Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
\(\frac{1}{6}\)
\(\frac{13}{20}\)
\(\frac{11}{30}\)
\(\frac{9}{4}\)
\(\frac{5}{3}\)
Correct answer is A
2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{15}{8}\) x \(\frac{6}{5}\)
= \(\frac{29}{12}\) - \(\frac{9}{4}\)
= \(\frac{29 - 27}{12}\)
= \(\frac{2}{12}\)
= \(\frac{1}{6}\)
1m
1.1m
1.2m
0.9m
1.3m
Correct answer is E
If tan\(\theta\) = 2, 4
\(\theta\) = tan-1(2.4)
= 67o 25
By sin formula \(\frac{x}{sin 90^o}\) = \(\frac{50}{sin 22^o 37}\)
= \(\frac{50}{sin(9o - \theta)}\)
sin90o = 1
x = 50 cosec 22o 37
= 50 x 2.604x
= 130cm
but 100cm = 1m
130cm = 1.3m
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
\(\frac{x^2 + y^2} {(x - y)^2}\)
\(\frac{2y^3} {y^2 - x^2}\)
\(\frac{3x^2 + y^2} {(2x - y)^2}\)
\(\frac{x^2 + y^2} {(x^2 - y)}\)
Correct answer is B
\(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\)
= \(\frac{-y^3 - y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{y^2 - x^2}\)
\(\frac{44}{3}\)\(\pi\)cm3
12\(\pi\)cm3
\(\frac{38}{3}\)\(\pi\)cm3
\(\frac{40}{3}\)\(\pi\)cm3
\(\frac{32}{33}\)\(\pi\)cm3
Correct answer is A
Volume of steel ball = \(\frac{4\pi r^2}{3}\)
= \(\frac{4}{3}\) \(\pi\) x 1
= \(\frac{4 \pi}{3}\)cm3
Vol. of cylinder = \(\pi\)r2h
= \(\pi\) x 22 x 3
Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\)
= \(\frac{48 - 4 \pi}{3}\)
= \(\frac{44 \pi}{3}\)cm3
Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
52x + 1
5x + 1
5-5
52
53
Correct answer is C
\(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{3x - 2}}{5^{3x + 3}}\)
= 5\(^{3x - 2 - 3x - 3}\)
= 5\(^{-5}\)