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Live Lecture
Quizzes
(CSIR-NET NOV 2020) A person invests a certain amount of money. Whenever the amount gets exactly doubled, he donates Rs. 200. After four such donations he is left with Rs. 200. The initial amount of money he invested was rupees.
200
Correct answer.
1000
Incorrect answer. If the initial amount is 1000, use backward induction to show that the balance will not be Rs 200.
800
Incorrect answer. If the initial amount is 800, use backward induction to show that the balance will not be Rs 200
400
Incorrect answer. If the initial amount is 400, use backward induction to show that the balance will not be Rs 200.
(CSIR-NET JUNE 2014) A merchant buys equal numbers of shirts and trousers and pays Rs.38000. If the cost of 3 shirts is Rs.800 and that of a trouser is Rs.1000, then how many shirts were bought?
30
Correct answer. Let the number of shirts and trousers be x. Then, the total cost is 800x/3 + 1000x = 38000. Solving for x, we get x = 30.
60
Incorrect answer. If the number of shirts and trousers is 60, then the total cost is 800*60/3 + 1000*60 = 76000.
15
Incorrect answer. If the number of shirts and trousers is 15, then the total cost is 800*15/3 + 1000*15 = 19000.
10
Incorrect answer. If the number of shirts and trousers is 10, then the total cost is 800*10/3 + 1000*10 = 12667.
(CSIR-NET FEB 2022) A and B have coins of Rs.1, Rs. 2, Rs. 5 and Rs. 10, in the ratio 4:3:6:2 and 3:5:7:3, respectively. A has Rs.6/- more than B. Which of the following can be the number of coins with A and B, respectively?
60, 54
This is the correct answer.
42, 36
This is incorrect. The total amount of money with A and B would not match.
45, 54
This is incorrect. The ratio of Rs.10 coins would not match.
60, 72
This is incorrect. The difference between A and B would not be Rs.6/-.
(CSIR-NET DEC 2016) A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The amount she started with is?
Rs. 32.14
This is the correct answer because if we let X = 0.14 and Y = 0.16, then the equation is satisfied.
Rs. 48.24
This is not the correct answer because if we let X = 0.24 and Y = 0.24, then the equation is not satisfied.
Rs. 28.64
This is not the correct answer because if we let X = 0.64 and Y = 0.14, then the equation is not satisfied.
Rs. 23.42
This is not the correct answer because if we let X = 0.42 and Y = 0.11, then the equation is not satisfied.
(CSIR-NET JUNE 2018) Mohan lent Geeta as much money as she already had. She then spent ₹10. Next day, he again lent as much money as Geeta now had and spent ₹10 again. On the third day, Mohan again lent as much money as Geeta now had, and she again spent ₹10. If Geeta was left with no money at the end of the third day, how much money did she have initially?
₹8.75
This is the correct answer. Let x be the initial amount of money Geeta had. Then, after the first day, she had 2x – 10. After the second day, she had 4x – 30. After the third day, she had 8x – 70. Since she was left with no money, we can set this equal to zero and solve for x: 8x – 70 = 0, x = 8.75.
₹11.25
This is incorrect. If Geeta had this amount initially, she would have ₹10 left at the end of the third day.
₹10
This is incorrect. If Geeta had this amount initially, she would have ₹30 left at the end of the third day.
₹7.75
This is incorrect. If Geeta had this amount initially, she would have ₹-10 left at the end of the third day.
(CSIR-NET NOV 2020) I bought some bananas for Rs 120. The vendor gave me two extra bananas and, in the process, incurred a loss of Rs. 10 per dozen on the earlier price. How many bananas did ultimately get for Rs.120?
18
Leave your thoughts in the comment below
16
Leave your thoughts in the comment below
14
Leave your thoughts in the comment below
12
Leave your thoughts in the comment below
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Live Lecture
Theory
Quizzes
(CSIR-NET JUNE 2023) A person takes loan of Rs. 1,50,000 at a compound interest rate of 10% per annum. If the loan is repaired at the end of the 3rd year, what is the total interest paid?
45000
That’s wrong! Check if you applied the right formula for compound interest (compounded annually)
82000
That’s wrong! Check if you applied the right formula for compound interest (compounded annually)
94600
That’s wrong! Check if you applied the right formula for compound interest (compounded annually)
49650
That’s true!
(CSIR-NET SEPT 2022 – LS) A deposit in a bank, which pays interest on its deposits compounded daily, grows to Rs. 80,000 for 500 days and to 88,000 for 1000 days. What would be its value (in Rs.) for 1500 days?
96000
That’s wrong! Hint: In the second 500days, they earned Rs. 8000 as interest. What is the percentage of interest?
96450
That’s wrong! Hint: In the second 500days, they earned Rs. 8000 as interest. What is the percentage of interest?
96800
That’s true!
97250
That’s wrong! Hint: In the second 500days, they earned Rs. 8000 as interest. What is the percentage of interest?
(CSIR-NET NOV 2020) A bank pays interest to its depositors compounded yearly. If a deposit becomes Rs. 54,000/- at the end of 3rd year and Rs. 64,800/- at the end of 6th year, what is the principal invested in the deposit?
40000
That’s wrong! Hint: Use compound interest with n = 3 and then n = 6. Square the equation for n = 3 and divide the right equations.
42500
That’s wrong! Hint: Use compound interest with n = 3 and then n = 6. Square the equation for n = 3 and divide the right equations.
45000
That’s true!
48000
That’s wrong! Hint: Use compound interest with n = 3 and then n = 6. Square the equation for n = 3 and divide the right equations.
(CSIR-NET June 2016) A person paid income tax at the rate of R% for the first Rs. 2 lakhs, and at the rate of (R+10)% for income exceeding Rs. 2 lakhs. If the total tax paid is (R+5)% of the annual income, then what is the annual income?
Rs 2.5 lakh
That’s wrong!
Rs 3 lakh
That’s wrong!
Rs 4 lakhs
That’s true!
Rs 5 lakhs
That’s wrong!
(CSIR-NET DEC 2014) A bank offers a scheme wherein deposits made for 1600 days are doubled in value, the interest being compounded daily. The interest accrued on the deposit of Rs.1000/- over the first 400 days would be Rs.
250
That’s wrong!
183
That’s wrong!
148
That’s wrong!
190
That’s true!
(CSIR-NET JUNE 2014) You get 20% returns on your investment annually, but also pay a 20% tax on the gain. At the end of 5 years, the net gain made by you (as percentage of the capital) is approximately
0
That’s wrong!
16
That’s wrong!
80
That’s true!
100
That’s wrong!
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Live Lecture
Theory
Types of Questions to Expect
Each row in the table above represents a type of question to expect. At least one data is missing and is left for the aspirant to find.
A shopkeeper invests Rs.600 on a product and sells it at Rs.690. What is the profit %?
20%
That’s wrong!
15%
That’s true!
25%
That’s wrong!
12%
That’s wrong!
A shopkeeper invests Rs.600 on a product and want to get 30% profit. At what price should he sell it?
Rs 700
That’s wrong!
Rs 720
That’s wrong!
Rs 750
That’s wrong!
Rs 780
That’s true!
By selling a product, the shopkeeper incurs a loss of 25%. What is the price in Rs. at which he sells the watch if the money he invested for the product is Rs. 300?
200
That’s wrong!
375
That’s wrong!
225
That’s true!
235
That’s wrong!
By selling a product at Rs.480, the shopkeeper incurs a loss of 20%. What is the price in Rs. at which he buys the product?
400
That’s wrong!
560
That’s wrong!
576
That’s wrong!
600
That’s true!
PYQs for Practice
(CSIR-NET JUNE 2023) Price of an item is increased by 20% of its cost price and is then sold at 10% discount for Rs. 2160. What is its cost price?
1680
That’s wrong!
1700
That’s wrong!
1980
That’s wrong!
2000
That’s true!
(CSIR NET FEB 2022, DEC 2015) A shopkeeper purchases a product for Rs.100 and sells it making a profit of 10%. The customer resells it to the same shopkeeper incurring a loss of 10%. In these dealings the shopkeeper makes
No profit no loss
That’s wrong!
Rs 11
That’s true!
Re 1
That’s wrong!
Rs 20
That’s wrong!
(CSIR-NET NOV 2020) Maximum retail price (MRP) of each of 3 different brands of biscuits A,B and C is Rs. 20 per 100g packet. During a festive offer, A is available at 25% off on MRP, B is available with 25% extra biscuits for the same MRP, and one packet of C is free on purchase of three packets of C. If a person wants to buy biscuits for Rs. 60, which brand should the person choose to get the maximum amount of biscuits by weight?
B Only
That’s wrong!
Either A or B, Not C
That’s wrong!
Either B or C, Not A
That’s wrong!
Either A or C, Not B
That’s true!
(CSIR NET JUNE 2015) I bought a shirt at 10% discount and sold it to a friend at a loss of 10%. If the friend paid me Rs. 729.00 for the shirt, what was the undiscounted price of the shirt?
Rs 900
That’s true!
Rs 800
That’s wrong! Hint: 9 times of 100 is X as 9 times of 81 is 729
Rs 1000
That’s wrong! Hint: 9 times of 100 is X as 9 times of 81 is 729
Rs 911.25
That’s wrong! Hint: 9 times of 100 is X as 9 times of 81 is 729
(CSIR-NET DEC 2013 ) A student buys a book from an online shop at 20% discount. His friend buys another copy of the same book in a book fair for Rs.192 paying 20% less than his friend. What is the full price of the book?
Rs 275
That’s wrong!
Rs 900
That’s true!
Rs 320
That’s wrong!
Rs 392
That’s wrong!
(GATE 2018) A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?
48
This question is left to you! 🙂 Leave your thoughts in the comment below!
52
This question is left to you! 🙂 Leave your thoughts in the comment below!
60
This question is left to you! 🙂 Leave your thoughts in the comment below!
108
This question is left to you! 🙂 Leave your thoughts in the comment below!
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Live Lecture
Theory
Solving linear equations means finding the value of the variable that makes the equation true. There are different methods to do this, such as using opposite operations, clearing out fractions, or using substitution or elimination. The general idea is to rewrite the equation in a form that has one term with the variable on one side, and a constant on the other side .
Here are some methods to solve linear equations:
Opposite Operations: This method involves performing the opposite operation on both sides of the equation to isolate the variable. For example, if the equation is 3x + 5 = 14, we can subtract 5 from both sides to get 3x = 9. Then, we can divide both sides by 3 to get x = 3.
Clearing Fractions: This method involves multiplying both sides of the equation by the least common multiple of the denominators to clear out the fractions. For example, if the equation is 2/3x - 1/4 = 1/2, we can multiply both sides by 12 to get 8x - 3 = 6. Then, we can add 3 to both sides to get 8x = 9. Finally, we can divide both sides by 8 to get x = 9/8.
Substitution: This method involves solving one equation for one variable and then substituting that expression into the other equation. For example, if the equations are x + y = 7 and 2x - y = 1, we can solve the first equation for y to get y = 7 - x. Then, we can substitute this expression for y in the second equation to get 2x - (7 - x) = 1. Simplifying this equation gives us 3x = 8, so x = 8/3. Substituting this value back into the first equation gives us y = 7 - 8/3 = 13/3.
Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. For example, if the equations are 2x + 3y = 11 and 4x - 5y = -13, we can multiply the first equation by 5 and the second equation by 3 to get 10x + 15y = 55 and 12x - 15y = -39. Adding these equations gives us 22x = 16, so x = 8/11. Substituting this value back into the first equation gives us y = (11 - 2(8/11))/3 = 5/11.
Quizzes
(CSIR-NET SEPT 2022 – MS) In a test with multiple choice questions candidates get 4 marks for a correct answer and lose 1 mark for an incorrect answer. Two candidates A and B attempting 18 and 13 questions, respectively, secure equal marks. How many more INCORRECT answers does A have compared to B?
3
That’s wrong! Hint: Let x, y be the number of questions A and B made mistake in. Find their marks and equate them based on x and y. Find x – y
4
That’s right!
5
That’s wrong! Hint: Let x, y be the number of questions A and B made mistake in. Find their marks and equate them based on x and y. Find x – y
6
That’s wrong! Hint: Let x, y be the number of questions A and B made mistake in. Find their marks and equate them based on x and y. Find x – y
(CSIR-NET SEPT 2022 – MS) A battalion consists of elephants, horses and soldiers totalling to 3500. There are twice as many horses as elephants and one-forth of the soldiers are riding these animals. In the stand still position, number of feet on ground is 7500. The number of horses in the battalion is
525
That’s wrong! Hint: Let y be the number of soldiers and x be the number of elephants.
625
That’s wrong! Hint: Let y be the number of soldiers and x be the number of elephants.
550
That’s wrong! Hint: Let y be the number of soldiers and x be the number of elephants.
600
That’s right!
(CSIR-NET SEPT 2022 – PS)
Sections A, B, C and D of a class have 24, 27, 30 and 36 students respectively. One section has boys and girls who are seated alternatively in three rows, such that the first and the last positions in each row are occupied by boys. Which section could this be?
A
That’s wrong! Hint: Let B denotes a boy and G denotes a girl.
In the required section, in a row boys and girls are in alternative positions, and first and last are boys.
So seating in a row will be BGBGB…GB.
B
That’s right!
C
That’s wrong! Hint: Let B denotes a boy and G denotes a girl.
In the required section, in a row boys and girls are in alternative positions, and first and last are boys.
So seating in a row will be BGBGB…GB.
D
That’s wrong! Hint: Let B denotes a boy and G denotes a girl.
In the required section, in a row boys and girls are in alternative positions, and first and last are boys.
So seating in a row will be BGBGB…GB.
(CSIR-NET SEPT 2022 – PS)
A boy has kites of which all but 9 are red, all but 9 are yellow, all but 9 are green, and all but 9 are blue. How many kites does he have?
12
That’s right!
13
That’s wrong! Hint: Let x be the total number of kites.
In that x-9 are red, x-9 are yellow, x-9 are green and x-9 are blue.
Summing all these gives x.
9
That’s wrong! Hint: Let x be the total number of kites.
In that x-9 are red, x-9 are yellow, x-9 are green and x-9 are blue.
Summing all these gives x.
18
That’s wrong! Hint: Let x be the total number of kites.
In that x-9 are red, x-9 are yellow, x-9 are green and x-9 are blue.
Summing all these gives x.
(CSIR-NET FEB 2022) In a class of 60 students, rank of Amar is double that of Akbar, three times that of Amita and seven times that of Anthony. Assuming that all ranks are distinct, the sum of the ranks of Amar, Akbar and Anthony is
41
That’s wrong! Hint: Possible Ranks Rank of Amar = Common Multiples of 2, 3 and 7
58
That’s wrong! Hint: Possible Ranks Rank of Amar = Common Multiples of 2, 3 and 7
69
That’s true!
83
That’s wrong! Hint: Possible Ranks Rank of Amar = Common Multiples of 2, 3 and 7
(CSIR-NET NOV 2020) Each person in a group of teachers and students is given the same number of chocolates as the number of students. If 4 more students are added then in order to have the same number of chocolates per person as earlier, 28 more chocolates are needed. The total number of students now is
7
That’s wrong!
11
That’s true!
13
That’s wrong!
5
That’s wrong!
(CSIR-NET FEB 2022) A book has 40 pages and each page has x lines. If the number of lines were reduced by 2 in each page, the number of pages would increase by 10 for the identical text. What is the value of x?
7
That’s wrong! Hint: Start with total Number of lines = 40x
10
That’s true!
20
That’s wrong! Hint: Start with total Number of lines = 40x
30
That’s wrong! Hint: Start with total Number of lines = 40x
(CSIR-NET Nov 2020)
Bottles are to be packed in boxes. If 4 bottles are packed in a box then 3 boxes are left unused, but if 3 bottles are packed in a box then 3 bottles are left unpacked. The total number of bottles is
36
That’s wrong! Hint: Start with x as the total number of boxes.
52
That’s wrong! Hint: Start with x as the total number of boxes.
40
That’s wrong! Hint: Start with x as the total number of boxes.
48
That’s true!
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Live Lecture
Ratio and Proportions
Quizzes
(CSIR-NET DEC 2013) In an enclosure there were both crows and cows. If there are 30 heads and 100 legs, what fraction of them are crows?
0.04375
That’s right!
0.0444444444444444
That’s wrong! Hint: Start with this question: “How many animals are there?” Continue with the fact that cows have 4 legs and crows have 2 legs.
0.0486111111111111
That’s wrong! Hint: Start with this question: “How many animals are there?” Continue with the fact that cows have 4 legs and crows have 2 legs.
0.131944444444444
That’s wrong! Hint: Start with this question: “How many animals are there?” Continue with the fact that cows have 4 legs and crows have 2 legs.
(CSIR-NET SEPT 2022 – LS) In a field there are some cows and ducks. If the number of heads are 33 and number of legs are 84, then ratio of the numbers of cows to ducks?
5/6
That’s wrong!
3/8
That’s right!
2/5
That’s wrong!
3/5
That’s wrong!
(CSIR-NET JUNE 2013) A king ordered that a golden crown be made for him from 8 kg of gold and 2 kg of silver. The goldsmith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. Archimedes knew that under water gold lost 1/20th of its weight, while silver lost 1/10th. When the crown was weighed under water, it was 9.25 kg. How much gold was stolen by the goldsmith?
1
That’s wrong! Hint: Calculate the lost weight under the water!
2
That’s wrong! Hint: Calculate the lost weight under the water!
3
That’s right!
4
That’s wrong! Hint: Calculate the lost weight under the water!
(CSIR-NET DEC 2016) To determine the number of parrots in a sparse population, an ecologist captures 30 parrots and puts rings around their necks and releases them. After a week he captures 40 parrots and finds that 8 of them have rings on their necks. What approximately is the parrot population?
70
That’s wrong!
150
That’s right!
160
That’s wrong!
100
That’s wrong!
(GATE 2022) If p:q = 1:2
q:r = 4:3
r:s = 4:5
and u is 50% more than s, what is the ratio p ∶ u?
2 ∶ 15
That’s wrong!
16 ∶ 15
That’s right!
1: 5
That’s wrong!
16: 45
That’s wrong!
(CSIR-NET DEC 2019 – ASSAM) In order to estimate the number of fish of species B in a pond, 100 fish of a foreign species A were released into the pond. Later, in a catch of 100 fish, the numbers of fish of species A and B were found to be 10 and 90 respectively. Assuming homogenous distribution of the fish, and no changes in the numbers of either species, the estimated number of fish of species B in the pond is
910
That’s wrong!
100
That’s right!
810
That’s wrong!
1000
That’s wrong!
(CSIR-NET DEC 2016) To determine the number of parrots in a sparse population, an ecologist captures 30 parrots and puts rings around their necks and releases them. After a week he captures 40 parrots and finds that 8 of them have rings on their necks. What approximately is the parrot population?
70
That’s wrong!
150
That’s right!
160
That’s wrong!
100
That’s wrong!
(GATE 2014) One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?
3.0
That’s wrong!
2.5
That’s wrong!
1.5
That’s wrong!
1.25
That’s right!
(GATE 2021) The number of students is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.
The total number of students in all the three classes in the beginning was:
22
That’s wrong!
66
That’s wrong!
88
That’s right!
110
That’s wrong!
(GATE 2019) The ratio of the number of boys and girls who participated in an examination is 4:3. The total percentage of candidates who passed the examination is 80 and the percentage of girls who passed is 90. The percentage of boys who passed is ______.
55.50
That’s wrong!
72.50
That’s right!
80.50
That’s wrong!
90.00
That’s wrong!
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Live Lecture
Etymology: Percentage
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.” The Latin phrase entered English in the 16th century. Later, it was abbreviated per cent.
Percentage and Fractions
Flashcard
Formula
Formula to find x percentage of “Total” = Total × x/100
More Questions
(CSIR-NET DEC 2012) 25% of 25% of a quantity is x% of the quantity, where x is
0.0625
That’s right!
0.125
That’s wrong! Hint: 25% of 25% of y = x% of y.
0.25
That’s wrong! Hint: 25% of 25% of y = x% of y.
0.5
That’s wrong! Hint: 25% of 25% of y = x% of y.
(CSIR-NET SEPT 2022 – PS) A plant grows by 10% of its height every three months. If the plant’s height today is 1m, its height after one year is the closest to
1.10m
That’s wrong! Hint: Plant grows by 10% of its height every three months, how much did it grow in 3rd month, and then from 3rd to 6th month and so on?
1.21m
That’s wrong! Hint: Plant grows by 10% of its height every three months, how much did it grow in 3rd month, and then from 3rd to 6th month and so on?
1.33m
That’s wrong! Hint: Plant grows by 10% of its height every three months, how much did it grow in 3rd month, and then from 3rd to 6th month and so on?
1.46m
That’s right
“
(CSIR-NET JUNE 2018) A water tank that is 40 % empty holds 40 L more water than when it is 40 % full. How much water does it hold when it is full?
100L
That’s wrong! Hint: “A water tank that is 40% empty holds 40L more water than when it is 40% full.”
That is, 40.100 x + 40 = 60/100 x. Then…
75L
That’s wrong! Hint: “A water tank that is 40% empty holds 40L more water than when it is 40% full.”
That is, 40.100 x + 40 = 60/100 x. Then…
120L
That’s wrong! Hint: “A water tank that is 40% empty holds 40L more water than when it is 40% full.”
That is, 40.100 x + 40 = 60/100 x. Then…
200L
That’s right!
“
(CSIR-NET DEC 2016) A mine supplies 10,000 tons of copper ore, containing an average of 1.5 weight % copper, to a smelter every day. The smelter extracts 80% of the copper from the ore on the same day. What is the production of copper in tons/day?
80
That’s wrong!
12
That’s wrong!
120
That’s right!
150
That’s wrong!
(CSIR-NET DEC 2014) 20% of students of a particular course get jobs within one year of passing. 20% of the remaining students get jobs by the end of second year of passing. If 16 students are still jobless, how many students had passed the course?
32
That’s wrong!
64
That’s wrong!
25
That’s right!
100
That’s wrong!
(CSIR-NET DEC 2019 – ASSAM) In a cricket match, team A needed to score 20 runs to win in the last 12 balls, with players A1 and A2 batting. A1 faced 8 out of 12 balls with a strike rate (defined as number of runs scored per hundred balls faced) of 75. What is the least strike rate A2 needed to score at, for team A to win (assuming team A did not lose any more wickets or get any extra runs)?
250
That’s wrong!
300
That’s wrong!
350
That’s right!
375
That’s wrong!
A candidate should score 45% marks of the total marks to pass the exam. He gets 520 marks and fails by 20 marks. The total marks in the exam are:
1000
That’s wrong!
1100
That’s wrong!
1200
That’s right!
1400
That’s wrong!
(DBT JRF-2018, 2019) A boy appears for a test and scores 35% but fails by 10 marks. If he had scored 46% marks, he would have passed by 12 marks. The pass mark is:
70
That’s wrong!
74
That’s wrong!
80
That’s right!
86
That’s wrong!
(GATE- 2019) In a country of 1400 million populations, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?
14.7
That’s wrong!
15
That’s wrong!
10.5
That’s right!
50
That’s wrong!
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Arithmetic Sequence
In an arithmetic sequence, each term of a sequence differs from its preceding term by a constant called the common difference.
For Example: 1, 4, 7, 10, 13, 16, 19, …
If a is the first term and d is the common difference,
The nth term is, tn = a + (n – 1)d
Sum of n terms of an A.P. =
(a) To select odd number of terms
a – d, a, a + d (three terms)
a – 2d, a – d, a, a + d, a + 2d (five terms)
a – 3d, a – 2d, a – d, a1a + d, a + 2d, a + 3d (seven terms)
(b) To select even number of terms
a – d, a + d (two terms)
a – 3d, a – d, a + d, a + 3d (four terms)
Geometric Sequence
In a geometric sequence, every term bears a constant ratio with its preceding term.
For Example: 2, 6, 18, 54, …
The nth term of a geometric series, tn = arn – 1
Sum of n terms of a Geometric sequence = a(rn – 1)/(r -1) (where a is the first term, r is the common ratio and r > 1)
Sum of terms of an infinite geometric progression = a/(1-r) (when r < 1)
An infinite row of boxes is arranged. Each box has half the volume of the previous box. If the largest box has a volume of 20 cc, what is the total volume of all the boxes? (CSIR-NET JUNE 2015)
Infinite
That’s wrong! Hint: Sum of terms of an infinite geometric progression = a/(1-r) (when r < 1)
400 cc
That's wrong! Hint: Sum of terms of an infinite geometric progression = a/(1-r) (when r < 1)
40 cc
That's right!
80 cc
That's wrong! Hint: Sum of terms of an infinite geometric progression = a/(1-r) (when r < 1)
Function
A function defines a relation between two sets – associating an object from one set to another unique object in another set.
For Example: Let f(x) = x2, where x is from the set of all real numbers. Then f(3) = 32 = 9.
Constant Function
A function given by f(x) = c, where c is a fixed number is called a constant function.
For Example: Let D = { a, b } and E = { 1, 2, 3 }, then the function f:D → E given by f(x) = 2 is a constant function.
Identity Function
A function given by f(x) = x, is called the identity function.
Depicts the correct sequence in which the operations are to be executed, to find out the value of a given mathematical expression.
Thus, in simplifying an expression, first of all the brackets must be removed (by solving the expressions in the brackets) strictly in the order ( ), { }, and [ ].
After removing the brackets, we must use the following operations strictly in the order, and priority given to the one that occurs first from the left:
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