Solve these
Tue, 2009-11-24 10:03
Q1.
Find the value of ‘k’ so that the following equations are consistent:
2x + 3y + 4 = 0 3x + 4y + 6 = 0 4x + 5y - k = 0
(A) - 2 (B) 7 (C) - 8 (D) 10.5 (E) 11
Q2.
The value of Σij, where the summation is for all i and j such 1 ≤ i ≤ j ≤ 10 and ij represents the product of the two digits, is:
(A) 1320 (B) 2640 (C) 3025 (D) 1705 (E) 1620
FOR A SYSTEM OF LINEAR EQUATION TO BE CONSISTENT THEY MUST HAVE ONE COMMON SOLUTION..
IN THIS CASE SINCE THE COEFFICIENT are LINEARLY DEPENDENT THE SOLUTION WILL ONLY BE COMMON WHEN IF AN ABSURD CONDITION DON'T PRESENT ITSELF ..
e.g in this case
-1 * Eqn 1 + 2*Eqn 2 -Eqn 3 gives
8+k=0
which is only "not-absurd" when k = -8.....
In case of second question ..
the series is equal to 1+1*2+2*2+1*3+2*3+3*3+...
which equals
1/2 of Sigma( square of n + Cube of n) : n varies from 1 to 10
which gives 1705
n/a
n/a