Except for the following questions, all the remaining questions have been asked in Set 1 and Set 2.
Q. 1. Express the following as a rational expression in lowest terms:
Ans:(X+2)
Q. 2. Find the 8th term from end of the A.P. 7, 10, 13, ...,184.
Ans:(163)
Q. 4. Find the L.C.M. of the following polynomials:
Ans:[3(X-3)(X+3)(X+6)(X2+3X+9)
Q. 6. Find the number of terms of the A.P. 63, 60, 57, ..., so that their sum is 693.
Ans(n = 21 or n = 22)
Q. 11. Solve the following system of equations graphically:
Find the points where the lines meet the x-axis.
Ans:C(4,0);B(-3,0)
Q. 12. The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Ans:(6,12; 12,6)
Q. 20. There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.
Ans:[2/3
Q. 21. Prove that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
Apply the above theorem on the following:
ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1 -5 cm, QC = 4-5 cm, prove that area of 
is one-sixteenth of the area of 
