Question – 1
1. Area of a right triangle is 504 sq.cm. The length of the hypotenuse is 65 cm.?
ColumnA  ColumnB 

Sum of the sides containing the right angle  Length of the hypotenuse 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
The sum of any two sides of a triangle is always greater than the third side. Hence, option A is correct.
Question – 2
2. Consider the sequence 9, 5, 1, 3,….?
ColumnA  ColumnB 

The 50th term  191 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Let the first term of the sequence be a and the common difference be d.
a= 9
d = 1(5) = 51=4
The nth term of the sequence is given byTn=a+(n1)d
=9+(501)4
=9+49*4
=9+196
=187
The 50th term is 187
Option B is correct
Question – 3
3.
ColumnA  ColumnB 

Number of ways in which one person can be selected from a group of 10  Number of ways in which two persons can be chosen from a group of 20 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
One person can be selected from a group of 10 in C(10,1) ways
C(10,1)=10!/[1!9!] =10
Two persons can be selected from a group of 20 in C(20,2) ways
C(20,2)=20!/[2!18!]
=20*19/2=10*19=190
Option B is correct.
Question – 4
4. logx/2=logy/3=logz/5.?
ColumnA  ColumnB 

xy  yz 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Let logx/2=logy/3=logz/5=k
logx=2k, logy=3k and logz=5k
logx+logy = 2k+3k=5k
log(xy) = 5klogy+logz = 3k+5k=8k
log(yz) = 8klog(xy)
Question – 5
5. The average of the marks obtained by 30 students of a class is 50. If the score of one student is removed, the average reduces by 1.?
ColumnA  ColumnB 

Average score of the remaining students  The score that was removed 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Average = Total marks/number of students
Total marks = Average*number of students
= 50*30 = 1500New average = 501=49
Number of students = 301=29
Total marks = 49*29
= 1421
Marks of the student = 15001421
= 79
The score that was removed = 79
Average score of the remaining students = 49
Option B is correct.
Question – 6
6. A square is constructed taking a side of a rectangle as a side of the square.?
ColumnA  ColumnB 

Perimeter of the square  Perimeter of the rectangle 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:D
 Answer Explanation:
We do not know whether the square is along the length or along the breath of the rectangle.
Hence, we cannot compare the perimeters.
Option D is correct.
Question – 7
7. A point divides the line joining (1,5) and (6,5) in the ratio 1:6.?
ColumnA  ColumnB 

Ordinate of the point  Abscissa of the point 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
The coordinates of the point are given by
((1*6+6*1)/(6+1), (5*6+5*1)/(6+1))
= ((6+6)/7, (30+5)/7)
= (0, 25/7)
Abscissa is the x coordinate and hence it is greater than the ordinate, which is the y coordinate.
Option B is correct.
Question – 8
8.
ColumnA  ColumnB 

Number of twodigit numbers  Number of threedigit numbers less than 250 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Number of twodigit numbers = 999=90
Number of threedigit numbers less than 250=25099=151
90<151
Option B is correct.
Question – 9
9.
ColumnA  ColumnB 

Number of vertices of a rectangle  Number of triangles that can be formed from the vertices of a rectangle 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
Number of vertices of a rectangle = 4
Number of triangles that can be formed from the vertices of a rectangle = C(4,3)
= 4!/(3!1!)
= 4
Hence, option C is correct.
Question – 10
10.
ColumnA  ColumnB 

Perimeter of a square with each side 29 cm long.  Perimeter of a rhombus whose diagonals are 40cm and 42cm long 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
Perimeter of the square = 29*4=116 cm
The diagonals of a rhombus bisect each other at right angles.
Thus, the rhombus is divided into 4 congruent right triangles.
The hypotenuse of any triangle is a side of the rhombus.
Applying Pythagoras theorem, we get
Hypotenuse = Sqrt[(40/2)^2+(42/2)^2]
= sqrt(20^2+21^2)
= sqrt(400+441)
= sqrt(841)
= 29cm
Perimeter of the rhombus = 4*29
= 116 cmOption C is correct.
[20^2=20*20]
Question – 11
11. The radius of a circle is 49cm. Each side of a square is equal to the diameter of the circle.?
ColumnA  ColumnB 

Area of the square  Area of the circle 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
Area of the circle = pi*r^2, where r is the radius of the circle
Area = 22/7*49*49=7546 sq.cm.Each side of the square = 2*radius
= 2*49 = 98cm
Area of square = side*side
= 98*98
=9604 sq.cm.Option A is correct.
[pi=22/7, r^2=r*r]
Question – 12
12. A chord of length 112 cm is at a distance of 33 cm from the centre. ?
ColumnA  ColumnB 

Length of the chord.  Radius of the circle 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
A line drawn from the center of the circle perpendicular to the chord will bisect the chord.
This line, the radius of the circle and the chord form a right triangle.
Applying the Pythagoras theorem to the triangle, we get
Hypotenuse = sqrt[base^2+perpendicular^2]
= sqrt[(112/2)^2+33^2]
= sqrt[56^2+1089]
= sqrt[3136+1089]
= sqrt(4225) = 65cm
Radius of the circle is 65 cm.
Length of the chord is 112 cm.
Option A is correct.
[x^2=x*x]
Question – 13
13. The population of a town is 140000. It increases by 5% in the first year. In the second year, it decreases by 10%.?
ColumnA  ColumnB 

Population after the first year  Population after the second year 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
This problem is similar to a problem of compound interest.
Population after 1 year = 140000(1+5/100) = 147000
Population after 2 years = 147000(110/100) = 132300
Option A is correct.
Question – 14
14.
ColumnA  ColumnB 

Number of factors of 20 that are smaller than 40  Number of multiples of 20 that are smaller than 45 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
Factors of 20 = 1, 2, 4, 5, 10, 20
Multiples of 20 that are smaller than 45 = 20, 40
Option A is correct.
Question – 15
15. A teacher prepares a test having 5 objectivetype questions. Each question has an incorrect and a correct option.?
ColumnA  ColumnB 

The number of correct ways in which the test can be answered  The number of incorrect ways in which the test can be answered 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Each question can be answered in 2 ways
There are in all 5 questions.
Number of ways in which the test can be answered = 2*2*2*2*2 = 32
Number of correct ways of answering the test = 1
Number of incorrect ways of answering the test = 321=31
Option B is correct.