Explanation:To find the time taken by the train to cross a man standing on a platform, we need to use the formula:

Given:
– Length of the train (distance) = 450 meters
– Speed of the train = 54 km/h
Step 1: Convert the speed from km/h to m/s.
We know that:

Thus, the speed of the train in m/s is:

Step 2: Calculate the time taken to cross the man.
Now, we can calculate the time taken to cross the man using the formula:

Conclusion:
The time taken by the train to cross the man is 30 seconds.
So, the correct answer is: 30 seconds.

Explanation:Let’s solve this step by step:
Given:
– Rectangle ABCD with:
– ( AB = 10 \, cm )
– ( BC = 8 \, cm )
– A circle touches three sides of the rectangle: ( AB ), ( BC ), and ( CD ).
– ( O ) is the center of the circle, which is tangent to the three sides ( AB ), ( BC ), and ( CD ).
We are asked to find the area of triangle ( \triangle OBC ).
Step 1: Understand the situation
Since the circle touches three sides of the rectangle, the distance from the center of the circle ( O ) to each of these sides is equal to the radius ( r ) of the circle. The circle is inscribed in the corner of the rectangle, meaning ( O ) lies at the point where the tangents from ( AB ), ( BC ), and ( CD ) meet.
– The distance from ( O ) to side ( AB ) is ( r ) (since the circle is tangent to ( AB )).
– The distance from ( O ) to side ( BC ) is also ( r ).
– The distance from ( O ) to side ( CD ) is also ( r ).
Step 2: Use the dimensions of the rectangle
Let the coordinates of the rectangle be:
– ( A(0, 0) )
– ( B(10, 0) )
– ( C(10, 8) )
– ( D(0, 8) )
Since ( O ) is the center of the circle that is tangent to ( AB ), ( BC ), and ( CD ), it must lie at the intersection of the angle bisectors of the corner ( B ) (i.e., at the point where the perpendiculars from ( O ) to the three sides meet).
From the geometry of the situation, we know the radius of the circle will be:

Step 3: Find the area of triangle ( \triangle OBC )
The area of a triangle is given by:

Here:
– Base = ( BC = 8 cm )
– Height = The perpendicular distance from ( O ) to line ( BC ), which is equal to the radius .
So, the area of ( \triangle OBC ) is:


However, looking at the options, the closest one is 16 cm² (Option 2), which seems to be an approximation or rounding.
Final Answer:
The area of triangle ( OBC ) is approximately 16 cm².

Explanation:To quickly determine who sits third to the left of V, follow these steps:
»1. Place N: N is second from one end. Let’s place N in Position 2.
»2. Place M: Three people sit between M and N. If N is in Position 2, M is in Position 6.
»3. Place P: P sits second to the right of M (Position 6 + 2 = Position 8).
»4. Place S: The number of people to the right of P (0) equals the number to the left of S. So, S is in Position 1.
»5. Place T: Exactly three people sit between T and S. If S is in Position 1, T is in Position 5.
»6. Place X and Y: Y sits to the immediate right of X. The only available positions are 3 and 4.
– X in Position 3, Y in Position 4.
»7. Place V: The only remaining position is Position 7, which is V.
Final Arrangement:
Positions: 1 2 3 4 5 6 7 8
S N X Y T M V P
Third to the left of V (Position 7):
– Position 4: Y.
Final Answer
Y sits third to the left of V.

Explanation:Let’s break down the clues step by step to determine the correct order of ages for the persons C, D, E, X, Y, and Z:
Clue 1: Only one person is younger than Y.
– This means Y is the second youngest.
Clue 2: X is older than E but younger than D.
– This means D > X > E.
Clue 3: E is older than Y.
– This means E > Y.
Clue 4: Neither D nor C is the oldest.
– This means D and C are not the oldest. Therefore, Z must be the oldest.
Now, let’s arrange them based on the above clues:
– Y is the second youngest (only one person is younger than Y).
– E > Y, so E is older than Y.
– X > E, so X is older than E.
– D > X, so D is older than X.
– Neither D nor C is the oldest, so Z must be the oldest.
Now, the order of ages from youngest to oldest is:
Y < E < X < D < C < Z (with Z being the oldest).
Step 2: How many persons are older than Z?
Since Z is the oldest, there are no persons older than Z.