If one of the equal angles of an isosceles triangle is 65°, then the angle at the vertex is

PAB and PCD are two secants to a circle . If PA 10 cm , AB = 12 cm and PC = 11 cm , then what is the value ( in cm ) of PD ?

The ratio of investment of Ram and Shyam is 11: 12 and the ratio of their profits is 2: 3. If Ram invested the money for 8 months, find for how much time Shyam invested his money?

The ratio of income of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save ₹ 1300 and ₹ 900 respectively. Their incomes are:

The mean of 20 items is 55. If two items 45 and 30 are removed, what will be the new mean of the remaining items?

Direction: Study the line graph carefully to answer the following questions.
Line graph shows the production (in thousand units) and percentage of exported mobiles, computers and laptops.

If the ratio between export prices of Mobiles, Laptops and Computers are 2: 1: 1.5 in the year 2014, then what is the proportion of their export earnings? 

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.
(A) x>y
(B) x≥y
(C) x˂y
(D) x≤y
(E) x=y or the relations ship cannot be established

I. $$ {9x^2+5=18x}$$
II. $${2y^2-9y+10=0}$$

Study the following graph carefully to answer the given questions

R started the work and left after some days, when 25% work was done. After it Z joined and completed it working for 25 days. In how many days R and Z can do the complete work, working together?