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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 get3x = 9. Then, we can divide both sides by 3 to getx = 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 get8x - 3 = 6. Then, we can add 3 to both sides to get8x = 9. Finally, we can divide both sides by 8 to getx = 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 = 7and2x - y = 1, we can solve the first equation foryto gety = 7 - x. Then, we can substitute this expression foryin the second equation to get2x - (7 - x) = 1. Simplifying this equation gives us3x = 8, sox = 8/3. Substituting this value back into the first equation gives usy = 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 = 11and4x - 5y = -13, we can multiply the first equation by 5 and the second equation by 3 to get10x + 15y = 55and12x - 15y = -39. Adding these equations gives us22x = 16, sox = 8/11. Substituting this value back into the first equation gives usy = (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?
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.
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.
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.
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?
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.
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.
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.
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
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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