Raial has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms, how many choices does she have?
Answer
(D)
210
10
Make R the subject of the formula if T = \(\frac {KR^2 + M}{3}\)
Answer
(B)
\(\sqrt\frac{3T - M}{K}\)
11
Find the remainder when X3 - 2X2 + 3X - 3 is divided by X2 + 1
Answer
(A)
2X - 1
12
Factorize completely 9y2 - 16X2
Answer
(D)
(3y - 4x)(3y + 4x)
13
Solve for x and y respectively in the simultaneous equations -2x - 5y = 3. x + 3y = 0
Answer
(C)
-9,3
14
If x varies directly as square root of y and x = 81 when y = 9, Find x when y = 1\(\frac{7}{9}\)
Answer
(D)
36
15
T varies inversely as the cube of R. When R = 3, T = \(\frac{2}{81}\), find T when R = 2
Answer
(B)
\(\frac{1}{12}\)
16
Solve the inequality -6(x + 3) \(\leq\) 4(x - 2)
Answer
(B)
x \(\geq\) -1
17
Solve the inequality x2 + 2x > 15.
Answer
(B)
-5 < x < 3
18
Find the sum of the first 18 terms of the series 3, 6, 9,..., 36.
Answer
(B)
513
19
The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms
Answer
(B)
62
20
A binary operation \(\oplus\) om real numbers is defined by x \(\oplus\) y = xy + x + y for two real numbers x and y. Find the value of 3 \(\oplus\) - \(\frac{2}{3}\).
Answer
(B)
\(\frac{1}{3}\)
21
If \(\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix}\) = \(\begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}\), find the value of x.
What is the size of each interior angle of a 12-sided regular polygon?
Answer
(B)
150o
25
A chord of circle of radius 7cm is 5cm from the centre of the circle.What is the length of the chord?
Answer
(A)
4√6 cm
26
A solid metal cube of side 3 cm is placed in a rectangular tank of dimension 3, 4 and 5 cm. What volume of water can the tank now hold
Answer
(B)
33 cm3
27
The perpendicular bisector of a line XY is the locus of a point
Answer
(D)
which is equidistant from the points X and Y
28
The midpoint of P(x, y) and Q(8, 6) is (5, 8). Find x and y.
Answer
(A)
(2, 10)
29
Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).
Answer
(B)
5y + 2x - 18 = 0
30
In a right angled triangle, if tan \(\theta\) = \(\frac{3}{4}\). What is cos\(\theta\) - sin\(\theta\)?
Answer
(C)
\(\frac{1}{5}\)
31
A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z.
Answer
(B)
135o
32
The derivatives of (2x + 1)(3x + 1) is
Answer
(D)
12x + 5
33
\(\begin{array}{c|c} Class Intervals & 0 - 2 & 3 - 5 & 6 - 8 & 9 - 11 & \\ \hline Frequency & 3 & 2 & 5 & 3 &\end{array}\)
Find the mode of the above distribution.
Answer
(D)
7
34
Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1
Answer
(A)
\(\frac{1}{3}\)
35
Evaluate \(\int^{1}_{0}\)(3 - 2x)dx
Answer
(C)
2
36
Find \(\int\) cos4 x dx
Answer
(D)
\(\frac{1}{4}\) sin 4x + k
37
The sum of four consecutive integers is 34. Find the least of these numbers
Answer
(A)
7
38
\(\begin{array}{c|c} No & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline Frequency & 1 & 4 & 3 & 8 & 2 & 5 \end{array}\). From the table above, find the median and range of the data respectively.
Answer
(B)
(3, 5)
39
\(\begin{array}{c|c}
Class Interval & 3 - 5 & 6 - 8 & 9 - 11 \\ \hline Frequency & 2 & 2 & 2 \end{array}\). Find the standard deviation of the above distribution.
Answer
(B)
√6
40
In how many was can the letters of the word ELATION be arranged?
Answer
(B)
7!
41
In how many ways can five people sit round a circular table?
Answer
(A)
24
42
Find the probability that a number picked at random from the set(43, 44, 45, ..., 60) is a prime number.
Answer
(C)
\(\frac{2}{9}\)
43
Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)
Answer
(A)
sec2 \(\theta\)
44
From the venn diagram above, the complement of the set P\(\cap\)Q is given by
Answer
(A)
{a, b, d, e}
45
The pie chart shows the distribution of courses offered by students. What percentage of the students offer English?
