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All questions of Algebra for Class 6 Exam
If 7 is subtracted from a number, we get 37, then what is that number?- a)42
- b)44
- c)46
- d)43
Correct answer is option 'B'. Can you explain this answer?
If 7 is subtracted from a number, we get 37, then what is that number?
a)
42
b)
44
c)
46
d)
43
|
Raksha Roy answered |
Let the number be x.
∴ x - 7 = 37 ⇒ x = 37 + 7 = 44
∴ x - 7 = 37 ⇒ x = 37 + 7 = 44
What is the co-efficient of m in –7 l2 mn ?- a)–7
- b)–7l2
- c)–7l2 n
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
What is the co-efficient of m in –7 l2 mn ?
a)
–7
b)
–7l2
c)
–7l2 n
d)
None of these
|
Coachify answered |
In the expression -7l2 mn, the coefficient of a variable is the constant factor that multiplies that variable.
The term involving m is -7l2 mn. The coefficient of m is everything multiplying m, which in this case is -7l2 n.
Thus, the correct coefficient of m is -7l2 n.
What must be subtracted from a3 – 4a2 + 5a – 6 to obtain a2 – 2a + 1?- a)a3 – 5a2 + 7a – 7
- b)a3 – 4a2 + 7a – 6
- c)a3 – 5a3 + 5a – 7
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
What must be subtracted from a3 – 4a2 + 5a – 6 to obtain a2 – 2a + 1?
a)
a3 – 5a2 + 7a – 7
b)
a3 – 4a2 + 7a – 6
c)
a3 – 5a3 + 5a – 7
d)
None of these
|
Shreya Sarkar answered |
Here, a3– 4a2 + 5a – 6 – (a2 – 2a + 1)
= a3– 4a2 + 5a – 6 – a2 + 2a – 1
= a3– 5a2 + 7a – 7
= a3– 4a2 + 5a – 6 – a2 + 2a – 1
= a3– 5a2 + 7a – 7
The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?- a)16m
- b)17m
- c)21m
- d)23m
Correct answer is option 'C'. Can you explain this answer?
The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?
a)
16m
b)
17m
c)
21m
d)
23m
|
Pranav Chatterjee answered |
Let the breadth be x m.
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32
Length = 16 + 5 = 21m
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32
Length = 16 + 5 = 21m
A man is thrice as old as his daughter. 5 years ago the man was four times as old as his daughter, what is the age of the daughter?- a)10 years
- b)12 years
- c)14 years
- d)15 years
Correct answer is option 'D'. Can you explain this answer?
A man is thrice as old as his daughter. 5 years ago the man was four times as old as his daughter, what is the age of the daughter?
a)
10 years
b)
12 years
c)
14 years
d)
15 years
|
Yashvi Choudhary answered |
Let the age of daughter be x years.
∴ Man's age = 3x.
and 5 years ago, daughter's age = x-5
∴ Man's age = 3x —5
⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20
⇒ x =15 years
∴ Man's age = 3x.
and 5 years ago, daughter's age = x-5
∴ Man's age = 3x —5
⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20
⇒ x =15 years
If a number is tripled and the result is increased by 7, we get 70, then what is the number?- a)21
- b)23
- c)24
- d)27
Correct answer is option 'A'. Can you explain this answer?
If a number is tripled and the result is increased by 7, we get 70, then what is the number?
a)
21
b)
23
c)
24
d)
27
|
Subham Rane answered |
Let the number be x.
∴ 3 × x + 7 = 70
⇒ 3x = 70 - 7
⇒ 3x = 63
∴ 3 × x + 7 = 70
⇒ 3x = 70 - 7
⇒ 3x = 63
What is the value of x? 3(x + 6) + 2 (x + 3) = 64- a)8
- b)6
- c)–8
- d)4
Correct answer is option 'A'. Can you explain this answer?
What is the value of x? 3(x + 6) + 2 (x + 3) = 64
a)
8
b)
6
c)
–8
d)
4
|
|
Yashvi Choudhary answered |
3(x + 6) + 2(x + ) = 64
⇒ 3x + 18 + 2x + 6 =64
⇒ 5x + 24 = 64
⇒ 5x = 64 - 24
⇒ 5x = 40
⇒ 3x + 18 + 2x + 6 =64
⇒ 5x + 24 = 64
⇒ 5x = 64 - 24
⇒ 5x = 40
A wire of length 86cm is bent in the form of a rectangle such that its length is 7 cm more than its breadth. What is its length ?- a)21 cm
- b)23 cm
- c)25 cm
- d)27 cm
Correct answer is option 'C'. Can you explain this answer?
A wire of length 86cm is bent in the form of a rectangle such that its length is 7 cm more than its breadth. What is its length ?
a)
21 cm
b)
23 cm
c)
25 cm
d)
27 cm
|
|
Yashvi Choudhary answered |
Let the breadth be x.
∴ Length = x + 7
Perimeter of wire = 86
∴ Length = x + 7 = 18 + 7 = 25 cm
∴ Length = x + 7
Perimeter of wire = 86
∴ Length = x + 7 = 18 + 7 = 25 cm
If 8 is subtracted from three times a number the result is 13. What is number?- a)7
- b)5
- c)8
- d)9
Correct answer is option 'A'. Can you explain this answer?
If 8 is subtracted from three times a number the result is 13. What is number?
a)
7
b)
5
c)
8
d)
9
|
Rounak Patel answered |
Understanding the Problem
To solve the problem, we need to translate the words into a mathematical equation. The statement "If 8 is subtracted from three times a number the result is 13" can be broken down as follows:
- Three times a number: If we denote the unknown number as x, then three times this number is 3x.
- Subtracting 8: When we subtract 8 from 3x, it becomes 3x - 8.
- The result is 13: This means that 3x - 8 equals 13.
Putting this all together, we can form the equation:
3x - 8 = 13
Solving the Equation
Now, let's solve for x:
1. Add 8 to both sides:
- 3x - 8 + 8 = 13 + 8
- This simplifies to 3x = 21.
2. Divide both sides by 3:
- 3x / 3 = 21 / 3
- This gives us x = 7.
Conclusion
The number we are looking for is x = 7.
- Final Answer: The correct answer is option 'A' (7).
By translating the given problem into an equation and solving it step by step, we find that the number is indeed 7.
To solve the problem, we need to translate the words into a mathematical equation. The statement "If 8 is subtracted from three times a number the result is 13" can be broken down as follows:
- Three times a number: If we denote the unknown number as x, then three times this number is 3x.
- Subtracting 8: When we subtract 8 from 3x, it becomes 3x - 8.
- The result is 13: This means that 3x - 8 equals 13.
Putting this all together, we can form the equation:
3x - 8 = 13
Solving the Equation
Now, let's solve for x:
1. Add 8 to both sides:
- 3x - 8 + 8 = 13 + 8
- This simplifies to 3x = 21.
2. Divide both sides by 3:
- 3x / 3 = 21 / 3
- This gives us x = 7.
Conclusion
The number we are looking for is x = 7.
- Final Answer: The correct answer is option 'A' (7).
By translating the given problem into an equation and solving it step by step, we find that the number is indeed 7.
How much less than l – 2m + 3n is 2l – 4m – n ?- a)l – 2m – 4n
- b)– l + 2m + 4n
- c)–l + 2m – 4n
- d)l – 2m + 4n
Correct answer is option 'B'. Can you explain this answer?
How much less than l – 2m + 3n is 2l – 4m – n ?
a)
l – 2m – 4n
b)
– l + 2m + 4n
c)
–l + 2m – 4n
d)
l – 2m + 4n
|
Meghana Iyer answered |
Required difference
= (l – 2m + 3n) – (2l – 4m – n)
= – l + 2m + 4n
= (l – 2m + 3n) – (2l – 4m – n)
= – l + 2m + 4n
If x = 4, y = –1 and z = –2 then what is the value of 2x2 – y2 + 3z2 ?- a)42
- b)43
- c)41
- d)45
Correct answer is option 'B'. Can you explain this answer?
If x = 4, y = –1 and z = –2 then what is the value of 2x2 – y2 + 3z2 ?
a)
42
b)
43
c)
41
d)
45
|
|
Shreya Sarkar answered |
2x2 –y2 + 3z2
= 2(4)2 – (–1)2 + 3(–2)2
= 32 – 1 + 12 = 44 – 1= 43
= 2(4)2 – (–1)2 + 3(–2)2
= 32 – 1 + 12 = 44 – 1= 43
If 9 is added to twice of a certain number, the result is 57, what is that number?
- a)38
- b)24
- c)46
- d)84
Correct answer is option 'B'. Can you explain this answer?
If 9 is added to twice of a certain number, the result is 57, what is that number?
a)
38
b)
24
c)
46
d)
84
|
Palak Nair answered |
Problem Analysis
To solve this problem, we need to find a number that satisfies the given condition. Let's assume the number as 'x'. According to the problem, if we add 9 to twice the number, the result is 57. So, we can write the equation as:
2x + 9 = 57
Solution
To find the value of 'x', we can solve the above equation using algebraic operations.
Adding -9 to both sides of the equation:
2x + 9 - 9 = 57 - 9
2x = 48
Now, we can isolate 'x' by dividing both sides of the equation by 2:
2x/2 = 48/2
x = 24
Therefore, the number that satisfies the given condition is 24.
Answer
The correct answer is option B) 24.
The sum of three consecutive natural numbers is 114. Which is the greatest number?- a)37
- b)38
- c)39
- d)41
Correct answer is option 'C'. Can you explain this answer?
The sum of three consecutive natural numbers is 114. Which is the greatest number?
a)
37
b)
38
c)
39
d)
41
|
Muskaan Joshi answered |
Understanding Consecutive Natural Numbers
Consecutive natural numbers are numbers that follow each other in order without any gaps. If we denote the first of these three consecutive natural numbers as 'x', then the next two can be expressed as 'x + 1' and 'x + 2'.
Setting Up the Equation
According to the problem, the sum of these three consecutive numbers equals 114. We can set up the equation as follows:
- x (first number)
- x + 1 (second number)
- x + 2 (third number)
The equation can be written as:
- x + (x + 1) + (x + 2) = 114
Simplifying the Equation
Let's simplify the equation:
- Combine like terms:
- 3x + 3 = 114
Next, we need to isolate 'x':
- Subtract 3 from both sides:
- 3x = 111
Now, divide by 3:
- x = 37
Identifying the Consecutive Numbers
Having found 'x', we can now identify the three consecutive numbers:
- First number (x) = 37
- Second number (x + 1) = 38
- Third number (x + 2) = 39
Conclusion: The Greatest Number
The greatest of these three consecutive natural numbers is:
- 39
Thus, the correct answer is option 'C', which is 39.
Consecutive natural numbers are numbers that follow each other in order without any gaps. If we denote the first of these three consecutive natural numbers as 'x', then the next two can be expressed as 'x + 1' and 'x + 2'.
Setting Up the Equation
According to the problem, the sum of these three consecutive numbers equals 114. We can set up the equation as follows:
- x (first number)
- x + 1 (second number)
- x + 2 (third number)
The equation can be written as:
- x + (x + 1) + (x + 2) = 114
Simplifying the Equation
Let's simplify the equation:
- Combine like terms:
- 3x + 3 = 114
Next, we need to isolate 'x':
- Subtract 3 from both sides:
- 3x = 111
Now, divide by 3:
- x = 37
Identifying the Consecutive Numbers
Having found 'x', we can now identify the three consecutive numbers:
- First number (x) = 37
- Second number (x + 1) = 38
- Third number (x + 2) = 39
Conclusion: The Greatest Number
The greatest of these three consecutive natural numbers is:
- 39
Thus, the correct answer is option 'C', which is 39.
Karan’s father is thrice as old as Karan. After 14 years his age will be twice that of his son. What is the age of Karan?- a)12 years
- b)14 years
- c)15 years
- d)16 years
Correct answer is option 'B'. Can you explain this answer?
Karan’s father is thrice as old as Karan. After 14 years his age will be twice that of his son. What is the age of Karan?
a)
12 years
b)
14 years
c)
15 years
d)
16 years
|
Pragati Khanna answered |
Let the age of karan be x years.
Father’s age = 3x years
After 14 years,
3x +14 = 2(x –14)
⇒ 3x + 14 = 2x + 28
⇒ x = 28 - 14
⇒ x = 14 years
Father’s age = 3x years
After 14 years,
3x +14 = 2(x –14)
⇒ 3x + 14 = 2x + 28
⇒ x = 28 - 14
⇒ x = 14 years
If x = – 2 y = – 1 and z = 3 then what is the value of x2 + y2 – z2- a)–2
- b)–4
- c)–8
- d)–12
Correct answer is option 'B'. Can you explain this answer?
If x = – 2 y = – 1 and z = 3 then what is the value of x2 + y2 – z2
a)
–2
b)
–4
c)
–8
d)
–12
|
|
Pranav Chatterjee answered |
Required value
= x2 + y2 – z2
= (–2)2 + (–1)2– (3)2 = 4 + 1 – 9
= 5 – 9 = – 4
= x2 + y2 – z2
= (–2)2 + (–1)2– (3)2 = 4 + 1 – 9
= 5 – 9 = – 4
By how much does 1 exceed 2x – 3y – 4 ?- a)3y – 2x + 3
- b)3y + 2x + 3
- c)2x – 3y – 5
- d)3y – 2x + 5
Correct answer is option 'D'. Can you explain this answer?
By how much does 1 exceed 2x – 3y – 4 ?
a)
3y – 2x + 3
b)
3y + 2x + 3
c)
2x – 3y – 5
d)
3y – 2x + 5
|
|
Shreya Sarkar answered |
Required difference = 1– (2x – 3y – 4)
= 3y – 2x + 5
= 3y – 2x + 5
By how much is 2x – 3y + 4z greater than 2x + 5y – 6z + 2?- a)8y – 10z + 2
- b)– 8y + 10z + 2
- c)8y – 10z – 2
- d)–8y + 10z – 2
Correct answer is option 'D'. Can you explain this answer?
By how much is 2x – 3y + 4z greater than 2x + 5y – 6z + 2?
a)
8y – 10z + 2
b)
– 8y + 10z + 2
c)
8y – 10z – 2
d)
–8y + 10z – 2
|
Ananya Das answered |
Understanding the Problem
To find how much one expression is greater than another, we need to subtract the second expression from the first. Here, we will evaluate the difference between the two expressions:
1. First Expression: 2x – 3y + 4z
2. Second Expression: 2x + 5y – 6z + 2
Step-by-Step Calculation
Let's perform the subtraction:
1. Subtraction Setup:
(2x - 3y + 4z) - (2x + 5y - 6z + 2)
2. Distributing the Negative Sign:
2x - 3y + 4z - 2x - 5y + 6z - 2
3. Combining Like Terms:
- The terms with x:
2x - 2x = 0
- The terms with y:
-3y - 5y = -8y
- The terms with z:
4z + 6z = 10z
- The constant term:
-2
Putting it all together, we get:
Final Expression
The result from the subtraction is:
-8y + 10z - 2
This is the expression that tells us how much 2x - 3y + 4z is greater than 2x + 5y - 6z + 2.
Conclusion
Therefore, the correct answer is option 'D':
-8y + 10z - 2.
To find how much one expression is greater than another, we need to subtract the second expression from the first. Here, we will evaluate the difference between the two expressions:
1. First Expression: 2x – 3y + 4z
2. Second Expression: 2x + 5y – 6z + 2
Step-by-Step Calculation
Let's perform the subtraction:
1. Subtraction Setup:
(2x - 3y + 4z) - (2x + 5y - 6z + 2)
2. Distributing the Negative Sign:
2x - 3y + 4z - 2x - 5y + 6z - 2
3. Combining Like Terms:
- The terms with x:
2x - 2x = 0
- The terms with y:
-3y - 5y = -8y
- The terms with z:
4z + 6z = 10z
- The constant term:
-2
Putting it all together, we get:
Final Expression
The result from the subtraction is:
-8y + 10z - 2
This is the expression that tells us how much 2x - 3y + 4z is greater than 2x + 5y - 6z + 2.
Conclusion
Therefore, the correct answer is option 'D':
-8y + 10z - 2.
What is the simplified value of 2x – [3y –{2x– (y – x)}]?- a)4x – 5y
- b)5x – 4y
- c)5x – 6y
- d)5x – 3y
Correct answer is option 'B'. Can you explain this answer?
What is the simplified value of 2x – [3y –{2x– (y – x)}]?
a)
4x – 5y
b)
5x – 4y
c)
5x – 6y
d)
5x – 3y
|
|
Pranav Chatterjee answered |
2x –[3y–{2x– (y–x)}]
= 2x –[3y–{2x– y + x)}]
= 2x –[3y–3x + y] = 2x – 4y + 3x = 5x–4y
= 2x –[3y–{2x– y + x)}]
= 2x –[3y–3x + y] = 2x – 4y + 3x = 5x–4y
What must be added to 5x3 – 2x2 + 6x + 7 to make the sum x3 + 3x2 – x + 1 ?- a)– 4x3 + 3x2 – 6x – 7
- b)– 4x3 + 5x2 – 7x – 6
- c)4x3 + 3x2 – 7x – 6
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
What must be added to 5x3 – 2x2 + 6x + 7 to make the sum x3 + 3x2 – x + 1 ?
a)
– 4x3 + 3x2 – 6x – 7
b)
– 4x3 + 5x2 – 7x – 6
c)
4x3 + 3x2 – 7x – 6
d)
None of these
|
|
Meghana Iyer answered |
x3 + 3x2 – x + 1 – 5x3 + 2x2 – 6x – 7
= –4 x3 + 5x2 – 7x – 6
= –4 x3 + 5x2 – 7x – 6
Five times the price of a radio is Rs 170 more than three times its price. What is the price of the radio?- a)Rs 85
- b)Rs 95
- c)Rs 105
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Five times the price of a radio is Rs 170 more than three times its price. What is the price of the radio?
a)
Rs 85
b)
Rs 95
c)
Rs 105
d)
None of these
|
|
Raksha Roy answered |
Let the price of the ratio be Rs x.
5x =170 + 3x
⇒ 2x =170
5x =170 + 3x
⇒ 2x =170
Kiran multiplies a certain number by 17 and adds 4 to the product, she gets 225. What is that number?- a)19
- b)15
- c)13
- d)17
Correct answer is option 'C'. Can you explain this answer?
Kiran multiplies a certain number by 17 and adds 4 to the product, she gets 225. What is that number?
a)
19
b)
15
c)
13
d)
17
|
Sagnik Chatterjee answered |
Let the number be x.
∴ x × 17 + 4 = 225
⇒ 17x = 225 - 4
⇒ 17x = 221
∴ x × 17 + 4 = 225
⇒ 17x = 225 - 4
⇒ 17x = 221
What is the value of xy – [yz – zx –{yx – (3y – xz) – (xy – zy)}]?- a)xy – xz – 3y
- b)xy + 2xz – 3y
- c)xy – xz + 3y
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
What is the value of xy – [yz – zx –{yx – (3y – xz) – (xy – zy)}]?
a)
xy – xz – 3y
b)
xy + 2xz – 3y
c)
xy – xz + 3y
d)
None of these
|
|
Pragati Khanna answered |
xy – [ yz – zx – {yx – (3y – xz) – (xy – zy)}]
= xy – [ yz – zx – {yx – 3y + xz– xy + zy}]
= xy – [ yz – zx – yx + 3y – xz + xy – zy]
= xy + 2xz –3y
= xy – [ yz – zx – {yx – 3y + xz– xy + zy}]
= xy – [ yz – zx – yx + 3y – xz + xy – zy]
= xy + 2xz –3y
What is the sum of the expressions 3a – 2b + 5c, 2a + 5b – 7c and –a – b + c?- a)4a – 2b + 2c
- b)4a + 2b – 2c
- c)4a – 2b – c
- d)4a + 2b – c
Correct answer is option 'D'. Can you explain this answer?
What is the sum of the expressions 3a – 2b + 5c, 2a + 5b – 7c and –a – b + c?
a)
4a – 2b + 2c
b)
4a + 2b – 2c
c)
4a – 2b – c
d)
4a + 2b – c
|
|
Raksha Roy answered |
Required result
= 3a –2b + 5c + 2a +5b –7c – a – b + c
= 4a + 2b – c
= 3a –2b + 5c + 2a +5b –7c – a – b + c
= 4a + 2b – c
What is the value of 2a – [3b –{a – (2c – 3b) + 4c – 3 (a – b – 2c)}]- a)2b + 6c
- b)3b + 8c
- c)4b + 5c
- d)3b + 7c
Correct answer is option 'B'. Can you explain this answer?
What is the value of 2a – [3b –{a – (2c – 3b) + 4c – 3 (a – b – 2c)}]
a)
2b + 6c
b)
3b + 8c
c)
4b + 5c
d)
3b + 7c
|
|
Subham Rane answered |
Required result
= 2a–[3b–{a – (2c + 3b) + 4c –3a + 3b + 6c}]
= 2a –[3b–{–2a +6b +8c}]
= 2a –[3b +2a – 6b – 8c]
= 2a –[2a–3b–8c] = 2a –2a + 3b +8c
= 3b + 8c
= 2a–[3b–{a – (2c + 3b) + 4c –3a + 3b + 6c}]
= 2a –[3b–{–2a +6b +8c}]
= 2a –[3b +2a – 6b – 8c]
= 2a –[2a–3b–8c] = 2a –2a + 3b +8c
= 3b + 8c
What is the value of P if 3(2 – 5P) – 2 (1 – 6P) = 1? - a)–2
- b)–1
- c)2
- d)1
Correct answer is option 'D'. Can you explain this answer?
What is the value of P if 3(2 – 5P) – 2 (1 – 6P) = 1?
a)
–2
b)
–1
c)
2
d)
1
|
|
Sagnik Chatterjee answered |
Here, 3(2 – 5p) –2 (1 – 6p) = 1
⇒ 6 - 15p - 2 + 12p =1
⇒ 4 - 3p = 1 ⇒ 3p = 4 -1
⇒ 6 - 15p - 2 + 12p =1
⇒ 4 - 3p = 1 ⇒ 3p = 4 -1
The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168m, what is its breadth?- a)17 m
- b)21m
- c)19m
- d)23m
Correct answer is option 'B'. Can you explain this answer?
The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168m, what is its breadth?
a)
17 m
b)
21m
c)
19m
d)
23m
|
|
Pragati Khanna answered |
Let the breadth be x m
Length = 3xm
Perimeter of rectangular park = 168
Length = 3xm
Perimeter of rectangular park = 168
The sum of three consecutive even numbers is 78. Which number is smallest among them?- a)24
- b)26
- c)28
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The sum of three consecutive even numbers is 78. Which number is smallest among them?
a)
24
b)
26
c)
28
d)
None of these
|
Pritam Majumdar answered |
Let the three consecutive even numbers are
x, x + 2, x + 4.
∴ x + x + 2 + x + 4 =78
⇒ 3x = 78 - 6
⇒ 3x = 72
x, x + 2, x + 4.
∴ x + x + 2 + x + 4 =78
⇒ 3x = 78 - 6
⇒ 3x = 72
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