Mathematics
Each of the letters of the word 'AUTHORIZES' is written on identical circular discs and put in a bag. If a disc is drawn at random from the bag, what is the probability that the letter is :
(i) a vowel ?
(ii) one of the first 9 letters of the English alphabet which appears in the given word ?
(iii) one of the last 9 letters of the English alphabet which appears in the given word ?
Related Questions
An empty tank can be filled by one pipe in 'x' minutes and emptied by another pipe in (x + 5) minutes. Both the pipes, when opened together, can fill the empty tank in 16.8 minutes. Find the value of x.
Use ruler and compass only to construct a triangle ABP such that AB = 8 cm, BP = 5 cm and angle ABP = 30°.
(i) Complete the rhombus ABCD such that P is equidistant from AB and BC.
(ii) Locate a point Q on line BP such that Q is equidistant from A and B.
Using remainder and factor theorem, factorize completely, the given polynomial :
2x3 + x2 - 13x + 6
Use graph paper for this question :
Use 1 cm = 1 unit on both the axes.
(i) Plot the points A(4, 5) and B(-1, -3)
(ii) A' is the image of A when reflected in the y-axis. Write down the co-ordinates of A' and plot it on the graph paper.
(iii) B' is the image of B when reflected in the x-axis followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.
(iv) Write down the geometrical name of the figure AA'BB'.
(v) Name two invariant points under reflection in y-axis.