CSAT

                            Exercise 1

1.   If P/Q = 7 ;    Then find the value of  (P^2 + Q^2) / (P^2 - Q^2)

2. IF a/b = 3 /5 , Then find the value of  (9a + 4 b) / ( 9a - 4 b)

3. Find the value of      [(0.5)^4 - (0.4)^4] / [(0.5)^2 + (0.4)^2]

4. The cost of 6 Hard disk is equal to 9 printers, the cost of 27 printers is equal to 30 scanners and the cost of 300 scanners is equal to 9 computers . If the cost of 3 computers is Rs. 24000 then find the cost of a hard disc .

5.There are 2 baskets  A & B containing balls . If 10 balls are transferred from A to B, then the number of balls in both the baskets become equal. If 20 balls had been transferred from B to A , then the number of balls in basket A would have been twice that of in B . Find the original number of balls in basket A .

6.A,B&C start a business in which A,s Investment is Rs. 20,000. If at the end of the year , in total profit of Rs. 2000 , A's share is Rs. 1000 and that of B's is Rs.600, Find the investment of C .

7. The cost of Nano car increases by 10% and that of Maruti car by 18% . The cost of an Nano car is thrice of Maruti car. Find the increase (in percentage) in  the cost of 10 Nano & 5 Maruti Car .

Graphs

HOW TO PLOT THE GRAPH OF CUBIC POLYNOMIALS?

LET  US  consider  a  general  3  degree  equation   F(x) -- ax³+bx²+cx+d , a >0

STEP -1) find f '(x) i.e.  3ax²+2bx+c,  if dicriminant of thif eqn. = D {=(2b)²-4(3a)(c) < o }, then only one real solution . and graph (of  F(x) ) is --- always inc.  from  -infinity to +infinit and cuitting x-axis at exactly one point .

STEP-2) if D =0 , then 3 real equal ruts . again cutting x-axis at only one point and graph ( of F(x) }  is from -infinity to +infinity. ( always increasing )

STEP-3) if D > 0 , then let two solutions of f ' (x)  be  a₁ &  a₂ .  SO, F(a₁)  will be minimum  and  F(a₂) will be maximum. and so, the graph of  f(x) will increase 4m  x= - infinity  to x= a₁ and decreases 4m x= a₁ to x-a_{2 .} again graph increases from x=a₂ to  =infinity