QUESTIONS

Over the New Year weekend,(1)/ that we spent at our farm house ( the New Year weekend is quite specific there is no need to further identify it with the restrictive clause.) ***.The question is how quickly will it come down.>> the question is how quickly it will come down’**.It will take A little bit longer.

1. The smallest value of k, for which both the roots of the equation x² − 8kx + 16(k² − k + 1) = 0 are real, distinct and both the roots are greater than or equal to 4. (2)

2. Let abc be the three digit number. If bca + bac + cab + cba + acb = 2982, then find a × b × c. (96)




3. If f is a function such that f(x + y) = f(xy) for all values of x, y ≥ 4. Domain of f is [8, ∞), andf(8) = 9, then find f(100).

4.  If;

 

Find the value of

 

(1)

5.Let N be the smallest natural number for which (33N + 4)/(22N + 3) is reducible. Find the remainder when N is divided by 11.

 (NO N)

6.

 

In the figure shown above, AB = 11, BC = 7 and CA = 9. AB, BC and CA are extended to D, E, and F respectively such that AD = 33, BE = 28 and CF = 27.

. Find ratio of areas of ΔABC and ΔDEF.

7. Let a, b be positive integers such that



Find the number of ordered pairs (a, b) which satisfy the above equation?

8. If x = 1/9, then what is the value of 1 + 2x + 3x² + 12x³ + 33x⁴ + 102x⁵ … up to infinite terms? (17-05)

9.In the given diagram, if area of triangle DOB is a, then find the total area of triangle ABC.

9.  If p is a prime less than 500, how many number of the form 3p + 1 are perfect squares? 5may