The sum of the progression is 1 + x + x2 + x3 + ......
Answer
(A)
\(\frac{1}{1 - x}\)
6
The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?
Answer
(B)
N = \(\frac{k P_{A} P_{B} }{D^2}\)
7
Find the square root of 170 - 20\(\sqrt{30}\)
Answer
(B)
2 \(\sqrt{5}\) - 5\(\sqrt{6}\)
8
If x\(^2\) + 4 = 0, then x ?
Answer
(E)
None of the above
9
What is the number whose logarithm to base 10 is 2.3482?
Answer
(A)
223
10
Five years ago, a father was 3 times as old as his son, now their combined ages amount to 110years. thus, the present age of the father is
Answer
(D)
80 years
11
If y = 2x2 + 9x - 35. Find the range of values for which y < 0.
Answer
(D)
-7 < x < \(\frac{5}{2}\)
12
Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased 15%. Thus the fractional increase in the family food bill is now
Answer
(D)
\(\frac{7}{200}\)
13
Given that \(a*b = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving * or ♦) for (a*b) ♦ (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers
Answer
(E)
ab + ac + 2a + b + c + 1
14
If a circular paper disc is trimmed in such a way that its circumference is reduced in the ratio 2:5, In what ratio is the surface area reduced?
Answer
(D)
4 : 25
15
If the four interior angles of a quadrilateral are (p + 10)°, (p - 30)°, (2p - 45)°, and (p + 15)°, then p is
A force of 5 units acts on a particle in the direction to the east and another force of 4 units acts on the particle in the direction north-east. The resultants of the two forces is
Answer
(C)
\(\sqrt{41 + 20 \sqrt{2}}\) units
18
The minimum point on the curve y = x2 - 6x + 5 is at
Answer
(D)
(3, -4)
19
If \(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is
Answer
(E)
x > \(\frac{9}{16}\)
20
A canal has rectangular cross section of width10cm and breadth 1m. If water of uniform density 1 gm cm-3 flows through it at a constant speed of1000mm per minute, the adjacent sea is
Answer
(A)
100000
21
A man runs a distance of 9km at a constant speed for the first 4 km and then 2 km\h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4 km is
Answer
(B)
8 km/h
22
A pyramid is constructed on a cuboid. The figure has
Answer
(E)
sixteen edges
23
In a geometric progression, the first term is 153 and the sixth term is \(\frac{17}{27}\). The sum of the first four terms is
Answer
(B)
\(\frac{680}{3}\)
24
An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is
Answer
(A)
351
25
A triangle has angles 30o, 15o and 135o. The side opposite to the angle 30o is length 6cm. The side opposite to the angle 135o is equal to
Answer
(C)
6\(\sqrt{2}\)cm
26
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
Answer
(B)
54\(\sqrt{3}\)cm2
27
In a soccer competition in one season, a club had scored the following goals: 2, 0, 3, 3, 2, 1, 4, 0, 0, 5, 1, 0, 2, 2, 1, 3, 1, 4, 1 and 1. The mean, median and mode are respectively
Answer
(B)
1.8, 1.5 and 1
28
If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to
Answer
(B)
45o
29
A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is
Answer
(C)
\(\frac{\pi}{24\sqrt{3}}\)
30
The set of value of x and y which satisfies the equations x2 - y - 1 = 0 and y - 2x + 2 = 0 is
Answer
(A)
1, 0
31
A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cycular of radius 3cm and height 4cm.Which of the following statements is true?
Answer
(C)
the total surface area of the cone is greater than that of the sphere
32
The quantity (x + y) is a factor of
Answer
(D)
2x3 + 2x2y - xy + 3x - y2 + 3y
33
Two triangles have the same areas if
Answer
(B)
three sides in one triangle are equal to three sides in the other
34
If (25)\(^{x - 1}\) = 64(\(\frac{5}{2}\))\(^6\), then x has the value
Answer
(B)
4
35
Assuming loge 4.4 = 1.4816 and loge 7.7 = 2.0142, then the value of loge \(\frac{7}{4}\) is
Answer
(A)
0.5326
36
The locus of all points having a distance of 1 unit from each of the two fixed points a and b is
Answer
(B)
a line perpendicular to the line ab through the mid-point of ab
37
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
If x4 - kx3 + 10x2 + lx - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and l
Answer
(A)
k = -7, 1 = -15
40
Evaluate without using tables sin(-1290º)
Answer
(E)
\(\frac{1}{2}\)
41
The angle of elevation of the top of a vertical tower from a point A on the ground is 60o. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the tower is 45o. Find the distance of A from the foot of the tower
Answer
(E)
\(\sqrt{3}\) + 1
42
The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b
Answer
(C)
\(\sqrt{10}\)
43
Add the same number to the numerator and denominator of \(\frac{3}{18}\). If the resulting fraction is \(\frac{1}{2}\), then the number added is
Answer
(D)
12
44
The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is
Answer
(C)
502
45
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
