For the following questions answer them individually
The average of the first 7 integers in a series of 13 consecutive odd integers is 37. What is the average of the entire series ?
A sum of Rs. 2800 is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at 9% p.a for 5 years and second part is for 6 years at 10% p.a., find the two sums.
On a certain sum of money, the simple interest for 2 years is Rs. 350 at the rate of 4% per annum. It was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned ?
The average marks of a class of 35 children is 35. The marks of one of the students, who got 35, was incorrectly entered as 65. What is the correct average of the class ?
In $$\triangle$$ABC, D is the mid-point of BC and G is the centroid. If GD = 5 cm, then the length of AD is:
What is the value of $$\frac{(cot\ \theta+cosec\ \theta-1)}{(cot\ \theta-cosec\ \theta+1)}$$?
If $$\ \sqrt{5}\ $$= 2.236, then what is the value of $$\ \frac{\sqrt{5}}{2}+\frac{5}{3\sqrt{5}}-\sqrt{45}$$?
If $$\ \frac{a}{b}=\frac{1}{2}$$, find the value of the expression $$\ \frac{(2a-5b)}{(5a+3b)}$$
A merchant marks an article 20% above cost price. He then sells it at a discount of 20%. The sale given him.
In the figure below, AB is a chord of a circle with center O. A tangent AT is drawn at point A so that $$\angle$$BAT= $$50^{0}$$. Then $$\angle$$ADB=?