The problem asks us to find the breadth of a rectangle given its perimeter and a relationship between its length and breadth. We will use the formula for the perimeter of a rectangle and the given relationship to set up an equation and solve for the breadth.
Correct Option: D) 6 cm
This is a linear arrangement puzzle. We need to deduce the seating positions of seven people (A, B, C, D, E, F, G) in a straight row, all facing north, based on the given clues. We will build the arrangement step-by-step, starting with the most restrictive clues.
"Only two people sit to the left of F."
Since everyone is facing north, "left" is to the left side of the row. This means F is the third person from the left end.
_ _ F _ _ _ _
"Only three people sit between F and E."
Given F's position, E must be to the right of F to have three people between them, as there are not enough spots to the left of F. This places E at the 7th position.
_ _ F _ _ _ E
"D is not an immediate neighbour of E."
This means D cannot be in the 6th position.
"D sits second to the right of A."
This implies a sequence A _ D. Let's look at the available spots: 1, 2, 4, 5, 6. If A is at 1, D is at 3 (but 3 is F). If A is at 2, D is at 4. If A is at 4, D is at 6. If A is at 5, D is at 7 (but 7 is E). So, the possibilities are A at 2, D at 4 OR A at 4, D at 6.
Therefore, Possibility 1 must be correct: A is at position 2, and D is at position 4.
_ A F D _ _ E
Update the arrangement with A and D:
_ A F D _ _ E
Now, let's recheck "D is not an immediate neighbour of E". D is at position 4, and E is at position 7. They are not immediate neighbours, so this is consistent.
"G sits to the immediate right of B."
This means we are looking for two consecutive empty spots (B G). The remaining empty spots are 1, 5, 6. The only consecutive empty spots are 5 and 6.
So, B is at position 5 and G is at position 6.
_ A F D B G E
Identify the last remaining person and spot:
The only person left is C, and the only spot left is position 1.
C A F D B G E
Final arrangement:
C A F D B G E
Answer the question: "Who sits at the extreme left end of the row?"
Based on our final arrangement, C sits at the extreme left end (position 1).
Correct Option: B) C
The question asks to identify the property that is NOT governed by the position of elements in the Periodic Table. We need to evaluate each option to see if its variation can be predicted or explained by an element's location (group and period) in the periodic table.
A) Colour of element — The color of an element is a physical property that is not systematically governed or predicted by its position in the periodic table. While some broad trends might exist (e.g., most metals are silvery-grey, many non-metals are colored), there isn't a direct, predictable relationship based on group and period number for all elements. For example, elements in the same group can exhibit different colors.
The question asks to identify which of the given points always lies on the principal axis of a lens. We need to understand the definitions of the principal axis, optical centre, point of incidence, and point of refraction in the context of a lens.
D) Only (ii). The optical centre is defined as a point on the principal axis, and any ray passing through it goes undeviated. Points of incidence and refraction are on the surface of the lens where light enters or leaves, and these points can be anywhere on the lens surface, not necessarily on the principal axis.
To find the total surface area of a solid cylinder, we need to sum the area of its two circular bases and its curved surface area. The formula for the total surface area of a cylinder is \(2\pi r (r + h)\), where \(r\) is the radius and \(h\) is the height.
Identify the given values:
Recall the formula for the total surface area of a solid cylinder:
The total surface area (\(TSA\)) of a cylinder is given by:
\[ TSA = 2\pi r (r + h) \]Substitute the given values into the formula:
\[ TSA = 2\pi (24 \text{ cm}) (24 \text{ cm} + 6 \text{ cm}) \]Perform the addition inside the parenthesis:
\[ TSA = 2\pi (24 \text{ cm}) (30 \text{ cm}) \]Multiply the numerical values:
\[ TSA = (2 \times 24 \times 30) \pi \text{ cm}^2 \]\[ TSA = (48 \times 30) \pi \text{ cm}^2 \]\[ TSA = 1440 \pi \text{ cm}^2 \]B) \(1440 \pi \text{ cm}^2\)
The question asks to identify an organism that exhibits a parasitic nutritive strategy. This requires understanding the definition of parasitism and distinguishing it from other modes of nutrition like saprophytic and holozoic.
Correct Option: B) Cuscuta is a parasitic plant that derives nutrition directly from a host plant, harming it in the process.
To find the length of the train, we need to use the relationship between speed, distance, and time. When a train crosses a pole, the distance covered by the train is equal to its own length. We are given the speed in km/h and time in seconds, so we must convert the speed to m/s to ensure consistent units.
Given speed \(S = 45 \text{ km/h}\).
To convert km/h to m/s, multiply by \(\frac{5}{18}\).
\[ S = 45 \times \frac{5}{18} \text{ m/s} \]\[ S = \frac{225}{18} \text{ m/s} \]\[ S = 12.5 \text{ m/s} \]Given time \(T = 24 \text{ seconds}\).
When a train crosses a pole, the distance covered is equal to the length of the train.
Using the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\)
Let \(L\) be the length of the train.
\[ L = S \times T \]\[ L = 12.5 \text{ m/s} \times 24 \text{ s} \]\[ L = 300 \text{ m} \]Therefore, the length of the train is 300 meters.
B) 300 m is the correct length of the train calculated from the given speed and time.
Simplify the given expression.
\(\left(13^2-5^2\right)^{\frac{3}{2}}\times8^{\frac{2}{3}}\div\left(\frac{1}{6}\right)^{-3}\)
To simplify the given expression, we will evaluate each term separately using the rules of exponents and then perform the multiplication and division operations in the correct order.
B) 32 is the correct answer as derived from the step-by-step simplification.
The appearance of clouds (white) is due to the scattering of sunlight by water droplets and ice crystals within them. The type of scattering depends on the size of these particles relative to the wavelength of light. White light is composed of different colours, each with a different wavelength.
The particles in clouds (water droplets/ice crystals) are larger than the wavelength of different colours in white light. Due to this size difference, Mie scattering occurs, where all colours of white light are scattered by about the same amount, making the clouds appear white.
To solve this problem, we need to track Rajesh's movements in a 2D coordinate system. We can assume Point A is the origin (0,0). We will calculate his final coordinates (Point P) and then determine the displacement vector from P to A.
Initial Position: Rajesh starts at Point A, which we can consider as the origin \((0,0)\).
First Movement: Drives 10 km towards the north. His new position is \((0, 10)\).
Second Movement: Takes a right turn (now facing East) and drives 10 km. His new position is \((0+10, 10) = (10, 10)\).
Third Movement: Turns right (now facing South) and drives 17 km. His new position is \((10, 10-17) = (10, -7)\).
Fourth Movement: Takes a right turn (now facing West) and drives 13 km. His new position is \((10-13, -7) = (-3, -7)\).
Fifth Movement: Takes a final right turn (now facing North) and drives 7 km. He stops at Point P. His final position (Point P) is \((-3, -7+7) = (-3, 0)\).
Determine displacement from P to A:
Conclusion: Rajesh needs to drive 3 km towards the East to reach Point A from Point P.
D) 3 km towards the east