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 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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Commissioner of Police (IPS) → Joint Commissioner (Crime) → Additional CP → DCP (Crime) → ACP → Police Inspector → Sub-Inspector/API → Constables The DGP sits above all of this — DGP is the head of the entire Maharashtra state police force, overseeing every district and city unit in the state, including Mumbai's own Commissioner.
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Probability Practice Set 5.3 Solutions Chapter 5 Maharashtra State Board 10th Std Textbook Solutions
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.
Probability Practice Set 5.2 Solutions Chapter 5 Maharashtra State Board 10th Std Textbook Solutions
Q1 For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating adigits.
Q2. The arrow is rotated and it stops
randomly on the disc. Find out on
which colour it may stop.
Q3. In the month of March 2019, find
the days on which the date is a
multiple of 5. (see the given page of
the calender)
Q4. Form a ‘Road safety commitee’ of two, from 2 boys (B1
, B2
) and 2 girls(G1
, G2
).
Complete the following activity to write the sample space.
(a) Committee of 2 boys = (b) Committee of 2 girls =
(c) Committee of one boy and one girl =
B1
G1
\ Sample space = {..., ..., ..., ..., ..., ...
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