The question asks to identify the specific program or scheme that launched India's first virtual science laboratory for children in November 2021, aimed at connecting students with scientists. We need to evaluate each option based on its known objectives and launch details.
D) CSIR Jigyasa — The CSIR Jigyasa program launched India's first virtual science laboratory for children in November 2021. This initiative aims to connect students across the country with scientists and provide them with a virtual platform to experience scientific experiments and learn from experts.
The question asks to identify the Article of the Indian Constitution that deals with preventive detention. This requires knowledge of the fundamental rights, specifically Articles 19-22, which cover the Right to Freedom.
Correct Option: B) Article 22 of the Indian Constitution provides protection against arrest and detention in certain cases. This article explicitly includes provisions related to preventive detention, outlining the safeguards available to persons arrested or detained under preventive detention laws. It specifies that a person cannot be detained for more than three months unless an advisory board recommends extended detention, and it also grants the right to be informed of the grounds of arrest and the right to consult a legal practitioner, though these rights are curtailed in cases of preventive detention.
The problem asks us to find the focal length of a lens given its power. We will use the fundamental relationship between the power of a lens and its focal length, ensuring consistent units.
The power \(P\) of a lens is the reciprocal of its focal length \(f\). When the focal length is in meters, the power is in diopters (D).
\[ P = \frac{1}{f \text{ (in meters)}} \]From the above formula, we can express the focal length as:
\[ f \text{ (in meters)} = \frac{1}{P} \]The given power of the lens is \(P = -5 \text{ D}\).
\[ f \text{ (in meters)} = \frac{1}{-5 \text{ D}} = -0.2 \text{ meters} \]Since 1 meter = 100 centimeters, we convert the focal length from meters to centimeters:
\[ f = -0.2 \text{ meters} \times 100 \frac{\text{cm}}{\text{meter}} = -20 \text{ cm} \]A negative focal length indicates that the lens is a concave (diverging) lens.
B) \(-20 \text{ cm}\) is the correct focal length calculated from the given power.
This question tests knowledge of basic human digestion, specifically the breakdown of macronutrients found in common food items like rice, potato, and bread. The key is to identify the primary macronutrient in these foods and its simplest digestible form.
Correct Option: A) carbohydrates, glucose
The problem asks us to identify the number of even numbers in a given series that are immediately preceded by an odd number and immediately followed by an odd number. We need to scan the series and check each even number against this condition.
A) Two. The even numbers that satisfy the condition are the first '6' (preceded by 5, followed by 5) and the last '8' (preceded by 7, followed by 3).
The question asks to identify the INCORRECT statement regarding respiration in plants. We need to evaluate each option based on our knowledge of plant physiology, specifically gas exchange and respiration.
B) Carbon dioxide is added to the atmosphere during the day. This statement is incorrect. During the day, the rate of photosynthesis in plants is much higher than the rate of respiration. Photosynthesis consumes CO₂, while respiration releases it. Therefore, there is a net uptake of CO₂ from the atmosphere by plants during the day, not an addition.
This is a logical reasoning problem involving arrangement in a row. We need to deduce the order of students based on the given clues and then count the total number of students.
"Only Radhika is standing between Sonia and Sujata."
This implies the arrangement is either Sonia - Radhika - Sujata or Sujata - Radhika - Sonia. Let's represent this as: S - R - S_u (where S_u is Sujata).
"Divya is standing immediately ahead of Sonia."
This means Divya is to the left of Sonia. So, the arrangement becomes: D - S - R - S_u.
"Two girls are standing immediately behind Sujata."
This means there are two more students after Sujata. Let's call them G1 and G2. So, the arrangement is: D - S - R - S_u - G1 - G2.
"Only one girl is standing immediately ahead of Divya."
This means there is one student to the left of Divya. Let's call her G3. So, the final arrangement is: G3 - D - S - R - S_u - G1 - G2.
Count the total number of students.
Counting the positions in the final arrangement: G3, D, S, R, S_u, G1, G2. There are 7 students in total.
A) 7 is the correct answer because, by arranging the students according to the given conditions, we find there are 7 students in the row.
The problem involves finding the values of unknown natural numbers \(x\) and \(y\) from given proportions and then calculating the value of the expression \(2x + 3y\). The concept of continued proportion (or mean proportion) will be used to find \(x\) and \(y\).
The first proportion is given as \(49 : x :: x : 81\). This can be written in fractional form as:
\[ \frac{49}{x} = \frac{x}{81} \]Cross-multiplying gives:
\[ x^2 = 49 \times 81 \]To find \(x\), take the square root of both sides:
\[ x = \sqrt{49 \times 81} \]\[ x = \sqrt{49} \times \sqrt{81} \]\[ x = 7 \times 9 \]\[ x = 63 \]Since \(x\) is a natural number, we take the positive root.
The second proportion is given as \(64 : y :: y : 169\). This can be written in fractional form as:
\[ \frac{64}{y} = \frac{y}{169} \]Cross-multiplying gives:
\[ y^2 = 64 \times 169 \]To find \(y\), take the square root of both sides:
\[ y = \sqrt{64 \times 169} \]\[ y = \sqrt{64} \times \sqrt{169} \]\[ y = 8 \times 13 \]\[ y = 104 \]Since \(y\) is a natural number, we take the positive root.
Now substitute the values of \(x = 63\) and \(y = 104\) into the expression \(2x + 3y\):
\[ 2x + 3y = 2(63) + 3(104) \]\[ 2x + 3y = 126 + 312 \]\[ 2x + 3y = 438 \]Correct Option: B) 438
This question asks us to identify which of the given assumptions can be logically inferred from the provided statement. We need to evaluate each assumption independently to see if it is a necessary underlying belief for the statement to hold true.
Correct Option: D) Neither I nor II can be assumed
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This rule dictates the sequence in which mathematical operations should be performed: Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, and Subtraction.
Thus, the value of the expression is \(7854\).
Correct Option: C) 7854