The question asks to identify the incorrect statement regarding Payment Banks. To answer this, we need to recall the key characteristics and permissible activities of Payment Banks as regulated by the Reserve Bank of India (RBI).
D) They can issue credit cards — This statement is incorrect. Payment Banks are not allowed to undertake lending activities, and issuing credit cards is a form of lending. Therefore, they cannot issue credit cards.
If 2a = 3b = 4c and a + b + c = 13\(\sqrt{2}\), then \( a^{2} + b^{2} + c^{2} \) is:
The problem provides a relationship between three variables \(a, b, c\) in the form of \(2a = 3b = 4c\) and their sum \(a + b + c = 13\sqrt{2}\). We need to find the value of \(a^2 + b^2 + c^2\). The strategy is to express \(a, b, c\) in terms of a common constant, then substitute these expressions into the sum equation to find the constant. Finally, substitute the values of \(a, b, c\) into the expression \(a^2 + b^2 + c^2\).
Establish a common constant:
Given \(2a = 3b = 4c\). Let this common value be \(k\).
So, \(2a = k \implies a = \frac{k}{2}\)
\(3b = k \implies b = \frac{k}{3}\)
\(4c = k \implies c = \frac{k}{4}\)
Substitute into the sum equation:
We are given \(a + b + c = 13\sqrt{2}\). Substitute the expressions for \(a, b, c\) in terms of \(k\):
\[ \frac{k}{2} + \frac{k}{3} + \frac{k}{4} = 13\sqrt{2} \]
To add the fractions, find a common denominator, which is 12:
\[ \frac{6k}{12} + \frac{4k}{12} + \frac{3k}{12} = 13\sqrt{2} \]
\[ \frac{6k + 4k + 3k}{12} = 13\sqrt{2} \]
\[ \frac{13k}{12} = 13\sqrt{2} \]
Solve for \(k\):
\[ 13k = 13\sqrt{2} \times 12 \]
Divide both sides by 13:
\[ k = 12\sqrt{2} \]
Find the values of \(a, b, c\):
Now substitute the value of \(k\) back into the expressions for \(a, b, c\):
\[ a = \frac{k}{2} = \frac{12\sqrt{2}}{2} = 6\sqrt{2} \]
\[ b = \frac{k}{3} = \frac{12\sqrt{2}}{3} = 4\sqrt{2} \]
\[ c = \frac{k}{4} = \frac{12\sqrt{2}}{4} = 3\sqrt{2} \]
Calculate \(a^2 + b^2 + c^2\):
\[ a^2 = (6\sqrt{2})^2 = 6^2 \times (\sqrt{2})^2 = 36 \times 2 = 72 \]
\[ b^2 = (4\sqrt{2})^2 = 4^2 \times (\sqrt{2})^2 = 16 \times 2 = 32 \]
\[ c^2 = (3\sqrt{2})^2 = 3^2 \times (\sqrt{2})^2 = 9 \times 2 = 18 \]
Finally, sum these values:
\[ a^2 + b^2 + c^2 = 72 + 32 + 18 = 122 \]
Correct Option: D) 122
To find the profit percentage, we need to determine the cost price (CP) for the retailer and the selling price (SP) for the 20 pens. The retailer buys 20 pens at the marked price of 15 pens, which gives him a discount on the purchase. Then, he sells these 20 pens with an additional discount. We will calculate the effective CP and SP per pen or for the lot of 20 pens.
Assume Marked Price (MP) per pen:
Let the Marked Price (MP) of one pen be \( \\(1 \). This is a convenient assumption for calculation.
Calculate the Cost Price (CP) for the retailer:
The retailer buys 20 pens at the marked price of 15 pens. This means the cost for 20 pens is equal to the marked price of 15 pens.
Calculate the Selling Price (SP) for the retailer:
The retailer sells these 20 pens, giving a discount of 1% on their marked price. The marked price of 20 pens would be \( 20 \times \\)1 = \\(20 \).
Calculate the Profit:
Profit is the difference between the Selling Price and the Cost Price.
Calculate the Profit Percent:
Profit percent is calculated on the Cost Price.
The profit percent of the retailer is 32%.
Correct Option: C) 32%
If (3x)(3y) = 9 and (25x)(5y) = 625, then what is (x, y)?
The problem involves solving a system of two exponential equations for two variables, \(x\) and \(y\). We will use the properties of exponents to simplify the given equations into a system of linear equations, and then solve this system using substitution or elimination.
The first equation is \((3^x)(3^y) = 9\).
Using the property \(a^m \cdot a^n = a^{m+n}\), we can rewrite the left side:
\[ 3^{x+y} = 9 \]Since \(9 = 3^2\), we have:
\[ 3^{x+y} = 3^2 \]Equating the exponents, we get our first linear equation:
\[ x+y = 2 \quad \text{(Equation 1)} \]The second equation is \((25^x)(5^y) = 625\).
We need to express all terms with the same base. Since \(25 = 5^2\) and \(625 = 5^4\), we can rewrite the equation as:
\[ (5^2)^x (5^y) = 5^4 \]Using the property \((a^m)^n = a^{mn}\), we get:
\[ 5^{2x} \cdot 5^y = 5^4 \]Using the property \(a^m \cdot a^n = a^{m+n}\), we combine the terms on the left:
\[ 5^{2x+y} = 5^4 \]Equating the exponents, we get our second linear equation:
\[ 2x+y = 4 \quad \text{(Equation 2)} \]We now have a system of two linear equations:
Equation 1: \(x+y = 2\)
Equation 2: \(2x+y = 4\)
We can solve this system by subtracting Equation 1 from Equation 2:
\[ (2x+y) - (x+y) = 4 - 2 \]\[ 2x+y-x-y = 2 \]\[ x = 2 \]Substitute \(x=2\) into \(x+y=2\):
\[ 2+y = 2 \]\[ y = 2-2 \]\[ y = 0 \]The solution is \((x, y) = (2, 0)\).
B) \((2, 0)\) is the correct solution derived from solving the system of equations.
The problem is a coding-decoding question. We need to identify the pattern used to convert letters into numbers for the given words "AGE" and "SEX". Once the pattern is established, we will apply it to the word "COME" to find its coded value.
C) 36 is the correct answer, as per the established pattern of summing the alphabetical positions of the letters.
The question asks to identify the plant hormone whose concentration is highest at the top of the plant and decreases towards the roots. This describes a hormone involved in apical dominance and gravitropism, which are key functions of auxins.
Correct Option: D) Auxin
Auxins are synthesized predominantly in the shoot apical meristem and young leaves. They are transported basipetally (downwards) from the shoot apex, resulting in the highest concentration at the top of the plant and a decreasing gradient towards the roots. This distribution is crucial for processes like apical dominance, cell elongation in stems, and gravitropism.
The question asks for the full form of "SLR" in the banking field. This is a direct knowledge-based question related to banking terminology often tested in competitive exams.
Correct Option: D) Statutory Liquidity Ratio
SLR (Statutory Liquidity Ratio) is a crucial term in banking and monetary policy. It refers to the percentage of Net Demand and Time Liabilities (NDTL) that commercial banks are required to maintain in the form of liquid assets such as cash, gold, or unencumbered approved securities. This ratio is stipulated by the Reserve Bank of India (RBI) and serves as a tool to control credit growth and ensure the solvency of banks.
This problem involves calculating the concentration of salt in a solution after some water has evaporated. The key principle is that the amount of salt remains constant, while the total volume of the solution changes due to evaporation.
The initial solution is 5 litres and contains 3% salt.
\[ \text{Amount of salt} = \text{Percentage of salt} \times \text{Total volume of solution} \]\[ \text{Amount of salt} = 3\% \times 5 \text{ litres} \]\[ \text{Amount of salt} = \frac{3}{100} \times 5 = 0.15 \text{ litres} \]2 litres of water is evaporated from the 5-litre solution.
\[ \text{Final volume of solution} = \text{Initial volume} - \text{Evaporated water} \]\[ \text{Final volume of solution} = 5 \text{ litres} - 2 \text{ litres} = 3 \text{ litres} \]The amount of salt remains constant (0.15 litres), but the total volume of the solution is now 3 litres.
\[ \text{New percentage of salt} = \frac{\text{Amount of salt}}{\text{Final volume of solution}} \times 100\% \]\[ \text{New percentage of salt} = \frac{0.15 \text{ litres}}{3 \text{ litres}} \times 100\% \]\[ \text{New percentage of salt} = 0.05 \times 100\% = 5\% \]A) The percentage of salt in the remaining solution is 5%.
Select the Venn diagram that best represents the relationship between computers, desktops and laptops.
To determine the correct Venn diagram, we need to understand the relationship between computers, desktops, and laptops. Both desktops and laptops are types of computers.
Correct Option: A) The diagram shows two smaller circles (desktops and laptops) within a larger circle (computers), correctly representing the relationship.
This question tests logical reasoning and the ability to identify implicit assumptions in a given statement. An assumption is something taken for granted or accepted as true without proof. We need to analyze the statement made by the marketing executive and determine what underlying beliefs or conditions must be true for that statement to be made effectively.
B) Only assumption 2 is implicit.
The marketing executive's statement directly appeals to the desire of people to grow their money. The promise to "double your money" is made because the executive assumes that people want to increase their income through investment. Without this underlying desire, the statement would have no persuasive power.
