What are the roots of the equation log₁₀(x²-6x+45) =2?

Population of a town increases by 12% every year. If the population of town will be 188160 after 2 years, then what is its present population?

Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is 30 cm 

Study the information carefully to answer the question that follow.
In a college there are 900 students who are doing Post Graduation (PG) in any one of the subjects, out of five different subjects, out of the five different subjects viz. Zoology, Botany, Mathematics, Physics and Statistics. The ratio between the boys and the girls among those is 5:4 respectively, 20% of the total girls are doing PG in Zoology and 25% of the total girls are doing PG in Statistics. Total number of students doing PG in Botany is 220. Total students who are doing PG in Mathematics is 150. Respectively ratio between the number of girls and the number of boys doing PG in statistics is 2:3. Twenty percent of the total number of boys are doing PG in Mathematics is 1:2 respectively. There are equal number of boys and girls who are doing PG in PG in Physics. 180 students are doing PG in Zoology.
In which PG course the number of girls is the highest and in which course the number of boys is the lowest (respectively)?

The value of $$(x^{b+c})^{b-c}. (x^{c+a})^{c-a}.(x^{a+b})^{a-b}$$ when (x≠0).

In how many years a sum of Rs. 3000 will yield an interest of Rs. 1080 at 12% per annum simple interest?