The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is $$ {18\sqrt{3}}$$ sq.cm. What is the area (in cm²) of the equilateral triangle ?

Direction: Study the pie chart carefully and answer the given questions. The pie chart shows the percentage breakup of students in different classes from VI to X in the year 2017

If the total number of boys in class VIII is “x” and the total number of boys in class IX is “x+40”. The total number of girls in class VIII and class IX together is 306. Then find the value of “x”.

A man can row downstream at a speed of 15 km/h and upstream at 11 km/h. Find his speed in still water and the speed of the current, respectively. [Give both your answers in km/h]

The speed of a  boat in still water is 20 kmph and the rate of current is 4 kmph. The distance travelled by the boat downstream in 30 minute is

A batsman scores 98 run in the 17^th match of his career. His average runs per match increased by 2.5. What is his average before the 17^th match?

A straight line parallel to the base QR of the ∆PQR intersect PQ and PR at the points S and T respectively. If the area of the ∆PQT be 36 cm² then area of the ∆PRS is:

Three partners started business by investing Rs.60,000, Rs.80,000 and Rs.1,20,000 respectively. First partner left the business after 4 months, second after 9 months and third rem ained in the business for the whole year. At the end of year the total profit earned is Rs. 1,60,480, then find their shares of profit.

If $$ {x^2} -4x-1 $$ then the value of $$ {{x^6} -{x^4}+{x^2}-1}\over {x^3}$$ will be