Find the value of the following expression: \[\frac{0.87\times 0.87\times 0.87+0.13\times 0.13\times 0.13}{0.87\times 0.87-0.87\times 0.13+0.13\times 0.13}\]
If the length and breadth of the square is increased by 30% and 20% respectively, then find the difference between the area of the rectangle so formed and that of the square.
A thread goes 140 round a wheel of radius 14 cm. If the radius of the wheel is increased to 20 cm, then find the number of round the same thread will make around the wheel.
The area of trapezium is \[105\,\,c{{m}^{2}}\]and its height is 7 cm. If one of the parallel sides is 6 cm longer than the other, then find the longer side of trapezium.
If m and n are two integers are such that\[{{m}^{*}}n\,\,=\,\,\frac{{{n}^{2}}}{m}\,\,-\,\,\frac{n}{m}\], then the value of \[9{{\,}^{*}}\,8\]is given by:
Three friends Robert, James and David entered into a business and earn certain amount of profit and share it in the ratio \[4:3:1\] respectively. If Robert receives Rs. 70 more than James, then find the total profit they earn in the business they entered __________.
Two pipes can fill a cistern in 14 hours and 16 hours respectively. Due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up if both the pipes are opened together. If the cistern is full, how much time will the leak take to empty them tank?
According to an estimate there are some 20 million students in the school of America studying in class 11th and 12th standard. Each student in the class needs a English text book which costs Rs. 30, a Mathematics book which costs Rs. 70, a Science book which costs Rs. 40 and a Social Science book which costs Rs. 60. If the books are to be purchased for all the students in the states by the government, then the cost required to purchase all the books is
If \[\Delta PQR\] is a right triangle right angled at Q, and \[QM=3cm\],\[MR=2cm\]and \[PR=x\]and \[PM=y\] units then find the value of \[{{x}^{2}}-{{y}^{2}}\].
The altitude of a triangle is \[\frac{3}{5}\]of its base. If the altitude is increased 4 cm and base is decreased by 2 cm, then the area will remain unchanged. The base of triangle is ________.
Martin is driving his car at the rate of 40 km in 50 minutes and takes 8 hours to reach his destination. If he drives his car with the speed of 70 km in 1.5 hours then find the time taken by him for the same distance.
In the \[\Delta ABC\], if \[\angle A=90{}^\circ \], then the measure of \[\angle BOC\], provided OB and OC are angle bisector of\[\angle B\] &\[\angle C\] respectively.
Martin went to the market to purchase materials for his physics project work. In the process he spent two rupees more than half of the amount he had in the first shop, one rupee more than half of the amount left in the second shop, one rupee more than half of what he had left after in the third shop and spent half of all he had left in the fourth shop. At the end he was left with Rs. 3. Find the amount he had initially.
Thomas is playing a game with rifle in which he has to hit a target. For every time he hits a target he get \[+\,4\] points and if he misses the target he gets \[-\,6\] points. After 20 rounds of game his score is 30. Find the number of times he missed the target.
Five friends Robert, James, Michael, Mary, and Smith were sitting on a bench in the library such that Robert is not sitting on the far right and James is not sitting on the far left. Michael is not sitting at either end. Mary is sitting to the right of James but not necessarily next to him. Smith is not sitting next to Michael and Michael is not sitting next to James. Who is sitting at the far right?
A detective agency uses a certain code to represent their mission to it employees. If some of the code used by them are SAT = 154, SET = 314, TEN = 321 respectively, then what digit will represent the code 'SENT' in their language?
If x, y, z are three positive integers such that \[\frac{x}{y}=8,\] and \[\frac{y}{z}=\frac{1}{6}\] and also \[x+z=42,\]then the value of y is given by: