Algebra: Test Item Construction

 

1. Epsilon borrowed Rs 4368 which he promises to pay in 6 annual installments, each installment being treble of the preceding one.
   (a) Which progression is associated with given situation ? [ 1K ]
   (b) Find the amount of first installment.[2U]
   (c) If 2k, 2k+3, 2k+9 are the first three terms of a geometric sequence. Find sixth term.[2A]
   
   
   
2. The sum of digits of a two-digit number is 7 and their product is 12.
   (a) If the digit in unit place be \( x \) then write digit in tenth place in terms of \(x\) [1K]
   (b) Find the two digit number.[2A]
   (c) By what percent this will be changed when the digits are reversed?[2HA]
   
   
   
3. (a) Simplify: \( \frac{x+3}{x^2+3x+9} + \frac{x-3}{x^2-3x+9}-\frac{54}{x^4+9x^2+81} \) [2U]
   (b) Solve: \( 4^{x-3} + 4^{3-x} = 1 \frac{1}{4} \) [3A]