This problem involves a neutralization reaction between a strong acid (HNO₃) and a strong base (NaOH). In a neutralization reaction, the moles of acid react completely with the moles of base. We can use the concept of molarity and volume to find the relationship between the two reactants and then apply it to the new scenario.
Understand the neutralization principle: At the point of complete neutralization, the number of moles of acid is equal to the number of moles of base. The formula for moles can be expressed as:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in Liters)} \]So, for neutralization:
\[ \text{Moles of acid} = \text{Moles of base} \] \[ M_1 V_1 = M_2 V_2 \]Where \(M_1\) and \(V_1\) are the molarity and volume of the acid, and \(M_2\) and \(V_2\) are the molarity and volume of the base.
Apply the given initial conditions: We are given that 20 ml of NaOH is neutralized by 10 ml of HNO₃.
Let \(M_{\text{NaOH}}\) be the molarity of NaOH and \(M_{\text{HNO}_3}\) be the molarity of HNO₃. At neutralization:
\[ M_{\text{NaOH}} \times V_{\text{NaOH}} = M_{\text{HNO}_3} \times V_{\text{HNO}_3} \] \[ M_{\text{NaOH}} \times 20 \text{ ml} = M_{\text{HNO}_3} \times 10 \text{ ml} \]From this, we can find the ratio of their molarities:
\[ \frac{M_{\text{NaOH}}}{M_{\text{HNO}_3}} = \frac{10 \text{ ml}}{20 \text{ ml}} = \frac{1}{2} \]This implies that \(M_{\text{HNO}_3} = 2 \times M_{\text{NaOH}}\). This means the concentration of HNO₃ is twice that of NaOH.
Apply the new conditions: Now, we need to find out how much NaOH will be required to neutralize 15 ml of HNO₃.
Using the same neutralization principle:
\[ M_{\text{NaOH}} \times V'_{\text{NaOH}} = M_{\text{HNO}_3} \times V'_{\text{HNO}_3} \]Substitute \(M_{\text{HNO}_3} = 2 \times M_{\text{NaOH}}\) into the equation:
\[ M_{\text{NaOH}} \times V'_{\text{NaOH}} = (2 \times M_{\text{NaOH}}) \times 15 \text{ ml} \]Divide both sides by \(M_{\text{NaOH}}\) (assuming \(M_{\text{NaOH}} \neq 0\)):
\[ V'_{\text{NaOH}} = 2 \times 15 \text{ ml} \] \[ V'_{\text{NaOH}} = 30 \text{ ml} \]Thus, 30 ml of NaOH will be required.
C) 30 ml
Hormonal contraceptives work by altering the body's natural hormonal cycle to prevent conception. Understanding the primary mechanisms of action of these hormones is key to identifying the correct answer.
Correct Option: C) By changing the hormonal balance to prevent egg release
The volume (in cm³) of a wire of diameter 56 cm and length 3 m is: (take π = \( \frac{22}{7} \))
The problem asks for the volume of a wire, which is cylindrical in shape. We are given its diameter and length. The volume of a cylinder is calculated using the formula \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height (or length in this case). We need to ensure all units are consistent, preferably in cm³.
The diameter is in cm, and the length is in m. We need to convert the length to cm.
\[ 1 \text{ m} = 100 \text{ cm} \] \[ L = 3 \text{ m} = 3 \times 100 \text{ cm} = 300 \text{ cm} \]The radius (\(r\)) is half of the diameter.
\[ r = \frac{D}{2} = \frac{56 \text{ cm}}{2} = 28 \text{ cm} \]The formula for the volume of a cylinder is \(V = \pi r^2 L\).
Substitute the values:
\[ V = \frac{22}{7} \times (28 \text{ cm})^2 \times 300 \text{ cm} \] \[ V = \frac{22}{7} \times (28 \times 28) \times 300 \text{ cm}^3 \]Simplify the calculation:
\[ V = 22 \times \frac{28}{7} \times 28 \times 300 \text{ cm}^3 \] \[ V = 22 \times 4 \times 28 \times 300 \text{ cm}^3 \] \[ V = 88 \times 28 \times 300 \text{ cm}^3 \]First, calculate \(88 \times 28\):
\[ 88 \times 28 = 2464 \]Now, multiply by 300:
\[ V = 2464 \times 300 \text{ cm}^3 \] \[ V = 739200 \text{ cm}^3 \]Correct Option: D) 739200
Which of the following was the venue of the 46th session of the UNESCO World Heritage Committee?
Dubai, United Arab Emirates
New Delhi, India
New York, United States
Paris, France
The question asks for the venue of the 46th session of the UNESCO World Heritage Committee. This requires knowledge of recent international events and the host cities for major UNESCO meetings.
Correct Option: B) New Delhi, India
The 46th session of the UNESCO World Heritage Committee was indeed held in New Delhi, India, from July 21 to July 31, 2024. This was a landmark event for India, as it hosted the session for the first time.
The question asks to identify which type of magnet produces a magnetic field pattern similar to that of a solenoid. We need to recall the magnetic field patterns for various magnets and compare them with the field pattern of a solenoid.
Correct Option: B) A bar magnet's magnetic field pattern is very similar to that of a current-carrying solenoid. Both have distinct North and South poles, and their magnetic field lines form continuous closed loops, emerging from one pole and entering the other.
To solve this problem, we need to apply the given rules to each digit of the original number: add 2 to odd digits and subtract 1 from even digits. After forming the new number, we will count the frequency of each digit to identify how many digits appear more than once.
D) Two. The digits 5 and 7 appear more than once in the new number 1579753.
If \(\frac{3x}{1+\frac{1}{1+\frac{x}{1-x}}}\) = 12, then find the value of 'x'.
To find the value of 'x', we need to simplify the given complex fraction step-by-step, starting from the innermost part of the denominator, and then solve the resulting linear equation.
Given equation:
\[ \frac{3x}{1+\frac{1}{1+\frac{x}{1-x}}} = 12 \]Simplify the innermost part of the denominator: \(1+\frac{x}{1-x}\)
\[ 1+\frac{x}{1-x} = \frac{1-x+x}{1-x} = \frac{1}{1-x} \]Substitute this back into the main expression:
\[ \frac{3x}{1+\frac{1}{\frac{1}{1-x}}} = 12 \]Simplify the term \[\frac{1}{\frac{1}{1-x}}\]:
\[ \frac{1}{\frac{1}{1-x}} = 1 \times (1-x) = 1-x \]Substitute this back into the equation:
\[ \frac{3x}{1+(1-x)} = 12 \]Simplify the denominator:
\[ 1+(1-x) = 1+1-x = 2-x \]The equation now becomes:
\[ \frac{3x}{2-x} = 12 \]Multiply both sides by \((2-x)\):
\[ 3x = 12(2-x) \]Distribute 12 on the right side:
\[ 3x = 24 - 12x \]Add \(12x\) to both sides:
\[ 3x + 12x = 24 \]\[ 15x = 24 \]Divide by 15 to find \(x\):
\[ x = \frac{24}{15} \]\[ x = \frac{8 \times 3}{5 \times 3} \]\[ x = \frac{8}{5} \]\[ x = 1.6 \]A) 1.6 — The step-by-step simplification of the complex fraction leads to \(x = 1.6\).
The question asks for the Indian state where the famous Kalighat Kali Temple is located. This is a direct factual question related to Indian geography and culture, specifically religious sites.
Correct Option: B) West Bengal
To solve this problem, we need to track Anmol's movements step-by-step, considering each turn and distance covered. We can visualize his path on a coordinate plane or by drawing a diagram. The final position relative to the starting point will help us determine the shortest distance and direction needed to return to the starting point.
C) 5 km to the north
Anmol's final position is 5 km South and 12 km East of Point A. To return to Point A, he must travel 5 km North and 12 km West. Since the options are given only in terms of "km to the north", the required vertical displacement to reach the original latitude of A is 5 km to the north.
The question asks to identify the author of a specific academic paper titled "Postcolonial Elements in Amitav Ghosh's 'The Shadow Lines,'" published in 2018. This requires knowledge of literary criticism and academic publications, specifically identifying the scholar who wrote this particular piece.
Correct Option: B) Nivedhaa Nivi