There are 90 students in a hostel. Due to new admissions, 30 new students join the mess and the daily expenses of the mess increases by ₹560, while the average expenditure per head diminishes by ₹10. What was the original daily expenditure (in ₹) of the mess?
The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?
\(4\sqrt{3}\ \text{m}\)
\(6\sqrt{2}\ \text{m}\)
\(3\sqrt{2}\ \text{m}\)
\(5\sqrt{3}\ \text{m}\)
If (2a + 3b)(2c - 3d) = (2a - 3b)(2c + 3d), then:
\(\frac{a}{b} = \frac{d}{c}\)
\(\frac{a}{b} = \frac{c}{d}\)
\(\frac{a}{d} = \frac{c}{b}\)
\(\frac{b}{a} = \frac{c}{d}\)