Simplify the following expression:
\(\frac{3}{5} + 2\frac{2}{5} \div \left[ \left( \frac{7}{8} - \frac{3}{4} \right) \times 4 - 6\frac{2}{3} \div \frac{4}{3} \right] \times \frac{1}{3}\)
\(\frac{19}{45}\)
-\frac{2}{9}
-\frac{13}{5}
\(\frac{17}{15}\)
Simplify the following expression:
(2a − b − 3c)(4a2 + b2 + 9c² + 2ab + 6ac − 3bc)
−8a3 + b3 + 27c³
8a3 + b3 + 27c³
8a3 - b3 - 27c³ -18abc
8a3 - b3 - 27c³ + 18abc
A soft drink company prepares drinks of three different flavors - A, B and C. The production of the three flavors over a period of five years from 2010 to 2014 has been expressed in the given bar graph.
Study the graph and answer the question that follows.
Production of three different flavors A, B and C (in lakh bottles) by a company over five years.
The difference between the average production of flavor A in 2012, 2013 and 2014 and the average production of flavor C in 2012, 2013 and 2014 is:
10 lakh bottles
12 lakh bottles
18 lakh bottles
15 lakh bottles
In a rectangular park having dimensions 60 m × 40 m, two circular flower beds with radius 7 m are developed. What is the area of the remaining portion of the park?\(\text{(USE }\pi = \frac{22}{7}\text{)}\)
Evaluate the following expression:
\(\frac{\tan^{2}60^{\circ} + \csc 30^{\circ}\,\sin 90^{\circ} + 3\sec^{2}30^{\circ}}{4\sin^{2}45^{\circ} + \sec^{2}60^{\circ} - \cot^{2}30^{\circ} - 5\cos^{2}90^{\circ}}\)