• Stairs refers to a set of steps.

• Stares means to look at someone or something intently.

When she fell down the stairs, she received many stares but little help."

So, the answer is (A)

• Errant means straying from the right course or standard.

The sentence implies that the person's behavior was incorrect or wrong.

So, the answer is (C) errant.

• Area of an equilateral triangle = (√3/4) * side^2

  • Given area = √3

  • So, (√3/4) * side^2 = √3

  • Side^2 = 4

  • Side = 2

• Perimeter of an equilateral triangle = 3 * side = 3 * 2 = 6

So, the answer is (C) 6.

To compare volumes, we need to calculate the volume of each shape.

• Volume of cuboid = length * breadth * height = 10 * 8 * 6 = 480 cm³

• Volume of cube = side^3 = 8^3 = 512 cm³

• Volume of cylinder = π * radius^2 * height = π * 7^2 * 7 ≈ 1077 cm³

• Volume of sphere = (4/3) * π * radius^3 = (4/3) * π * 7^3 ≈ 1436 cm³

So, the descending order of volumes is sphere, cylinder, cube, cuboid.

So, the answer is (D) (iv), (iii), (ii), (i).

The car travels from A to B at 60 km/h.

The car travels from B to A at 90 km/h.

A common misconception is to simply average the two speeds (60 km/h + 90 km/h) / 2 = 75 km/h. However, this is incorrect because average speed depends on both distance and time.

Let's assume the distance between A and B is 'd' kilometers.

• Time taken for the onward journey = distance/speed = d/60 hours

• Time taken for the return journey = distance/speed = d/90 hours

Total distance traveled = d + d = 2d kilometers 

Total time taken = d/60 + d/90 = 5d/180 hours

Average speed = Total distance / Total time = (2d) / (5d/180) = (2d * 180) / 5d = 72 km/h

Therefore, the average speed for the entire journey is 72 km/h.

So, the answer is (A) 72.

When two sets of parallel lines intersect, they form a grid of rectangles. Parallelograms are formed by selecting two vertical lines and two horizontal lines from this grid of intersections.

The number of ways to choose 2 vertical lines out of 5 lines is 5C2 = 10

The number of ways to choose 2 horizontal lines out of 4 lines 4C2 = 6

Therefore, the total number of parallelograms formed is the product of these two combinations:

= 10 x 6 = 60 

Thus, 60 parallelograms will be formed . option (C) will be Answer

• A = answered question A correctly

• B = answered question B correctly

• C = answered question C correctly

Given:

• A ∩ B ∩ C = X (number of candidates who answered all 3 questions correctly)

• A ∩ B = 100000

• B ∩ C = 90000

• A ∩ C = 80000

• number of candidates who answered all 3 questions incorrectly = X

Total candidates who answered at least one question

A ∪ B ∪ C = A + B + C - (A ∩ B) - (B ∩ C) - (A ∩ C) + (A ∩ B ∩ C) 

= 330000 + 250000 + 260000 - 100000 - 90000 - 80000 + X

= 570000 +X

Total number of students = number of candidates who answered all 3 questions incorrectly + number of candidates who answered at least one question

T = A ∪ B ∪ C + X

630000 = 570000 + X + X

X = 30000

Number of candidates who answered exactly 2 questions correctly = Calculate the total number of candidates who passed the test

• Candidates who answered A and B but not C = A ∩ B - A ∩ B ∩ C = 100000 - x

• Candidates who answered B and C but not A = B ∩ C - A ∩ B ∩ C = 90000 - x

• Candidates who answered A and C but not B = A ∩ C - A ∩ B ∩ C = 80000 - x

Total candidates who answered exactly 2 questions correctly 

= (100000 - x) + (90000 - x) + (80000 - x)

= 270000 - 3x

= 210000

Number of candidates who failed = Total students - passed students

= 630000 - 210000

= 420000

Answer is option (D)

Both lines show a similar pattern: they remain relatively flat from 2002 to 2004, then spike in 2005, and finally decline in 2006.

Based on this data, the most appropriate inference is:

• A. There is a strong correlation between crow birth and cracker sales. This is because the changes in both crow births and cracker sales follow a similar trend, suggesting a possible connection between the two. However, the graph alone cannot prove causation; further research would be needed to establish whether one directly influences the other.

Here's a breakdown of why the other options are less likely:

• B. Cracker usage increases crow birth rate. While the graph shows a correlation, it doesn't necessarily prove that cracker usage causes an increase in crow births. There could be other factors involved.

• C. If cracker sale declines, crow birth will decline. This is a possible prediction based on the observed correlation, but it's not definitive. Other factors could influence crow birth rates.

• D. Increased birth rate of crows will cause an increase in the sale of crackers. This is unlikely, as there's no logical reason why an increase in crow births would lead to an increase in cracker sales.