Directions for Questions from 1 to 2: A class of ten students took a math exam. 

Each problem was solved by exactly seven of the ten students. The first nine students in the class 

solved exactly four problems each.

Question 1.

(linear equations)

What is the number of problems solved by the tenth student? Correct Answer: 2 6 4 7 3 Skip this question

Question 2.

(linear equations)

What is the number of problems on the test? Correct Answer: 2 5 6 4 7 3 Skip this question

Question 3.

Find the number of positive integral solutions of the equation (xy)z = 64. Correct Answer: 3 14 15 16 17 18 Skip this question

Question 4.

5 concentric squares each having different area are drawn on a sheet of paper.  If the area of the circle inscribed in the smallest square is 77 square units and the distance between  the corresponding vertices of consecutive squares is 1.5 units, then find the difference between  the areas of the largest and the smallest square in square units. (Take pie = 22/7) Correct Answer: 1 240 264 224 216 256 Skip this question

Question 5.

A class of 24 boys was divided into two sub-sections containing 12 boys each.  What is the probability that the two shortest boys of the class are in different sub-sections,  if all boys have different heights? Correct Answer: 3 7/24 6/23 12/23 14/23 None of these Skip this question

Question 6.

Two wheels of diameters 7 cm and 14 cm start rolling simultaneously towards each other from  two points which are 1990.5 cm apart. Both wheels make the same number of revolutions per second.  If both the wheels meet (touch externally) after 10 seconds, then what is the speed of the smaller wheel? Correct Answer: 2 132 cm/sec 66 cm/sec 44 cm/sec 22 cm/sec 67 cm/sec Skip this question

Directions for Questions from 7 to 8:

 ABC is a right – angled triangle right angled at B. BC is parallel to the X – axis. 
Given that the co-ordinates (x, y) of A, B and C are integers such - 9 < x < 10 and 8 < y < 18. 

Question 7.

(permutaion and combination)

How many distinct triangles ABC are possible? Correct Answer: 2 24000 22032 18724 27564 Infinitely Many Skip this question

Question 8.

(permutaion and combination)

The maximum possible area (in square units) of such a triangle ABC is  Correct Answer: 2 84 100 104 120 92 Skip this question

Question 9.

‘S’ denotes the sum to infinity and ‘Sn’ denotes the sum to ‘n’ terms of the series  1 + 4/5 + 16/25 + ...+ If S - Sn < 5/2. then the least value of ‘n’ is Correct Answer: 3 2 3 4 5 6 Skip this question

Directions for Questions from 10 to 10:

 A family consists of the husband, wife and six children. 
The age of the eldest child and the average age of the entire family at present is 27 years and 28 years
 respectively. The average age of the entire family after the fifth, fourth, third and second child
 was born is 24, 20, 16 and 18 respectively.

Question 10.

(linear equations)

What is the difference between the age of the first and the second child Correct Answer: 3 3 years 2 years 1 year 5 years Cannot be determined. Skip this question