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What is the next number in the sequence: 2, 4, 8, 16, ___?- a)24
- b)32
- c)64
- d)18
Correct answer is option 'B'. Can you explain this answer?
a)
24
b)
32
c)
64
d)
18
|
Rahul Kumar answered |
Each number is doubled to get the next number: 16 * 2 = 32.
What is the product of the first five prime numbers?- a)1320
- b)2310
- c)1350
- d)1300
Correct answer is option 'B'. Can you explain this answer?
a)
1320
b)
2310
c)
1350
d)
1300
|
|
Rahul Kumar answered |
The first five prime numbers are 2, 3, 5, 7, and 11. Their product is 2 * 3 * 5 * 7 * 11 = 2310.
If 2x + 3 = 11, what is the value of x?- a)4
- b)3
- c)2
- d)5
Correct answer is option 'A'. Can you explain this answer?
a)
4
b)
3
c)
2
d)
5
|
Dipanjan Chatterjee answered |
Understanding the Equation
To solve the equation 2x + 3 = 11, we need to isolate the variable x. This means we will rearrange the equation to find the value of x.
Step 1: Subtract 3 from both sides
- We start with the equation: 2x + 3 = 11.
- To eliminate the +3, we subtract 3 from both sides:
2x + 3 - 3 = 11 - 3
- This simplifies to:
2x = 8
Step 2: Divide by 2
- Now, we need to get x by itself. Since 2x means 2 multiplied by x, we can divide both sides by 2:
2x / 2 = 8 / 2
- This simplifies to:
x = 4
Conclusion
- We have found that the value of x is 4.
Thus, the correct answer is option 'A' (4).
You can verify this by substituting x back into the original equation:
- If x = 4, then 2(4) + 3 = 8 + 3 = 11, which is correct.
This confirms that our solution is accurate!
To solve the equation 2x + 3 = 11, we need to isolate the variable x. This means we will rearrange the equation to find the value of x.
Step 1: Subtract 3 from both sides
- We start with the equation: 2x + 3 = 11.
- To eliminate the +3, we subtract 3 from both sides:
2x + 3 - 3 = 11 - 3
- This simplifies to:
2x = 8
Step 2: Divide by 2
- Now, we need to get x by itself. Since 2x means 2 multiplied by x, we can divide both sides by 2:
2x / 2 = 8 / 2
- This simplifies to:
x = 4
Conclusion
- We have found that the value of x is 4.
Thus, the correct answer is option 'A' (4).
You can verify this by substituting x back into the original equation:
- If x = 4, then 2(4) + 3 = 8 + 3 = 11, which is correct.
This confirms that our solution is accurate!
What is the next number in the sequence: 1, 4, 9, 16, ___?- a)24
- b)25
- c)36
- d)49
Correct answer is option 'B'. Can you explain this answer?
a)
24
b)
25
c)
36
d)
49
|
Anuj Kulkarni answered |
Next Number in the Sequence
Pattern:
- The given sequence is a series of perfect squares.
- The sequence starts with 1 (1^2 = 1) and then follows with 4 (2^2 = 4), 9 (3^2 = 9), and 16 (4^2 = 16).
- The next number should be the square of the next consecutive natural number.
Calculation:
- The next number in the sequence should be the square of 5, which is 25 (5^2 = 25).
Therefore, the next number in the sequence is 25. So, the correct answer is option 'B' - 25.
Pattern:
- The given sequence is a series of perfect squares.
- The sequence starts with 1 (1^2 = 1) and then follows with 4 (2^2 = 4), 9 (3^2 = 9), and 16 (4^2 = 16).
- The next number should be the square of the next consecutive natural number.
Calculation:
- The next number in the sequence should be the square of 5, which is 25 (5^2 = 25).
Therefore, the next number in the sequence is 25. So, the correct answer is option 'B' - 25.
What is the value of 10 divided by 1/2?- a)5
- b)10
- c)20
- d)15
Correct answer is option 'C'. Can you explain this answer?
a)
5
b)
10
c)
20
d)
15
|
Ashish Malik answered |
Understanding Division by a Fraction
When we divide a number by a fraction, it can be thought of as multiplying by the reciprocal of that fraction.
Step 1: Identify the Problem
- The problem is to find the value of 10 divided by 1/2.
Step 2: Convert Division to Multiplication
- Dividing by a fraction means multiplying by its reciprocal.
- The reciprocal of 1/2 is 2/1 (or simply 2).
Step 3: Rewrite the Problem
- Therefore, 10 divided by 1/2 can be rewritten as:
10 × 2
Step 4: Calculate the Result
- Now, perform the multiplication:
10 × 2 = 20
Final Answer
- Hence, 10 divided by 1/2 equals 20.
Key Takeaways
- When dividing by a fraction, multiply by the reciprocal.
- The calculation 10 ÷ (1/2) simplifies to 10 × 2 = 20.
Thus, the correct answer is option C: 20.
When we divide a number by a fraction, it can be thought of as multiplying by the reciprocal of that fraction.
Step 1: Identify the Problem
- The problem is to find the value of 10 divided by 1/2.
Step 2: Convert Division to Multiplication
- Dividing by a fraction means multiplying by its reciprocal.
- The reciprocal of 1/2 is 2/1 (or simply 2).
Step 3: Rewrite the Problem
- Therefore, 10 divided by 1/2 can be rewritten as:
10 × 2
Step 4: Calculate the Result
- Now, perform the multiplication:
10 × 2 = 20
Final Answer
- Hence, 10 divided by 1/2 equals 20.
Key Takeaways
- When dividing by a fraction, multiply by the reciprocal.
- The calculation 10 ÷ (1/2) simplifies to 10 × 2 = 20.
Thus, the correct answer is option C: 20.
If a rectangle has a length of 10 cm and a width of 5 cm, what is its area?- a)50 sq. cm
- b)20 sq. cm
- c)30 sq. cm
- d)15 sq. cm
Correct answer is option 'A'. Can you explain this answer?
a)
50 sq. cm
b)
20 sq. cm
c)
30 sq. cm
d)
15 sq. cm
|
|
Rahul Kumar answered |
Area = length * width = 10 cm * 5 cm = 50 sq. cm.
If 3x + 5 = 20, what is the value of x?- a)5
- b)3
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
a)
5
b)
3
c)
4
d)
6
|
|
Rahul Kumar answered |
Subtracting 5 from both sides gives 3x = 15. Dividing both sides by 3 yields x = 5.
What is the next number in the sequence: 2, 6, 12, 20, ___?- a)24
- b)30
- c)36
- d)42
Correct answer is option 'B'. Can you explain this answer?
a)
24
b)
30
c)
36
d)
42
|
|
Yashvi Pillai answered |
Understanding the Sequence
The sequence given is: 2, 6, 12, 20. To find the next number, we need to identify a pattern.
Identifying Differences
Let's examine the differences between consecutive numbers:
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
The differences are: 4, 6, 8.
Recognizing a Pattern
Now, let's analyze the differences:
- The first difference is 4.
- The second difference is 6 (which is 4 + 2).
- The third difference is 8 (which is 6 + 2).
We can see that the differences are increasing by 2 each time.
Continuing the Pattern
Following this pattern, the next difference should be:
- 8 + 2 = 10.
Calculating the Next Number
Now, we add this next difference to the last number in the sequence:
- 20 + 10 = 30.
Thus, the next number in the sequence is 30.
Conclusion
The correct answer is option 'B': 30.
This process illustrates how recognizing patterns and differences can help in predicting the next number in a sequence.
The sequence given is: 2, 6, 12, 20. To find the next number, we need to identify a pattern.
Identifying Differences
Let's examine the differences between consecutive numbers:
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
The differences are: 4, 6, 8.
Recognizing a Pattern
Now, let's analyze the differences:
- The first difference is 4.
- The second difference is 6 (which is 4 + 2).
- The third difference is 8 (which is 6 + 2).
We can see that the differences are increasing by 2 each time.
Continuing the Pattern
Following this pattern, the next difference should be:
- 8 + 2 = 10.
Calculating the Next Number
Now, we add this next difference to the last number in the sequence:
- 20 + 10 = 30.
Thus, the next number in the sequence is 30.
Conclusion
The correct answer is option 'B': 30.
This process illustrates how recognizing patterns and differences can help in predicting the next number in a sequence.
What is the sum of the interior angles of a triangle?- a)90°
- b)180°
- c)270°
- d)360°
Correct answer is option 'B'. Can you explain this answer?
a)
90°
b)
180°
c)
270°
d)
360°
|
Pranab Choudhury answered |
Understanding the Sum of Interior Angles in a Triangle
The sum of the interior angles of a triangle is a fundamental concept in geometry. Here's a detailed explanation:
What is a Triangle?
- A triangle is a polygon with three edges and three vertices.
- It is one of the simplest shapes in geometry.
Interior Angles of a Triangle
- The interior angles are the angles formed inside the triangle.
- In any triangle, there are three interior angles, typically denoted as angle A, angle B, and angle C.
Sum of the Angles
- The sum of the interior angles in a triangle always equals 180 degrees.
- This can be understood through various methods, such as drawing parallel lines or using geometric principles.
Why 180 Degrees?
- If you imagine cutting a triangle into two right triangles, each right triangle will contain angles that sum up to 90 degrees.
- Since there are two right triangles in total, adding their angles together gives you 180 degrees.
Examples of Triangle Types
- Acute Triangle: All angles are less than 90 degrees, still summing to 180 degrees.
- Right Triangle: One angle is exactly 90 degrees, and the other two angles sum to 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees, but the total still remains 180 degrees.
Conclusion
- Regardless of the type of triangle, the sum of the interior angles will always be 180 degrees.
- Therefore, the correct answer to the question is option 'B'.
The sum of the interior angles of a triangle is a fundamental concept in geometry. Here's a detailed explanation:
What is a Triangle?
- A triangle is a polygon with three edges and three vertices.
- It is one of the simplest shapes in geometry.
Interior Angles of a Triangle
- The interior angles are the angles formed inside the triangle.
- In any triangle, there are three interior angles, typically denoted as angle A, angle B, and angle C.
Sum of the Angles
- The sum of the interior angles in a triangle always equals 180 degrees.
- This can be understood through various methods, such as drawing parallel lines or using geometric principles.
Why 180 Degrees?
- If you imagine cutting a triangle into two right triangles, each right triangle will contain angles that sum up to 90 degrees.
- Since there are two right triangles in total, adding their angles together gives you 180 degrees.
Examples of Triangle Types
- Acute Triangle: All angles are less than 90 degrees, still summing to 180 degrees.
- Right Triangle: One angle is exactly 90 degrees, and the other two angles sum to 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees, but the total still remains 180 degrees.
Conclusion
- Regardless of the type of triangle, the sum of the interior angles will always be 180 degrees.
- Therefore, the correct answer to the question is option 'B'.
If a triangle has angles measuring 30°, 60°, and 90°, which side is the longest?- a)The side opposite the 30° angle
- b)The side opposite the 60° angle
- c)The side opposite the 90° angle
- d)All sides are equal
Correct answer is option 'C'. Can you explain this answer?
a)
The side opposite the 30° angle
b)
The side opposite the 60° angle
c)
The side opposite the 90° angle
d)
All sides are equal
|
Ruchi Basu answered |
Understanding Triangle Angles
In a triangle, the relationship between the angles and the lengths of the sides is crucial. The side opposite the largest angle is always the longest.
Characteristics of a 30°-60°-90° Triangle
- A triangle with angles measuring 30°, 60°, and 90° is a special right triangle.
- In this triangle, the angles are distinct, where:
- 30° is the smallest angle
- 60° is the medium angle
- 90° is the largest angle
Identifying the Longest Side
- The side opposite the 90° angle is the longest side.
- This side is known as the hypotenuse.
Side Length Relationships
- In a 30°-60°-90° triangle, the ratio of the lengths of the sides is:
- The side opposite the 30° angle is the shortest.
- The side opposite the 60° angle is longer than the side opposite the 30° but shorter than the hypotenuse.
- The side opposite the 90° angle (the hypotenuse) is the longest.
Conclusion
Therefore, the correct answer is:
- Option C: The side opposite the 90° angle is the longest side.
This understanding of triangle properties and side relationships is essential for solving various geometric problems.
In a triangle, the relationship between the angles and the lengths of the sides is crucial. The side opposite the largest angle is always the longest.
Characteristics of a 30°-60°-90° Triangle
- A triangle with angles measuring 30°, 60°, and 90° is a special right triangle.
- In this triangle, the angles are distinct, where:
- 30° is the smallest angle
- 60° is the medium angle
- 90° is the largest angle
Identifying the Longest Side
- The side opposite the 90° angle is the longest side.
- This side is known as the hypotenuse.
Side Length Relationships
- In a 30°-60°-90° triangle, the ratio of the lengths of the sides is:
- The side opposite the 30° angle is the shortest.
- The side opposite the 60° angle is longer than the side opposite the 30° but shorter than the hypotenuse.
- The side opposite the 90° angle (the hypotenuse) is the longest.
Conclusion
Therefore, the correct answer is:
- Option C: The side opposite the 90° angle is the longest side.
This understanding of triangle properties and side relationships is essential for solving various geometric problems.
What is the value of (8 + 2) * (4 - 1)?- a)30
- b)36
- c)24
- d)20
Correct answer is option 'A'. Can you explain this answer?
a)
30
b)
36
c)
24
d)
20
|
|
Rahul Kumar answered |
(8 + 2) * (4 - 1) = 10 * 3 = 30.
If a square has an area of 36 sq. cm, what is the length of one side?- a)6 cm
- b)9 cm
- c)12 cm
- d)18 cm
Correct answer is option 'A'. Can you explain this answer?
a)
6 cm
b)
9 cm
c)
12 cm
d)
18 cm
|
Devika Chakraborty answered |
Understanding the Area of a Square
The area of a square is calculated using the formula:
Area = Side × Side
This can also be written as:
Area = Side²
In this case, we know the area of the square is 36 square centimeters.
Finding the Length of One Side
To find the length of one side of the square, we need to take the square root of the area:
Side = √Area
Since the area is 36 sq. cm, we can substitute it into the formula:
Side = √36
Now, calculating the square root of 36:
Side = 6 cm
Thus, the length of one side of the square is 6 cm.
Answer Options
Let's review the provided options to confirm:
The correct answer is indeed option 'A' (6 cm) as calculated.
Conclusion
In summary, the area of a square helps us determine the length of one side through the square root operation. For this problem, since the area was given as 36 sq. cm, we concluded that each side measures 6 cm.
The area of a square is calculated using the formula:
Area = Side × Side
This can also be written as:
Area = Side²
In this case, we know the area of the square is 36 square centimeters.
Finding the Length of One Side
To find the length of one side of the square, we need to take the square root of the area:
Side = √Area
Since the area is 36 sq. cm, we can substitute it into the formula:
Side = √36
Now, calculating the square root of 36:
Side = 6 cm
Thus, the length of one side of the square is 6 cm.
Answer Options
Let's review the provided options to confirm:
- a) 6 cm
- b) 9 cm
- c) 12 cm
- d) 18 cm
The correct answer is indeed option 'A' (6 cm) as calculated.
Conclusion
In summary, the area of a square helps us determine the length of one side through the square root operation. For this problem, since the area was given as 36 sq. cm, we concluded that each side measures 6 cm.
What is the sum of the first 10 positive integers?- a)55
- b)45
- c)65
- d)50
Correct answer is option 'A'. Can you explain this answer?
a)
55
b)
45
c)
65
d)
50
|
|
Divyansh Basu answered |
Understanding the Sum of the First 10 Positive Integers
To find the sum of the first 10 positive integers, we can use a simple formula or manual addition. Let’s explore both methods.
Manual Addition
The first 10 positive integers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Now, let's add them together:
- 1 + 2 = 3
- 3 + 3 = 6
- 6 + 4 = 10
- 10 + 5 = 15
- 15 + 6 = 21
- 21 + 7 = 28
- 28 + 8 = 36
- 36 + 9 = 45
- 45 + 10 = 55
So, the total sum is 55.
Using the Formula
There is a formula to calculate the sum of the first n positive integers:
Sum = n(n + 1) / 2
For n = 10:
Sum = 10(10 + 1) / 2
Sum = 10 × 11 / 2
Sum = 110 / 2
Sum = 55
Thus, both methods confirm that the sum of the first 10 positive integers is 55.
Conclusion
The correct answer to the question is option 'A' (55). This method can be applied to find the sum of any series of consecutive positive integers quickly and efficiently.
To find the sum of the first 10 positive integers, we can use a simple formula or manual addition. Let’s explore both methods.
Manual Addition
The first 10 positive integers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Now, let's add them together:
- 1 + 2 = 3
- 3 + 3 = 6
- 6 + 4 = 10
- 10 + 5 = 15
- 15 + 6 = 21
- 21 + 7 = 28
- 28 + 8 = 36
- 36 + 9 = 45
- 45 + 10 = 55
So, the total sum is 55.
Using the Formula
There is a formula to calculate the sum of the first n positive integers:
Sum = n(n + 1) / 2
For n = 10:
Sum = 10(10 + 1) / 2
Sum = 10 × 11 / 2
Sum = 110 / 2
Sum = 55
Thus, both methods confirm that the sum of the first 10 positive integers is 55.
Conclusion
The correct answer to the question is option 'A' (55). This method can be applied to find the sum of any series of consecutive positive integers quickly and efficiently.
If a clock reads 3:45, what is the angle between the hour hand and the minute hand?
- a)60°
- b)90°
- c)75°
- d)135°
Correct answer is option 'D'. Can you explain this answer?
If a clock reads 3:45, what is the angle between the hour hand and the minute hand?
a)
60°
b)
90°
c)
75°
d)
135°
|
|
Rahul Kumar answered |
The minute hand is at 9 and the hour hand is between 3 and 4. So, the angle is 90° + 45° = 135°.
If 3y + 7 = 25, what is the value of y?- a)6
- b)5
- c)4
- d)9
Correct answer is option 'A'. Can you explain this answer?
a)
6
b)
5
c)
4
d)
9
|
|
Rahul Kumar answered |
Subtracting 7 from both sides gives 3y = 18. Dividing both sides by 3 yields y = 6.
If a rectangle has a length of 8 cm and a perimeter of 28 cm, what is its width?- a)5 cm
- b)6 cm
- c)7 cm
- d)8 cm
Correct answer is option 'B'. Can you explain this answer?
a)
5 cm
b)
6 cm
c)
7 cm
d)
8 cm
|
|
Rahul Kumar answered |
Perimeter = 2 * (length + width). Given that perimeter is 28 cm and length is 8 cm, substitute these values into the equation and solve for the width: 28 = 2 * (8 + width). Simplifying, we get 28 = 16 + 2 * width. Subtracting 16 from both sides gives 12 = 2 * width. Dividing both sides by 2 gives width = 6 cm.
How many sides does a decagon have?- a)8
- b)10
- c)12
- d)6
Correct answer is option 'B'. Can you explain this answer?
a)
8
b)
10
c)
12
d)
6
|
|
Rahul Kumar answered |
A decagon has 10 sides.
If 4x = 36, what is the value of x?- a)9
- b)6
- c)12
- d)8
Correct answer is option 'A'. Can you explain this answer?
a)
9
b)
6
c)
12
d)
8
|
|
Rahul Kumar answered |
Dividing both sides by 4 gives x = 36 / 4 = 9.
What is the value of 6 divided by 1/3?- a)2
- b)12
- c)18
- d)36
Correct answer is option 'C'. Can you explain this answer?
a)
2
b)
12
c)
18
d)
36
|
|
Rahul Kumar answered |
Dividing by a fraction is the same as multiplying by its reciprocal. So, 6 divided by 1/3 is the same as 6 multiplied by 3/1, which equals 18.
If a rectangle has a length of 12 cm and a width of 4 cm, what is its perimeter?
- a)20 cm
- b)48 cm
- c)32 cm
- d)56 cm
Correct answer is option 'C'. Can you explain this answer?
If a rectangle has a length of 12 cm and a width of 4 cm, what is its perimeter?
a)
20 cm
b)
48 cm
c)
32 cm
d)
56 cm
|
|
Rahul Kumar answered |
Perimeter = 2 * (length + width) = 2 * (12 + 4) = 2 * 16 = 32 cm.
If a circle has a diameter of 14 cm, what is its radius?- a)7 cm
- b)14 cm
- c)28 cm
- d)21 cm
Correct answer is option 'A'. Can you explain this answer?
a)
7 cm
b)
14 cm
c)
28 cm
d)
21 cm
|
|
Rahul Kumar answered |
The radius of a circle is half of its diameter, so the radius is 14 cm / 2 = 7 cm.
What is the value of 5 squared plus 3 squared?- a)25
- b)33
- c)34
- d)16
Correct answer is option 'C'. Can you explain this answer?
a)
25
b)
33
c)
34
d)
16
|
|
Rahul Kumar answered |
5 squared plus 3 squared (5^2 + 3^2) = 25 + 9 = 34.
If a rectangle has a length of 15 cm and a width of 3 cm, what is its area?- a)30 sq. cm
- b)45 sq. cm
- c)50 sq. cm
- d)60 sq. cm
Correct answer is option 'B'. Can you explain this answer?
a)
30 sq. cm
b)
45 sq. cm
c)
50 sq. cm
d)
60 sq. cm
|
|
Rahul Kumar answered |
Area = length * width = 15 cm * 3 cm = 45 sq. cm.
What is the value of 2 cubed plus 4 squared?
- a)32
- b)28
- c)24
- d)36
Correct answer is option 'C'. Can you explain this answer?
What is the value of 2 cubed plus 4 squared?
a)
32
b)
28
c)
24
d)
36
|
|
Rahul Kumar answered |
2 cubed (2^3) is 8, and 4 squared (4^2) is 16. Adding them together gives 8 + 16 = 24.
What is the value of 7 squared?- a)14
- b)49
- c)77
- d)56
Correct answer is option 'B'. Can you explain this answer?
a)
14
b)
49
c)
77
d)
56
|
|
Rahul Kumar answered |
7 squared (7^2) = 7 * 7 = 49.
How many degrees are there in a right angle?- a)90°
- b)180°
- c)45°
- d)60°
Correct answer is option 'A'. Can you explain this answer?
a)
90°
b)
180°
c)
45°
d)
60°
|
|
Rahul Kumar answered |
A right angle measures 90 degrees.
What is the value of 3 cubed?- a)6
- b)27
- c)9
- d)12
Correct answer is option 'B'. Can you explain this answer?
a)
6
b)
27
c)
9
d)
12
|
|
Rahul Kumar answered |
3 cubed (3^3) = 3 * 3 * 3 = 27.
If the perimeter of a square is 20 cm, what is the length of one side?- a)4 cm
- b)5 cm
- c)10 cm
- d)6 cm
Correct answer is option 'B'. Can you explain this answer?
a)
4 cm
b)
5 cm
c)
10 cm
d)
6 cm
|
|
Rahul Kumar answered |
The perimeter of a square is four times the length of one side. So, if the perimeter is 20 cm, then one side is 20 cm / 4 = 5 cm.
How many sides does an octagon have?- a)7
- b)8
- c)9
- d)10
Correct answer is option 'B'. Can you explain this answer?
a)
7
b)
8
c)
9
d)
10
|
|
Rahul Kumar answered |
An octagon has 8 sides.
How many sides does a hexagon have?- a)5
- b)6
- c)7
- d)8
Correct answer is option 'B'. Can you explain this answer?
a)
5
b)
6
c)
7
d)
8
|
|
Rahul Kumar answered |
A hexagon has 6 sides.
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