In the diagram, P, Q and R are the mid-points of AB, AC and BC respectively and AB = AC. Prove that:(i) ΔPBR and ΔQRC are congruent.(ii) ∠APR = ∠AQR.(iii) AR and PQ bisect each other at right angles.
In the given figure, AD = AQ and AB = AC, prove that (i) DC = QB (ii) ∠ACD = ∠ABQ
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1.Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C). (1) One die is rolled, Event A : Even number on the upper face. Event B : Odd number on the upper face. Event C : Prime number on the upper face.
(2) Two dice are rolled simultaneously, Event A : The sum of the digits on upper faces is a multiple of 6. Event B : The sum of the digits on the upper faces is minimum 10. Event C : The same digit on both the upper faces.
3. Three coins are tossed simultaneously. Condition for event A : To get at least two heads. Condition for event B : To get no head. Condition for event C : To get head on the second coin.
(4) Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits. Condition for event A : The number formed is even Condition for event B : The number formed is divisible by 3. Condition for event C : The number formed is greater than 50
5. From three men and two women, environment committee of two persons is to be formed. Condition for event A : There must be at least one woman member. Condition for event B : One man, one woman committee to be formed. Condition for event C : There should not be a woman member.
(6) One coin and one die are thrown simultaneously. Condition for event A : To get head and an odd number. Condition for event B : To get a head or tail and an even number. Condition for event C : Number on the upper face is greater than 7 and tail on the coin.
