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
Police Structure | Complete Police Hierarchy Explained
Police Structure | Complete Police Hierarchy Explained | DGP to Constable
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POLICE STATION PR KIS KIS KI POSTING HOTI H पुलिस क्या-क्या काम करती है FIR कौन दर्ज करता है
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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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percentages word problems for practice icse class 8 maths solutions
3. Smitha went to school for 192 days in a year. If her attendance was 75%, find the total number of working days of the school in that year.
4. A fruitseller had some mangoes. After selling 60% of the mangoes, he still has 576 mangoes. How many mangoes did he have originally?
5. The population of a town in the year 2018 was 1,32,300. If the population of the town increases every year by 5%, what was the population of the town in the year 2016?
6. The population of a town increases every year by 10%. If the present population is 1,80,000, what will be the population of the town after 2 years?
7. In the month of October, 34,000 people visited a museum but only 32,300 people visited the museum in the month of November. Find the decrease per cent in the number of visitors.
8. Aman’s monthly income is ₹30,000. If his income increases every year by 9%, what will be his monthly income after 2 years?
9. Anmol’s salary after an increase of 12% is ₹44,800. What was his salary before the increase?
10. The value of a machine depreciates (decreases) every year by 5%. If the present value of the machine is ₹24,000, what will be the value of the machine after 2 years?
11. There were two candidates A and B contesting for the municipal corporation election in a town. The total number of voters in the town were 80,000. If 90% of the voters had voted and 60% of the votes polled went in favour of A, find the number of votes received by B.
12. A number is first increased by 20% and then decreased by 20%. Find the net increase or decrease per cent.
13. Ajit’s salary is 25% more than Alok’s salary. How much per cent is Alok’s salary less than Ajit’s salary?
14. Ajit got 10% less marks than Baljit and Kumar got 20% more than Baljit. If Kumar scored 960, how much did Ajit and Baljit score?
15. Ameeta spends 30% of her income on house rent and 60% of the rest on other expenditures. If she saves ₹7560 every month, what is her monthly income?
16. A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees.
17. In a class of 35 students, 60% are interested in mathematics. How many students are not interested in mathematics?
18. A cricket team won 60% of the matches they played. If they had lost 24 matches, find the total number of matches played by them. What fraction of the matches have they lost?
19. After spending 85% of the money he had with him, Mr Sharma had ₹810 left with him. What was the amount that he had originally?
20. A man travels 50% of the distance by air, 35% by train and 10% by bus and the remaining by taxi. If he travels a distance of 144 km by taxi, find the total distance and the distance travelled by air, train and bus.
21. In a locality 65% of the families read Times of India, 75% read Indian Express, 15% read neither. If 330 families read both the newspapers, how many families lived in that locality? Draw a Venn diagram to solve the problem.
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