Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
27
9
\(\frac{1}{27}\)
18
81
Correct answer is A
\((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
Let \(\log_{3} x = a\).
\(a^{2} - 6a + 9 = 0\)
\(a^{2} - 3a - 3a + 9 = 0\)
\(a(a - 3) - 3(a - 3) = 0\)
\((a - 3)(a - 3) = 0\)
\(\implies a = 3 (twice)\)
\(\log_{3} x = 3 \implies x = 3^{3} = 27\)
x + 8x2 - 5 = 0
2x2 - 5x + 8 = 0
2x2 - 8x + 5 = 0
x2 + 8x - 5 = 0
Correct answer is B
x2 - (sum of roots) x + (product of roots) = 0
x2 - \(\frac{5x}{2}\) + 4 = 0
2x2 - 5x + 8 = 0
What is the size of an exterior angle of a regular pentagon?
36o
60o
72o
120o
360o
Correct answer is C
Pentagon is a polygon with 5 sides. Sum of interior angles of polygon (regular) = (2n - 4) x 90o
= 5
= (10 - 4) x 90o
= 540o
each interior angle = \(\frac{540}{5}\)
= 108o
= 180o let x represent ext. angle
x + 108o = 180v
x = 180o - 108o
= 72o
The difference between 4\(\frac{5}{7}\) and 2\(\frac{1}{4}\) greater by
\(\frac{23}{28}\)
\(\frac{24}{28}\)
\(\frac{50}{56}\)
\(\frac{27}{28}\)
\(\frac{48}{56}\)
Correct answer is C
Difference between 4\(\frac{5}{7}\) and 2\(\frac{1}{4}\)
\(\frac{33}{7}\) - \(\frac{9}{4}\) = \(\frac{69}{24}\)
The sum of \(\frac{1}{14}\) and 1\(\frac{1}{14}\) + \(\frac{3}{2}\)
= \(\frac{11}{7}\)
\(\frac{69}{28}\) - \(\frac{11}{7}\) = \(\frac{25}{28}\)
= \(\frac{50}{56}\)
12.25kg
6.75kg
8.75kg
15.75kg
8.25kg
Correct answer is C
Sugar : flour = 2.5 : 4.5
Total = 7
sugar used = \(\frac{2.5}{7}\) x 24.5
= \(\frac{61.25}{7}\)
= 8.75