - 3\)
22
Find the unit vector in the direction of the vector \(-12i + 5j\).
Trả lời
(C)
\(\frac{-12i}{13} + \frac{5j}{13}\)
23
In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean
Trả lời
(B)
21
24
Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
Trả lời
(B)
3
25
Which of the following is nor a measure of central tendency?
Trả lời
(B)
Variance
26
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.
Trả lời
(D)
\(\frac{1}{36}\)
27
If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).
Trả lời
(C)
2
28
Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x - 3\) and the lines \(y + x = 1\).
Trả lời
(D)
(1, -4)
29
Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
Trả lời
(A)
90720
30
A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.
Trả lời
(D)
-2x + 3y - 6 =0
31
Find the number of different arrangements of the word IKOTITINA.
Trả lời
(A)
30240
32
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
Trả lời
(C)
45°
33
A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.
Trả lời
(A)
\(\frac{4}{7}\)
34
The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.
Trả lời
(C)
\(3 ms^{-2}\)
35
The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.
