To find the new average weight, we first need to calculate the total weight of the 11 students. Then, we add the teacher's weight to this total to get the new total weight. Finally, we divide the new total weight by the new total number of people (11 students + 1 teacher) to find the new average weight.
Given that the average weight of 11 students is 50 kg.
\[ \text{Total weight of 11 students} = \text{Average weight} \times \text{Number of students} \]\[ \text{Total weight of 11 students} = 50\ \text{kg} \times 11 \]\[ \text{Total weight of 11 students} = 550\ \text{kg} \]The teacher's weight is 70 kg.
\[ \text{New total weight} = \text{Total weight of 11 students} + \text{Teacher's weight} \]\[ \text{New total weight} = 550\ \text{kg} + 70\ \text{kg} \]\[ \text{New total weight} = 620\ \text{kg} \]Initially, there were 11 students. With the teacher, the number of people becomes:
\[ \text{New number of people} = 11\ \text{students} + 1\ \text{teacher} \]\[ \text{New number of people} = 12 \]Now, divide the new total weight by the new number of people.
\[ \text{New average weight} = \frac{\text{New total weight}}{\text{New number of people}} \]\[ \text{New average weight} = \frac{620\ \text{kg}}{12} \]\[ \text{New average weight} \approx 51.666...\ \text{kg} \]Rounding 51.666... to two decimal places gives 51.67. However, looking at the options, 51.66 is provided, which implies rounding down or truncation, or that the exact value is not required beyond two decimal places.
Correct Option: D) 51.66
This is a circular arrangement problem. We need to deduce the seating positions of five people around a circular table based on the given clues. We will place individuals one by one, using the clues to fix their positions relative to each other, until the complete arrangement is known. Then we can identify who is sitting to the immediate left of Supriya.
This means Supriya is between Tanmay and Wasim. So the arrangement must be T-S-W or W-S-T. Let's represent this as a block: (T S W).
If we consider the block (T S W), and Umesh (U) is to the immediate right of Tanmay (T), then the arrangement extends to U-T-S-W. (Remember, they are facing the center, so 'right' is clockwise and 'left' is anti-clockwise).
This means Viplav (V) is between Umesh (U) and Wasim (W). From our current arrangement U-T-S-W, we can see that U and W are already present. If V is between U and W, then the arrangement becomes U-V-W. Combining this with U-T-S-W, we get the full circular arrangement:
Starting from U and moving clockwise:
So the complete circular arrangement, moving clockwise, is U - V - W - S - T - (U). Or, written linearly to show the cycle: U-V-W-S-T.
In the arrangement U-V-W-S-T, if Supriya (S) is facing the center, her immediate left will be the person who comes before her in the clockwise direction, or after her in the anti-clockwise direction. Looking at the sequence U-V-W-S-T, the person immediately to the left of S (anti-clockwise) is W (Wasim).
B) Wasim — Based on the step-by-step deduction, Wasim is seated to the immediate left of Supriya.
To identify bisexual flowers, we need to understand the definition of a bisexual flower and then classify the given plants based on whether their flowers contain both male (stamen) and female (pistil/carpel) reproductive organs.
Correct Option: B) Hibiscus and mustard
Both hibiscus and mustard flowers contain both male (stamens) and female (pistil) reproductive parts within the same flower, making them bisexual flowers.
The question asks to identify which chess champion was defeated by the Indian chess prodigy Rameshbabu Praggnanandhaa in 2022. This is a factual question related to recent events in the world of chess.
D) Magnus Carlsen was defeated by Rameshbabu Praggnanandhaa in a rapid chess game at the Airthings Masters in February 2022, when Praggnanandhaa was 16 years old. He repeated this feat in May 2022 at the Chessable Masters and again in August 2022 at the FTX Crypto Cup.
If the area of a square is 11025 cm², then the length of its diagonal is:
105\(\sqrt{2}\) cm
125\(\sqrt{2}\) cm
135\(\sqrt{2}\) cm
115\(\sqrt{2}\) cm
To find the length of the diagonal of a square, we first need to determine the side length of the square. The side length can be found from the given area. Once the side length is known, the diagonal can be calculated using the Pythagorean theorem or the formula for the diagonal of a square.
Find the side length of the square:
The area of a square is given by the formula \( \text{Area} = \text{side}^2 \). Let the side length be \(s\).
Given Area \( = 11025 \text{ cm}^2 \).
\[ s^2 = 11025 \]To find \(s\), we take the square root of 11025.
\[ s = \sqrt{11025} \]We can find the square root by prime factorization or by estimation.
Since \(100^2 = 10000\) and \(110^2 = 12100\), the number is between 100 and 110. The last digit is 5, so the square root must end in 5. Thus, \(s\) must be 105.
\[ s = 105 \text{ cm} \]Calculate the length of the diagonal:
For a square with side length \(s\), the length of the diagonal \(d\) can be found using the Pythagorean theorem (\(d^2 = s^2 + s^2\)) or the direct formula \(d = s\sqrt{2}\).
Using the formula:
\[ d = s\sqrt{2} \]Substitute the value of \(s = 105 \text{ cm}\):
\[ d = 105\sqrt{2} \text{ cm} \]A) \(105\sqrt{2}\) cm is the correct length of the diagonal, as calculated.
The question asks about Fleming's right-hand rule, which is used to determine the direction of induced current, electromotive force (EMF), or motion in a conductor when it moves in a magnetic field. We need to identify what the thumb represents in this rule.
C) the motion of the conductor. As explained, in Fleming's right-hand rule, the thumb represents the direction in which the conductor is moving within the magnetic field.
This question tests understanding of fundamental macroeconomic concepts related to consumption and saving. Specifically, it asks for the term that defines the ratio of a change in savings to a change in income. We need to recall the definitions of marginal and average propensities to save and consume.
A) Marginal propensity to save is the correct answer because it is defined as the ratio of the change in savings to the change in income. This is represented as:
\[ \text{MPS} = \frac{\Delta S}{\Delta Y} \]Simplify the given expression:
[13 − (−2) × {6 − (7 − 3)}] ÷ [4 × {5 + (−2) × (−6)}]
\( \frac{1}{4} \)
\( \frac{7}{34} \)
\( \frac{-17}{68} \)
\( \frac{-1}{3} \)
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). We will evaluate the numerator and the denominator separately and then perform the final division.
The question asks to identify an animal that can change its sex, thereby demonstrating that sex determination is not solely genetic in that species. This phenomenon is known as sequential hermaphroditism.
Correct Option: D) Snail. Many snail species are known to be hermaphroditic and can change their sex during their lifetime, demonstrating that their sex is not solely genetically determined.
The problem requires us to manipulate a given set of three-digit numbers by reversing their first two digits. Then, we need to identify the greatest and lowest numbers from this new set and find the difference between their respective first digits.
D) 5 — As calculated in the step-by-step explanation, the difference between the first digit of the greatest number (8) and the first digit of the lowest number (3) is 5.