Part - А
After how many places will the decimal expansion of 15586/125
Terminate?
Ifp.gare zeros of x²+2x +5, then find the value of 1/p+1/9
On comparing the ratios of the coefficients, find out whether the
equations x +3y-30 and 3x-9y 2=0 is consistent or inconsistent.
For what value of k lines (k+1)x +3ky +15 #0 and 5x *ky +5 -0 are co
lines
In AABC. DE || BC, <ADE=80º and <BAC-40", the <BCA=
2
Answers
Given : 15586/125
To Find : After how many places will the decimal expansion of 15586/125
Terminate
Solution:
Any rational number is terminating decimal expansion if written in simplest form , its denominator have only prime factor of 2 & 5
and number of decimal would be equal to power of 2 or 5 which is higher
15586/125 will terminate decimal if 125 has prime factor of 2 & 5 only
125 = 5 * 5 * 5
=> 125 = 5³
only 5 is the factor in denominator with power 3
Hence 15586/125 will terminate after 3 decimal places
15586/125 = 124.688
zeros of x²+2x +5 are p & g
p + g = - 2
pg = 5
1/p + 1/g
= (g + p)/pg
= -2/5
x +3y-30 and 3x-9y- 2=0
1/3 ≠ 3/-9
hence consistent and unique solution
(k+1)x +3ky +15 = 0 and 5x + ky +5 = 0 are colines
iff (k + 1)/5 = 3k/k = 15/5
=> (k + 1)/5 = 3 = 3
=> k + 1 = 15
=> k = 14
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