21.

The ratio between the length and the perimeter of a rectangular plot is 1 : 3. What is the ratio between the length and breadth of the plot?

• 2:1
  
  

• 3:2
  
  

• Data inadequate
  
  

• 1:2

If a, b and c are three natural numbers in ascending order, then

• c² - a² = b²

• c² - a² < b²

• c² + b² = a²

• c² - a² > b

If a * b = a² + b²and  $\mathrm{a}﮲\mathrm{b}$= a² - b², then the value of (5 * 2)$﮲25$ is 

• 225
  
  

• 226
  
  

• 216
  
  

• 215

Unit's digit in 13²⁰⁰³ is

• 3
  
  

• 7
  
  

• 9
  
  

• 1

The smallest number by which 68600 must be multiplied to get a perfect cube is

• 10

• 8

• 12

• 5

'Buy three, get one free.' What is the percentage of discount being offered here?

• 25
  
  

• 20
  
  

• 28.56
  
  

• 33.33

A cyclist at 'C' is cycling towards 'B'. How far will he have to cycle from C before he is equidistant from both A and B?

• 3 km
  
  

• 6 km
  
  

• 5 km
  
  

• 4 km

Given linear equations, I, II and III, a learner is not able to solve III algebraically. The most likely area of difficulty is that the learner has not understood

• that two equations can be solved by method of substitution
  
  

• the method of solving equations using graphs
  
  

• that both the equations in III can be altered by multiplying with suitable numbers
  
  

• that two equations can be added or subtracted to solve then

When doing exponents, the work observed in a learner's notebook was as follows

4³ x 4² = 4⁵ , 6⁴ x 6⁴ = 6⁸ , 7³ x 3⁷ = 21¹⁰

The learner has not understood how to

• add exponents and multiply
  
  

• multiply numbers with same base
  
  

• multiply numbers with different bases
  
  

• add exponents

A square sheet ABCD, when rotated on its diagonal AC as its axis of rotation, sweeps a

• spindle
  
  

• cylinder
  
  

• trapezium
  
  

• cone