The question asks for the location where India's first Demonstration Facility for Biopolymers was inaugurated by Dr. Jitendra Singh in October 2024. This is a factual question related to current affairs and scientific infrastructure development in India.
Correct Option: C) Pune
The question asks about the individual who launched the 'Create in India Challenge-Season One' in New Delhi on August 22, 2024. This is a factual question related to current affairs and government initiatives, specifically concerning the Ministry of Information and Broadcasting or related sectors. Identifying the relevant minister responsible for such initiatives is key.
D) Ashwini Vaishnaw — Ashwini Vaishnaw, the Union Minister for Railways, Communications, and Electronics & Information Technology, launched the 'Create in India Challenge-Season One' in New Delhi on August 22, 2024. This initiative is aimed at fostering innovation and creativity in the audio-visual and entertainment sector, aligning with his ministerial portfolios.
The pH scale measures the acidity or alkalinity of a solution. A pH of 7 is neutral, less than 7 is acidic, and greater than 7 is basic (alkaline). The question describes a solution with a pH of 8, which is basic. We need to determine how diluting this basic solution with an equal volume of water will affect its pH.
A) The pH will decrease. As calculated, diluting a basic solution (pH 8) with water reduces the concentration of hydroxide ions, making it less basic and thus lowering its pH towards 7. The new pH is approximately 7.7.
The question asks to identify the article of the Indian Constitution that mandates elections to the House of the People (Lok Sabha) and State Legislative Assemblies based on adult suffrage. This requires knowledge of specific articles related to elections and constitutional provisions.
A) 326 — Article 326 of the Indian Constitution clearly lays down the principle of adult suffrage for elections to the Lok Sabha and State Legislative Assemblies.
This problem involves setting up and solving a system of linear equations based on the given information about ages at different points in time. We will define variables for the present ages of Reena and her mother, then translate the past and future age conditions into equations. Finally, we will solve these equations to find their present ages and their ratio.
Define variables for present ages:
Let Reena's present age be \(R\) years.
Let Reena's mother's present age be \(M\) years.
Formulate the first equation (12 years ago):
Twelve years ago:
According to the problem, the mother's age was three times Reena's age:
\[ M - 12 = 3(R - 12) \] \[ M - 12 = 3R - 36 \] \[ M = 3R - 24 \quad \text{(Equation 1)} \]Formulate the second equation (2 years hence):
Two years hence (in the future):
According to the problem, the mother's age will be 2 times Reena's age:
\[ M + 2 = 2(R + 2) \] \[ M + 2 = 2R + 4 \] \[ M = 2R + 2 \quad \text{(Equation 2)} \]Solve the system of equations:
We have two expressions for \(M\). We can equate them:
\[ 3R - 24 = 2R + 2 \]Subtract \(2R\) from both sides:
\[ 3R - 2R - 24 = 2 \] \[ R - 24 = 2 \]Add \(24\) to both sides:
\[ R = 2 + 24 \] \[ R = 26 \]So, Reena's present age is 26 years.
Now substitute \(R = 26\) into Equation 2 (or Equation 1) to find \(M\):
\[ M = 2(26) + 2 \] \[ M = 52 + 2 \] \[ M = 54 \]So, Reena's mother's present age is 54 years.
Find the ratio of their present ages:
The ratio of Reena's age to her mother's age is \(R : M\):
\[ \text{Ratio} = \frac{R}{M} = \frac{26}{54} \]Simplify the ratio by dividing both numbers by their greatest common divisor, which is 2:
\[ \text{Ratio} = \frac{26 \div 2}{54 \div 2} = \frac{13}{27} \]So, the ratio is \(13 : 27\).
Correct Option: C) 13 : 27
The average price of three items of furniture is Rs 16,890. If their prices are in the ratio 3:5:7, the price of the cheapest item (in Rs) is
The problem involves finding the price of the cheapest item given the average price of three items and their price ratio. We will first use the average price to find the total price of the three items. Then, we will use the given ratio to express the individual prices in terms of a common variable and solve for that variable to find the price of the cheapest item.
Calculate the total price of the three items:
The average price of three items is given as Rs 16,890.
The formula for average is:
\[ \text{Average} = \frac{\text{Sum of prices}}{\text{Number of items}} \]So, the sum of prices (total price) can be calculated as:
\[ \text{Total Price} = \text{Average Price} \times \text{Number of items} \]\[ \text{Total Price} = 16,890 \times 3 = 50,670 \text{ Rs} \]Represent the prices using the given ratio:
The prices of the three items are in the ratio 3:5:7. Let the prices of the three items be \(3x\), \(5x\), and \(7x\) respectively, where \(x\) is a common multiplier.
Formulate an equation and solve for \(x\):
The sum of these prices must be equal to the total price calculated in Step 1:
\[ 3x + 5x + 7x = 50,670 \]\[ 15x = 50,670 \]Now, solve for \(x\):
\[ x = \frac{50,670}{15} \]\[ x = 3,378 \]Calculate the price of the cheapest item:
The cheapest item corresponds to the smallest ratio part, which is \(3x\).
\[ \text{Price of cheapest item} = 3x \]\[ \text{Price of cheapest item} = 3 \times 3,378 \]\[ \text{Price of cheapest item} = 10,134 \text{ Rs} \]Correct Option: A) 10134
The problem asks us to find a pair of letter groups that follows the same pattern as the two given pairs: PMN : RPI and VHS : XKN. We need to analyze the positional shifts of the letters in the English alphabet for each pair to identify the underlying rule.
B) NFF : PIA
Find the value of 2.3\(\overline{8}\) ÷ 0.5\(\overline{4}\).
4 \( \frac{19}{49} \)
3 \( \frac{17}{21} \)
5 \( \frac{26}{51} \)
6 \( \frac{29}{57} \)
To solve this problem, we need to convert the given recurring decimals into fractions. Then, we will perform the division of these fractions and simplify the result to a mixed fraction.
Correct Option: A) 4 \( \frac{19}{49} \)
The question asks to identify a device that operates based on the heating effect of electric current. This effect, also known as Joule heating, occurs when electric current flows through a conductor, generating heat due to resistance. We need to evaluate each option based on its primary operating principle.
C) Electric iron operates by intentionally generating heat through the resistance of its heating element when electric current passes through it, directly utilizing the heating effect of electric current.
The problem asks us to find the value of P given that the mean proportional of P and 125 is 100. We will use the definition of mean proportional to set up an equation and solve for P.
Correct Option: B) 80