The question asks to identify the state whose Medical and Health Department received an award from the WHO in 2019 for its efforts in tobacco control. This is a factual question requiring knowledge of specific awards and recognitions related to public health initiatives in India.
In 2019, the World Health Organization (WHO) awarded the Medical and Health Department of Rajasthan for its outstanding achievements in the field of tobacco control. This award recognized the state's comprehensive efforts to curb tobacco use, including the implementation of various policies and awareness campaigns.
A) Rajasthan — In 2019, the World Health Organization (WHO) presented the "World No Tobacco Day Award" to the Medical and Health Department of Rajasthan for its commendable work in tobacco control. This included initiatives like banning flavored tobacco products, increasing awareness, and enforcing tobacco control laws.
The question asks to identify the hormone responsible for the simultaneous increase in heartbeat and breathing rate. This physiological response is typically associated with the body's "fight or flight" mechanism, which prepares the body for immediate action in stressful or dangerous situations.
Correct Option: B) Adrenaline is the hormone primarily responsible for mediating the "fight or flight" response, which includes the simultaneous increase in heartbeat and breathing rate, along with other physiological changes like increased blood pressure and diversion of blood to muscles.
The question asks to identify the third cricketer to receive the Rajiv Gandhi Khel Ratna award (now known as Major Dhyan Chand Khel Ratna Award). This requires knowledge of the history of this prestigious sports award and its recipients, specifically among cricketers.
D) Virat Kohli became the third cricketer to receive the Rajiv Gandhi Khel Ratna award in 2018.
We are given the HCF and LCM of two numbers. We know that the product of two numbers is equal to the product of their HCF and LCM. We can use this property to find the numbers. Since the numbers are between 25 and 40, we can test possible pairs of factors of the product of HCF and LCM that satisfy this condition.
Let the two numbers be \(a\) and \(b\).
Given HCF \(= 5\) and LCM \(= 210\).
The fundamental property relating HCF and LCM of two numbers is:
\[ a \times b = \text{HCF} \times \text{LCM} \]Substitute the given values:
\[ a \times b = 5 \times 210 = 1050 \]Since the HCF is 5, both numbers must be multiples of 5. We can express the numbers as \(a = 5x\) and \(b = 5y\), where \(x\) and \(y\) are co-prime integers (their HCF is 1).
Substitute these into the product equation:
\[ (5x) \times (5y) = 1050 \] \[ 25xy = 1050 \]Solve for \(xy\):
\[ xy = \frac{1050}{25} = 42 \]Now we need to find pairs of co-prime integers \((x, y)\) whose product is 42. The pairs are:
For each pair, calculate the numbers \(a = 5x\) and \(b = 5y\):
The numbers are 30 and 35.
The sum of the numbers is \(30 + 35 = 65\).
C) 65 — The numbers are 30 and 35, and their sum is \(30 + 35 = 65\).
The question asks for a system designed to prevent unauthorized access to or from a private network. This points directly to a security mechanism that filters network traffic based on predefined rules.
Correct Option: D) Firewall is a network security system that monitors and controls incoming and outgoing network traffic based on predetermined security rules. It acts as a barrier between a trusted internal network and untrusted external networks (like the internet), preventing unauthorized access and protecting the private network from various cyber threats.
The question asks to identify the historical figure who proclaimed the formation of the Provisional Government of Azad Hind on October 21, 1943. This requires knowledge of key events and personalities related to India's independence movement, specifically the Azad Hind Fauj (Indian National Army).
Correct Option: D) Subhash Chandra Bose is the correct answer. He was the leader who proclaimed the formation of the Provisional Government of Azad Hind in Singapore on October 21, 1943, and was also the Supreme Commander of the Azad Hind Fauj.
To find the relation between \(x\) and \(y\) such that the point \((x, y)\) is equidistant from two given points, we use the distance formula. We set the square of the distance from \((x, y)\) to the first point equal to the square of the distance from \((x, y)\) to the second point. This eliminates the need for square roots and simplifies the algebraic manipulation.
Let the point be \(P(x, y)\). Let the two given points be \(A(6, 2)\) and \(B(4, 6)\).
The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]Since point \(P(x, y)\) is equidistant from \(A(6, 2)\) and \(B(4, 6)\), we have \(PA = PB\). Squaring both sides, we get \(PA^2 = PB^2\).
Calculate \(PA^2\):
\[ PA^2 = (x - 6)^2 + (y - 2)^2 \]\[ PA^2 = (x^2 - 12x + 36) + (y^2 - 4y + 4) \]\[ PA^2 = x^2 + y^2 - 12x - 4y + 40 \]Calculate \(PB^2\):
\[ PB^2 = (x - 4)^2 + (y - 6)^2 \]\[ PB^2 = (x^2 - 8x + 16) + (y^2 - 12y + 36) \]\[ PB^2 = x^2 + y^2 - 8x - 12y + 52 \]Set \(PA^2 = PB^2\):
\[ x^2 + y^2 - 12x - 4y + 40 = x^2 + y^2 - 8x - 12y + 52 \]Cancel out \(x^2\) and \(y^2\) from both sides:
\[ -12x - 4y + 40 = -8x - 12y + 52 \]Rearrange the terms to group \(x\) and \(y\) terms on one side and constants on the other:
\[ -12x + 8x - 4y + 12y = 52 - 40 \]\[ -4x + 8y = 12 \]Divide the entire equation by 4 to simplify:
\[ -x + 2y = 3 \]Multiply by -1 to make the coefficient of \(x\) positive (or rearrange):
\[ x - 2y = -3 \]D) The derived relation is \(x - 2y = -3\).
This problem involves relative speed. We need to calculate the distance covered by A before B starts, then find the relative speed of B with respect to A, and finally determine the time B takes to cover that initial distance.
Therefore, B will take 160 minutes to catch up with A.
Correct Option: D) 160 min
The problem asks us to find the original price of an air cooler before tax was added. We are given the final price (including tax) and the tax percentage. We can set up an equation where the original price plus the tax calculated on the original price equals the final price.
Let the price of the air cooler before tax be \(P\).
The tax amount is 10% of the original price \(P\). So, Tax Amount \( = 0.10 \times P \).
The price including tax is the original price plus the tax amount:
\[ \text{Price including tax} = \text{Original Price} + \text{Tax Amount} \]\[ 3300 = P + 0.10P \]Combine the terms involving \(P\):
\[ 3300 = (1 + 0.10)P \]\[ 3300 = 1.10P \]Divide both sides by 1.10:
\[ P = \frac{3300}{1.10} \]\[ P = \frac{33000}{11} \]\[ P = 3000 \]The price of the air cooler before tax was ₹3,000.
C) ₹3,000. This is the price calculated before the 10% tax was added.
The question asks to identify the organization responsible for incorporating New Space India Limited (NSIL) to commercialize space research and development activities. This requires knowledge of India's space sector and its commercial arms.
Correct Option: D) ISRO. New Space India Limited (NSIL) is a Central Public Sector Enterprise (CPSE) under the administrative control of the Department of Space (DoS), Government of India. It was incorporated on March 6, 2019, to commercially exploit the products and services emanating from the Indian space programme, making it the commercial arm of ISRO.