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All questions of Algebra for Grade 6 Exam
Ramu's father is thrice as old as Ramu. If father's age is 45 years, how old is Ramu?- a)45 years
- b)30 years
- c)15 years
- d)10 years
Correct answer is option 'C'. Can you explain this answer?
Ramu's father is thrice as old as Ramu. If father's age is 45 years, how old is Ramu?
a)
45 years
b)
30 years
c)
15 years
d)
10 years
|
Rainbow Rise Classes answered |
Let, Ramu's age be x years
∴ Ramu's father's age will be 3x years
∴ Ramu's father's age will be 3x years
Father's age is 45
∴3x = 45
∴3x = 45
⟹ x = 45/3 = 15
∴ Ramu's age is 15 years
What is the method of finding a solution by trying out various values for the variable called?- a)Error method
- b)Trial and error method
- c)Testing method
- d)Checking method
Correct answer is option 'B'. Can you explain this answer?
What is the method of finding a solution by trying out various values for the variable called?
a)
Error method
b)
Trial and error method
c)
Testing method
d)
Checking method
|
Ananya Choudhary answered |
Trial and error is a fundamental method of problem solving.It is characterised by repeated, varied attempts which are
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
Write an equation for the statement 'thrice the length of a room is 340 metres'.
- a)3l = 430
- b)3l = 340
- c)3+l = 340
- d)340 − 3l
Correct answer is option 'B'. Can you explain this answer?
Write an equation for the statement 'thrice the length of a room is 340 metres'.
a)
3l = 430
b)
3l = 340
c)
3+l = 340
d)
340 − 3l
|
Coachify answered |
⇒ The length of room is l.
⇒ So, thrice the length means 3l.
∴ According to the statement given in question,
⇒ 3l = 340
+10+5
What do literals usually represent?- a)Known quantities
- b)Variables
- c)Constants
- d)Depends on the problem.
Correct answer is option 'B'. Can you explain this answer?
What do literals usually represent?
a)
Known quantities
b)
Variables
c)
Constants
d)
Depends on the problem.
|
Bhavana Bajaj answered |
Literals usually represent variables.
The length of a rectangle is twice its breadth. If its area is 72 sq. m, find the breadth of the rectangle.- a)12 m
- b)24 m
- c)6 m
- d)72 m
Correct answer is option 'C'. Can you explain this answer?
The length of a rectangle is twice its breadth. If its area is 72 sq. m, find the breadth of the rectangle.
a)
12 m
b)
24 m
c)
6 m
d)
72 m
|
Anoushka Sharma answered |
Let the breadth of the rectangle be b units. The length is twice its breadth.
⇒ Its length = 2b units
∴ Area = b × 2b sq units
⇒2×b×b = 72 b × b= 72/2 ⇒b × b = 36 = 6 × 6
⇒ b = 6m
In a piggy bank the number of 25 paise coins is five times the number of 50 paise coins. If there are 120 coins, find the amount in the bank.- a)Rs. 25
- b)Rs. 10
- c)Rs. 35
- d)Rs. 40
Correct answer is option 'C'. Can you explain this answer?
In a piggy bank the number of 25 paise coins is five times the number of 50 paise coins. If there are 120 coins, find the amount in the bank.
a)
Rs. 25
b)
Rs. 10
c)
Rs. 35
d)
Rs. 40
|
Arshiya Sen answered |
Let the number of 50 paise coins be x.
⇒ 25 paise coins = 5x
Given that total coins = 120
⇒ x + 5x = 120
⇒ 6x = 120
⇒ x = 120/6 = 20
∴ 50 paise coins = 20
⇒ Amount = 20×50 p = Rs. 10
Value of 25 paise coins = 25p × 5 × 20
= 25p × 100 = Rs. 25
Total amount Rs. (25 + 10) = Rs. 35
⇒ 25 paise coins = 5x
Given that total coins = 120
⇒ x + 5x = 120
⇒ 6x = 120
⇒ x = 120/6 = 20
∴ 50 paise coins = 20
⇒ Amount = 20×50 p = Rs. 10
Value of 25 paise coins = 25p × 5 × 20
= 25p × 100 = Rs. 25
Total amount Rs. (25 + 10) = Rs. 35
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.
Determine the value ofxgiven6x−1 = 2x+9.a) 1(1/2)b) -2(1/2c) 1(3/12)d) 5/2Correct answer is option 'D'. Can you explain this answer?
|
Kunal Ghosh answered |
To determine the value of x in the given equation 6x - 1 = 2x + 9, we can solve for x by isolating it on one side of the equation.
Step 1: Simplify the equation
Start by simplifying both sides of the equation.
6x - 1 = 2x + 9
Step 2: Combine like terms
Combine the x terms on one side and the constant terms on the other side.
6x - 2x = 9 + 1
4x = 10
Step 3: Solve for x
To solve for x, divide both sides of the equation by 4.
4x/4 = 10/4
x = 5/2
Therefore, the value of x is 5/2, which is option D - 5/2.
Step 1: Simplify the equation
Start by simplifying both sides of the equation.
6x - 1 = 2x + 9
Step 2: Combine like terms
Combine the x terms on one side and the constant terms on the other side.
6x - 2x = 9 + 1
4x = 10
Step 3: Solve for x
To solve for x, divide both sides of the equation by 4.
4x/4 = 10/4
x = 5/2
Therefore, the value of x is 5/2, which is option D - 5/2.
The rule, which gives the number of matchsticks required to make the matchstick pattern L, is- a)2n
- b)3n
- c)4n
- d)5n
Correct answer is option 'A'. Can you explain this answer?
The rule, which gives the number of matchsticks required to make the matchstick pattern L, is
a)
2n
b)
3n
c)
4n
d)
5n
|
Lavanya Menon answered |
from the figure it is confirmed that we need 2 matchstick minium for a 'L' shape. so matchsticks will be multiple of 2. so, we need 2n matchsticks
Which of the following are used to represent unknown quantities in algebra?- a)Upper case letters.
- b)Lower case letters.
- c)Depends on the problem.
- d)Only letters A, B,..... K.
Correct answer is option 'B'. Can you explain this answer?
Which of the following are used to represent unknown quantities in algebra?
a)
Upper case letters.
b)
Lower case letters.
c)
Depends on the problem.
d)
Only letters A, B,..... K.
|
Vandana Nair answered |
In algebra, unknown quantities are represented by lower case letters.
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
What is the next step to solve the equation 3y - 4 = 8?- a)Add 4 to both sides
- b)Subtract 4 from both sides
- c)Multiply both sides by 3
- d)Divide both sides by 3
Correct answer is option 'A'. Can you explain this answer?
a)
Add 4 to both sides
b)
Subtract 4 from both sides
c)
Multiply both sides by 3
d)
Divide both sides by 3
|
Shanaya Desai answered |
Understanding the Equation
The equation we need to solve is 3y - 4 = 8. Our goal is to isolate the variable y on one side of the equation.
Identifying the Next Step
To solve for y, we want to eliminate the -4 from the left side. The best way to do this is to perform the opposite operation. Since -4 is being subtracted, we can add 4 to both sides of the equation.
Options Analysis
- a) Add 4 to both sides: This is the correct step. Adding 4 will cancel out the -4 on the left side.
- b) Subtract 4 from both sides: This would make the equation more complicated, as it would lead to 3y - 8 = 8, which is not helpful.
- c) Multiply both sides by 3: This is unnecessary at this stage and would complicate the equation further.
- d) Divide both sides by 3: Similar to multiplication, this does not help in isolating y effectively right now.
Performing the Operation
By adding 4 to both sides, we get:
3y - 4 + 4 = 8 + 4
This simplifies to:
3y = 12
Now, we can easily solve for y by dividing both sides by 3 in the next step.
Conclusion
Therefore, the next step to solve the equation 3y - 4 = 8 is indeed option 'A'—add 4 to both sides. This will help us move closer to finding the value of y.
The equation we need to solve is 3y - 4 = 8. Our goal is to isolate the variable y on one side of the equation.
Identifying the Next Step
To solve for y, we want to eliminate the -4 from the left side. The best way to do this is to perform the opposite operation. Since -4 is being subtracted, we can add 4 to both sides of the equation.
Options Analysis
- a) Add 4 to both sides: This is the correct step. Adding 4 will cancel out the -4 on the left side.
- b) Subtract 4 from both sides: This would make the equation more complicated, as it would lead to 3y - 8 = 8, which is not helpful.
- c) Multiply both sides by 3: This is unnecessary at this stage and would complicate the equation further.
- d) Divide both sides by 3: Similar to multiplication, this does not help in isolating y effectively right now.
Performing the Operation
By adding 4 to both sides, we get:
3y - 4 + 4 = 8 + 4
This simplifies to:
3y = 12
Now, we can easily solve for y by dividing both sides by 3 in the next step.
Conclusion
Therefore, the next step to solve the equation 3y - 4 = 8 is indeed option 'A'—add 4 to both sides. This will help us move closer to finding the value of y.
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.
In the given figure, what are the magnitudes of the angles shown? 
- a)40∘, 135∘
- b)45∘, 130∘
- c)45∘,135∘
- d)180∘
Correct answer is option 'C'. Can you explain this answer?
In the given figure, what are the magnitudes of the angles shown?
a)
40∘, 135∘
b)
45∘, 130∘
c)
45∘,135∘
d)
180∘
|
Rajat Menon answered |
From the figure,x∘ + 3x∘ = 180∘ (straight angle)
⇒ 4x∘ =180∘
⇒x∘ = 45∘
∴ 3x∘ = 3×45∘ = 135∘
⇒ 4x∘ =180∘
⇒x∘ = 45∘
∴ 3x∘ = 3×45∘ = 135∘
For what value of 'a' is 6(2a-1)+8 = 14 true?
- a)-1
- b)
- c)
- d)1
Correct answer is option 'D'. Can you explain this answer?
For what value of 'a' is 6(2a-1)+8 = 14 true?
a)
-1
b)
c)
d)
1
|
Dr Manju Sen answered |
6(2a-1)+8 = 14
12a-6+8 = 14
12a+2 = 14
12a = 12
a = 1
12a-6+8 = 14
12a+2 = 14
12a = 12
a = 1
Choose a value of 'a' that satisfies the equation 6a = -30.- a)5
- b)30
- c)-5
- d)10
Correct answer is option 'C'. Can you explain this answer?
Choose a value of 'a' that satisfies the equation 6a = -30.
a)
5
b)
30
c)
-5
d)
10
|
|
Rajat Menon answered |
6a = −30 ⇒ a = -30/6 = -5
Which of the following does 2n -1 represent?- a)1 subtracted from the product of n and 2.
- b)The difference of two times n and 2.
- c)2n added to 1.
- d)n subtracted from 2.
Correct answer is option 'A'. Can you explain this answer?
Which of the following does 2n -1 represent?
a)
1 subtracted from the product of n and 2.
b)
The difference of two times n and 2.
c)
2n added to 1.
d)
n subtracted from 2.
|
|
Athira Basak answered |
2n - 1 is 1 subtracted from the product of 2 and n.
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
If the length of a cuboid is 7 cm, the width is 4 cm, and the height is 3 cm, what is its volume?- a)84 cm3
- b)56 cm3
- c)48 cm3
- d)24 cm3
Correct answer is option 'A'. Can you explain this answer?
If the length of a cuboid is 7 cm, the width is 4 cm, and the height is 3 cm, what is its volume?
a)
84 cm3
b)
56 cm3
c)
48 cm3
d)
24 cm3
|
Torcia Education answered |
Substitute the values into the formula: Volume = 7 cm × 4 cm × 3 cm = 84 cm3.
In the equation a + 7 = 12, what is the value of a?- a)2
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
a)
2
b)
3
c)
4
d)
5
|
|
Torcia Education answered |
Subtract 7 from both sides to isolate a: a = 12 - 7 = 5.
Libby earns £30 a day plus £10 for every pet she sells. If she sells 6 pets in one day, how much does she earn?
- a)£80
- b)£90
- c)£100
- d)£110
Correct answer is option 'B'. Can you explain this answer?
Libby earns £30 a day plus £10 for every pet she sells. If she sells 6 pets in one day, how much does she earn?
a)
£80
b)
£90
c)
£100
d)
£110
|
|
Torcia Education answered |
Substitute the number of pets sold into the formula: Amount earned = £30 + (10 × 6) = £30 + £60 = £90.
Which of the following is the perimeter of a regular hexagon of side 's' units?- a)6 s units
- b)12 s units
- c) 6 s2 sq units
- d)-6 s units
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the perimeter of a regular hexagon of side 's' units?
a)
6 s units
b)
12 s units
c)
6 s2 sq units
d)
-6 s units
|
Aryan Desai answered |
A regular hexagon has 6 equal sides. Hence perimeter = 6s units.
A number is multiplied by 6 and 12 is added to the product. The result is 84. What is the number?
- a)-12
- b)72
- c)12
- d)-72
Correct answer is option 'C'. Can you explain this answer?
A number is multiplied by 6 and 12 is added to the product. The result is 84. What is the number?
a)
-12
b)
72
c)
12
d)
-72
|
Sagnik Chatterjee answered |
Let the number be x
Then, x×6 + 12 = 84
⇒ 6x = 84−12 = 72
⇒x = 72/6 = 12
Hence required number is x = 12
Then, x×6 + 12 = 84
⇒ 6x = 84−12 = 72
⇒x = 72/6 = 12
Hence required number is x = 12
Find the length of a side of an equilateral triangular garden whose perimeter is 66 m.- a)66 m
- b)11 m
- c)3 m
- d)22 m
Correct answer is option 'D'. Can you explain this answer?
Find the length of a side of an equilateral triangular garden whose perimeter is 66 m.
a)
66 m
b)
11 m
c)
3 m
d)
22 m
|
Sagar Mehra answered |
Let the side of an equilateral triangular garden be x m.
So, 3x = 66 ⇒ x = 22m
So, 3x = 66 ⇒ x = 22m
What is the formula to calculate the volume of a cuboid?- a)Volume = length + width + height
- b)Volume = length × width × height
- c)Volume = length × width ÷ height
- d)Volume = length + width ÷ height
Correct answer is option 'B'. Can you explain this answer?
a)
Volume = length + width + height
b)
Volume = length × width × height
c)
Volume = length × width ÷ height
d)
Volume = length + width ÷ height
|
|
Torcia Education answered |
The volume of a cuboid is calculated by multiplying the length, width, and height together, expressed as Volume = l × w × h.
If the length of a cuboid is 5 cm, the width is 3 cm, and the height is 4 cm, what is its volume?- a)60 cm3
- b)45 cm3
- c)40 cm3
- d)30 cm3
Correct answer is option 'A'. Can you explain this answer?
If the length of a cuboid is 5 cm, the width is 3 cm, and the height is 4 cm, what is its volume?
a)
60 cm3
b)
45 cm3
c)
40 cm3
d)
30 cm3
|
|
Torcia Education answered |
Substitute the values into the formula: Volume = 5 cm × 3 cm × 4 cm = 60 cm3.
Convert 
in the simplest form.- a) 1:4
- b)3:2
- c)4:1
- d)7:3
Correct answer is option 'A'. Can you explain this answer?
Convert in the simplest form.
in the simplest form.a)
1:4
b)
3:2
c)
4:1
d)
7:3
|
Samiksha bajaj answered |
On multiplying both sides of the ratio by 8, we get 1 on left sids and 4 on right side.
Hence, 1:4.
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
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