For the following questions answer them individually
A sum invested at compound inrerest amounts to ₹7,800 in 3 years and ₹11,232 in 5 years. What is the rate per cent?
The width of the path around a square field is 4.5 m and its area is 105.75 $$m^{2}$$. Find the cost of fencing the path at the rate of ₹100 per metre.
The length and the breadth of a rectangle are made to increase and decrease, respectively, by 8% and 10%. What is the percentage increase or decrease in its area?
A vertical pole and a vertical tower are on the same level of ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is $$60^{\circ}$$ and the angle of depression of the bottom of the tower is $$30^{\circ}$$. If the height of the tower is 76 m. then find the height (in ₹) of the pole.
A pole 23 m long reaches a window which is 3 $$\sqrt{5}$$ m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4 $$\sqrt{15}$$ is m high. What is the width (in m) of the street?
X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning, then for how many days did X work?
What is the value of:
$$8 \sqrt{3} \sin 30^{\circ} \tan 60^{\circ} - 3 \cos 0^{\circ} + 3 \sin^{2} 45^{\circ} + 2 \cos^{2} 30$$?
A car runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed (in km/h) for the entire journey?
If $$\left(4x + 2y\right) 3 + \left(4x - 2y\right) 3 = 16 \left(Ax^{3} + Bxy^{2}\right)$$, then what is the value of $$\frac{1}{2}\left(\sqrt{A^{2} + B^{2}}\right)$$?
