If two graphs y = px\(^2\) + q and y = 2x\(^2\) -1 intersect at x = 2, find the value of p in terms q.
Answer
(B)
\(\frac{7-q}{4}\)
10
Solve the equations
m2 + n2 = 29
m + n = 7
Answer
(B)
(2, 5) and (5, 2)
11
An operation * is defined on the set of real numbers by a*b = a + b + 1. If the identity elements is -1, find the inverse of the element 2 under *.
Answer
(D)
-4
12
The sixth term of an A.P is half of its twelfth term. The first term of the A.P is equal to
Answer
(D)
the common difference
13
Factorize 4x2 - 9y2 + 20x + 25
Answer
(C)
(2x - 3y +5)(2x + 3y + 5)
14
A sector of a circle of radius 7.2cm which subtends an angle of 300° at the centre is used to form a cone. What is the radius of the base of the cone?
Answer
(B)
6cm
15
A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°
Answer
(C)
8√3cm
16
A straight line makes an angle of 30° with the positive x-axis and cuts the y-axis at y = 5. Find the equation of the straight line.
Answer
(D)
√3y = x + 5√3
17
Find the value of P if the line joining (P, 4) and (6, -2) is perpendicular to the line joining (2, P) and (-1, 3).
Answer
(A)
4
18
Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.
Answer
(A)
6
19
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
Answer
(A)
6.5 units
20
The bearings of P and Q from a common point N are 020° and 300° respectively. If P and Q are also equidistant from N, find the bearing of P from Q.
Answer
(B)
070°
21
A cylindrical tank has a capacity of 3080 m3. What is the depth of the tank if the diameter of its base is 14 m?
(Take pi = 22/7)
Answer
(C)
20 m
22
Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k.
Answer
(A)
y = 4 \(\pm\) k
23
The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.
Answer
(D)
πr/3
24
If the gradient of the curve y = 2kx2 + x + 1 at x = 1 is 9, find k.
Answer
(C)
2
25
Evaluate \(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)
Answer
(A)
3/5(2x-3)5/3 + k
26
Differentiate \((2x+5)^{2} (x-4)\) with respect to x.
Answer
(D)
(2x+5)(6x-11)
27
Find the area bounded by the curves y = 4 - x2 and y = 2x + 1
Answer
(C)
10(2/3) sq. units
28
Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
Answer
(B)
4π
29
If y = x sinx, find dy/dx when x = π/2.
Answer
(C)
1
30
Find the dimensions of a rectangle of greatest area which has a fixed perimeter p.
Answer
(D)
square of sides (p/4)
31
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. Find the square of the mode.
Answer
(B)
121
32
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. The mean score is
Answer
(B)
8.7
33
Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?
Answer
(C)
1/3
34
If 6Pr = 6, find the value of 6Pr+1
Answer
(A)
30
35
Find the variance of 2, 6, 8, 6, 2 and 6
Answer
(B)
5
36
Find the number of ways of selecting 8 subjects from 12 subjects for an examination
Answer
(B)
495
37
Find the range of \(\frac{1}{6}\), \(\frac{1}{3}\), \(\frac{3}{2}\), \(\frac{2}{3}\), \(\frac{8}{9}\), and \(\frac{4}{3}\)
Answer
(D)
4/3
38
Triangle SPT is the solution of the linear inequalities
Answer
(C)
2y - x - 2 ≤ 0, y + 2x + 2 ≤ 0, y ≥ 0, x ≤ 0
39
⊗
k
l
m
k
l
m
k
l
m
k
l
m
k
l
m
The identity element with respect to the multiplication shown in the table above is
Answer
(B)
m
40
The bar chart above shows different colours of passing a particular point of a certain street in two minutes. What fraction of the total number of cars is yellow?
Answer
(A)
3/25
41
In the figure PQR a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, < SRQ is 75º and < QPT IS 25º. Calculate the value of < RST
Answer
(C)
55o
42
Find the value of \(\theta\) in the diagram
Answer
(C)
120o
43
The bar chart shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the cars is yellow
Answer
(D)
\(\frac{3}{25}\)
44
The graph shows the cumulative frequency of the distribution of masses of fertilizer for 48 workers in one institution. Which of the following gives the inter-quartile range?
Answer
(D)
Q3 - Q1
45
The histogram shows the distribution of passengers in taxis at a certain motor park. How many taxis have more than 4 passengers?
