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MATHEMATICS - 2006

(Two hours and a half)

Question 8

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28.

(a) In the given figure, PT touches a circle with centre O at R. Diameter SQ when produced meets PT at P. If ∠SPR = x° and ∠QRP = y°, show that x° + 2y° = 90°.
 

29.

(b) The line segment joining A (2, 3) and B (6, −5) is intercepted by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
(Type in the answers separated by commas. Leave no spaces around the commas and the : (colon) symbol.)
 

30.

(c) Mr. Ram Gopal invested Rs. 8,000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested the proceeds (including his dividend) in 18%, Rs. 25 shares at Rs. 41.
Find:-
(i) his dividend for the first year
 

31.

(ii) his annual income in the second year
 

32.

(iii) the percentage increase in his return on his original investment.
(Type in the answers separated by commas. Leave no spaces around the commas.)
 


 
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