For the following questions answer them individually
If the measure of one angle of a right triangle is $$30^{\circ}$$ more than the measure of the smallest angle, then the measure of the smallest angle is:
How many of the following numbers are divisible by 3 but NOT by 9?
5826, 5964, 6039, 6336, 6489, 6564, 6867 and 6960
The distribution of monthly expenditure of Ramesh on various items is shown in the following pie chart.
If the monthly income of Ramesh is ₹45,000, then find his total monthly expenditure (in ₹) on housing and transportation.
The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the positive difference between the cubes of the two given numbers?
A circular arc whose radius is 4 cm makes an angle $$45^{\circ}$$ at the centre. Find the perimeter of the sector formed.
[Use $$\pi = \frac{22}{7}$$]
The curved surface area of a right circular cylinder of height 56cm is 1408 $$cm^{2}$$. Find the diameter of the base of the cylinder.
Sara can finish a work in 18 days and Tara can complete the same work in 15 days. Tara worked for 10 days and left the job. In how many days can Sara finish the remaining work alone?
If $$\left(x + \frac{1}{x}\right) = 6$$, and x > 1, find the value of $$\left(x^{2} - \frac{1}{x^{2}}\right)$$?