If \( x + \frac{1}{x} = 2\sqrt{10} \) , where x>1, then the value of \( x^3 - \frac{1}{x^3} \) is:
In an election between two candidates P and Q, P got 78% of the total valid votes. If the total votes of the electorate were 75,60,000, then what was the number of valid votes that Q got if 10% of the voters did not cast their vote and 15% of the votes polled were declared invalid?
In a ΔABC right-angled at C, if tan A=\(\sqrt{3}\), then the value of sin A cos B cot(A+B) is:
The inner and outer radii of a circular track are 28 m and 25 m, respectively. The cost (in ₹) of levelling the track at ₹28 per m² is:
\(\text{(Use } \pi = \dfrac{22}{7}\text{)}\)
There are two pipes to fill a tank. Together, they can fill the tank in 15 minutes. If one pipe can fill the tank in one and a half times as fast as the other, the faster pipe alone can fill the tank in:
10 minutes
25 minutes
20 minutes
\( 32 \tfrac{1}{2} \text{ minutes} \)
Find the value of \( \frac{\sec 35^\circ}{\csc 55^\circ} - \frac{\cos 25^\circ}{\sin 65^\circ} \)
If the perimeter of an equilateral triangle is 36 units, then its area is (in square units):
144\(\sqrt{2}\)
36\(\sqrt{2}\)
144\(\sqrt{3}\)
36\(\sqrt{3}\)