Factorise each of the following:
(i) 27y 3 + 125z 3
(ii) 64m3 – 343n 3
[ Hint : See Question 9. ]
Express the given complex number in the form \(a + ib: (1 - i) - (-1 + i6)\)
Solve system of linear equations, using matrix method. x-y+2z=7 3x+4y-5z=-5 2x-y+3z=12
Prove: \(2\ tan^{-1}(cos\ x)=tan^{-1}(2\ cosec\ x)\)
According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence makes flights bumpy and often delays the flights. Assume that an airplane observes severe turbulence, moderate turbulence or light turbulence with equal probabilities. Further, the chance of an airplane reaching late to the destination are 55\%, 37\% and 17\% due to severe, moderate and light turbulence respectively. On the basis of the above information, answer the following questions: Find the probability that an airplane reached its destination late. If the airplane reached its destination late, find the probability that it was due to moderate turbulence.
Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross - streets can be referred to as (4, 3).
(ii) how many cross - streets can be referred to as (3, 4).