The question asks about the total financial outlay under the Agriculture Infrastructure Fund (AIF) for a specific period. To answer this, one needs to recall the announced corpus of the fund.
D) The Agriculture Infrastructure Fund has a corpus of ₹1 lakh crore, which is to be disbursed from FY 2020-21 to FY 2025-26 (and further extended to FY 2029-30).
The problem asks us to find the principal amount given the difference between compound interest (CI) and simple interest (SI) for three years at a specific annual interest rate. We will use the standard formulas for CI and SI and their difference for three years to solve for the principal.
Let the Principal be \(P\), the Rate of interest be \(R\), and the Time be \(T\).
Given values:
The formula for the difference between Compound Interest and Simple Interest for 3 years is:
\[ \text{CI} - \text{SI} = P \left[ \left(1 + \frac{R}{100}\right)^3 - 1 \right] - \frac{P \cdot R \cdot T}{100} \]A more direct formula for the difference between CI and SI for 3 years is:
\[ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 \left( \frac{R}{100} + 3 \right) \]Substitute the given values into the formula:
\[ 152 = P \left( \frac{4}{100} \right)^2 \left( \frac{4}{100} + 3 \right) \]Simplify the terms:
\[ 152 = P \left( \frac{1}{25} \right)^2 \left( \frac{1}{25} + 3 \right) \]\[ 152 = P \left( \frac{1}{625} \right) \left( \frac{1 + 75}{25} \right) \]\[ 152 = P \left( \frac{1}{625} \right) \left( \frac{76}{25} \right) \]Now, solve for \(P\):
\[ 152 = P \left( \frac{76}{625 \times 25} \right) \]\[ 152 = P \left( \frac{76}{15625} \right) \]\[ P = \frac{152 \times 15625}{76} \]Perform the division:
\[ P = 2 \times 15625 \]\[ P = 31250 \]Therefore, the principal amount is ₹31,250.
Correct Option: D) 31,250
In this question, a group of number/symbol is coded using letter codes as per the codes given below and the conditions which follow. The correct combination of codes following the conditions is your answer.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/symbol | 9 | 6 | + | @ | 8 | & | 3 | * | % | 5 | $ | 4 | 7 |
| Code | W | C | E | J | F | A | D | Q | G | P | R | B | U |
Conditions:
(I) If the first element is a number and the last a symbol, the codes for these two (the first and the last elements) are to be interchanged.
(II) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.
(III) If both second and third elements are perfect squares, the third element is to be coded as the code for the second element.
What is 843% coded as?
The problem requires us to code a given number/symbol sequence based on a provided table and a set of conditions. We need to first identify the codes for each element from the table, then check if any of the given conditions apply. If a condition applies, we modify the codes accordingly. If no condition applies, we use the direct codes.
A) GBDF is the correct code after applying Condition (I).
This problem involves calculating the combined work rate of two pipes, one filling and one emptying, to determine the time required to fill a specific fraction of a tank. We will calculate the individual rates, find the net filling rate, and then use this rate to find the time for two-thirds of the tank to be filled.
The question asks to identify the recipient of the 'CA in Public Service' award from the Institute of Chartered Accountants of India (ICAI) in February 2025. This requires knowledge of recent awards and recognitions in the field of chartered accountancy in India.
Based on available information, Deepak Kumar Kedia was honored with the 'CA in Public Service' award by the Institute of Chartered Accountants of India (ICAI) in February 2025.
B) Deepak Kumar Kedia — Deepak Kumar Kedia was indeed the recipient of the 'CA in Public Service' award from the Institute of Chartered Accountants of India (ICAI) in February 2025. This award recognizes chartered accountants who have made significant contributions in public service.
The question asks to identify the input device least likely to be the primary means of navigation and interaction in a Virtual Reality (VR) environment. We need to evaluate each option based on its suitability for immersive VR interaction.
D) Optical mouse connected to the computer — An optical mouse is a traditional 2D input device. It is designed for interacting with a flat desktop interface, not for 3D navigation and interaction within an immersive virtual reality environment. Its use would be highly unnatural and ineffective for primary VR interaction.
The question asks to identify the physiographic region located north of the Narmada River. This requires knowledge of the geographical location of the Narmada River and the major plateaus of Peninsular India.
Correct Option: A) The Malwa Plateau is situated north of the Narmada River, forming a significant part of the Central Highlands in India.
The given equation is that of a circle. We need to rewrite the equation in the standard form of a circle, \((x-h)^2 + (y-k)^2 = r^2\), by completing the square. Once in this form, we can identify the center \((h, k)\) and the radius \(r\). However, the question asks for the value of \(x^2 + y^2\). This suggests that the equation might simplify in a particular way, or that the given equation represents a point circle, meaning its radius is zero.
The given equation is:
\[ x^{2} + y^{2} - 16x + 38y + 425 = 0 \]Rearrange the terms to group \(x\) terms and \(y\) terms:
\[ (x^{2} - 16x) + (y^{2} + 38y) + 425 = 0 \]Complete the square for the \(x\) terms. To complete the square for \(x^2 - 16x\), we need to add \((\frac{-16}{2})^2 = (-8)^2 = 64\). So, \(x^2 - 16x + 64 = (x-8)^2\).
Complete the square for the \(y\) terms. To complete the square for \(y^2 + 38y\), we need to add \((\frac{38}{2})^2 = (19)^2 = 361\). So, \(y^2 + 38y + 361 = (y+19)^2\).
Add and subtract these values to the equation:
\[ (x^{2} - 16x + 64 - 64) + (y^{2} + 38y + 361 - 361) + 425 = 0 \]Rewrite the squared terms:
\[ (x - 8)^{2} - 64 + (y + 19)^{2} - 361 + 425 = 0 \]Combine the constant terms:
\[ (x - 8)^{2} + (y + 19)^{2} - 64 - 361 + 425 = 0 \]\[ (x - 8)^{2} + (y + 19)^{2} - 425 + 425 = 0 \]\[ (x - 8)^{2} + (y + 19)^{2} = 0 \]For the sum of two squares to be zero, each square must be zero. This means:
\[ (x - 8)^{2} = 0 \implies x - 8 = 0 \implies x = 8 \]\[ (y + 19)^{2} = 0 \implies y + 19 = 0 \implies y = -19 \]Now, substitute these values of \(x\) and \(y\) into the expression \(x^2 + y^2\):
\[ x^{2} + y^{2} = (8)^{2} + (-19)^{2} \]\[ x^{2} + y^{2} = 64 + 361 \]\[ x^{2} + y^{2} = 425 \]Correct Option: D) 425
The question asks about the recipient of the Comptroller and Auditor General (CAG) reports concerning state accounts. This falls under the constitutional provisions related to the CAG's functions and reporting.
Correct Option: B) Governor of the concerned state
As per Article 151(2) of the Indian Constitution, the reports of the Comptroller and Auditor General of India relating to the accounts of a State are submitted to the Governor of that State. The Governor then causes them to be laid before the State Legislature.
To find the roots of a quadratic equation of the form \(ax^2 + bx + c = 0\), we can use either factorization, completing the square, or the quadratic formula. In this case, the equation is given in a form that suggests factorization might be straightforward by looking for two numbers whose sum is \((2a+3)\) and whose product is \((a^2+3a)\).
The given quadratic equation is:
\[ x^{2} + (2a + 3)x + (a^{2} + 3a) = 0 \]We need to find two numbers that add up to \((2a + 3)\) and multiply to \((a^{2} + 3a)\).
Let's factor the constant term \((a^{2} + 3a)\):
\[ a^{2} + 3a = a(a + 3) \]Now, let's check if the sum of these two factors, \(a\) and \((a+3)\), equals the coefficient of \(x\), which is \((2a+3)\):
\[ a + (a + 3) = 2a + 3 \]This matches the coefficient of \(x\).
Since we found two numbers, \(a\) and \((a+3)\), whose product is \((a^2+3a)\) and whose sum is \((2a+3)\), we can factor the quadratic equation as:
\[ (x + a)(x + (a + 3)) = 0 \]To find the roots, set each factor to zero:
\[ x + a = 0 \implies x = -a \] \[ x + (a + 3) = 0 \implies x = -(a + 3) = -a - 3 \]Thus, the roots of the equation are \(x = -a\) and \(x = -a - 3\).
A) x = −a, −a − 3. This matches our calculated roots.