The question asks about the specific Constitutional Amendment Act that established the Parliament's power to amend the Constitution as a constitutive power. This refers to a landmark amendment that clarified and asserted Parliament's authority in constitutional amendments, particularly in the context of fundamental rights.
A) Twenty-Fourth Amendment Act — This Act, passed in 1971, explicitly affirmed Parliament's power to amend any part of the Constitution, including Fundamental Rights, and clarified that such an amendment would not be subject to the limitations of Article 13. This established Parliament's power as a constitutive power.
The given problem is a number series. We need to identify the pattern or rule governing the sequence of numbers and then apply it to find the missing number.
A) 4 is the correct number that replaces the question mark, as it fits the established pattern of multiplying by an increasing factor of 0.5 (i.e., 0.5, 1, 1.5, 2, 2.5).
This problem involves a simple age calculation. We are given the age difference between Raju and his sister, and the sister's current age. We need to find Raju's age by subtracting the age difference from the sister's age.
Since Raju's sister is 6 years older than Raju, this means Raju is 6 years younger than his sister. We can write this as:
\[ \text{Raju's sister's age} = \text{Raju's age} + 6 \text{ years} \]We know Raju's sister's age is 38 years. Substitute this into the equation:
\[ 38 = \text{Raju's age} + 6 \]To find Raju's age, subtract 6 from both sides of the equation:
\[ \text{Raju's age} = 38 - 6 \]\[ \text{Raju's age} = 32 \text{ years} \]Correct Option: B) 32 years
The question asks to identify the specific Article in the Indian Constitution that mandates the State to organize village panchayats and empower them for self-governance. This falls under the Directive Principles of State Policy (DPSP).
Correct Option: D) Article 40 is the correct answer. It explicitly states: "The State shall take steps to organise village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government." This Article reflects Mahatma Gandhi's vision of 'Gram Swaraj' (village self-rule).
Select the term from among the given options that can replace the question mark (?) in the following alpha-numeric series to make it logically complete. O5U, L7S, I10Q, F14O,?
The given series is an alpha-numeric series. We need to identify the pattern in the letters and the numbers separately to find the missing term.
Let's break down each term into its components: the first letter, the number, and the second letter.
1. Pattern in the first letter:
The pattern is a decrease of 3 positions in the English alphabet each time:
Following this pattern, the next first letter will be \(6 - 3 = 3\), which corresponds to the letter C.
2. Pattern in the number:
Let's find the differences between consecutive numbers:
The differences are increasing by 1 each time (\(2, 3, 4\)). So, the next difference should be 5.
Following this pattern, the next number will be \(14 + 5 = 19\). So, the number is 19.
3. Pattern in the second letter:
The pattern is a decrease of 2 positions in the English alphabet each time:
Following this pattern, the next second letter will be \(15 - 2 = 13\), which corresponds to the letter M.
Combining these three parts, the next term in the series is C19M.
Correct Option: C) C19M
To find the new quadratic equation, we first need to determine the roots of the given equation. Once we have the values of \(p\) and \(q\), we can find the new roots \((p-1)\) and \((q+1)\). Finally, we use the formula for a quadratic equation given its roots: \(x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0\).
Find the roots of the given equation \(x^2 + 4x - 21 = 0\):
We can factorize the quadratic equation or use the quadratic formula. Factoring is usually quicker if possible.
We need two numbers that multiply to \(-21\) and add up to \(4\). These numbers are \(7\) and \(-3\).
\[ x^2 + 7x - 3x - 21 = 0 \]\[ x(x+7) - 3(x+7) = 0 \]\[ (x-3)(x+7) = 0 \]\[ x = 3 \quad \text{or} \quad x = -7 \]Assign \(p\) and \(q\) based on the condition \(p < q\):
Given that \(p\) and \(q\) are the roots and \(p < q\), we have:
\[ p = -7 \]\[ q = 3 \]Calculate the new roots:
The new roots are \((p-1)\) and \((q+1)\).
\[ \text{New root 1} = p - 1 = -7 - 1 = -8 \]\[ \text{New root 2} = q + 1 = 3 + 1 = 4 \]Form the new quadratic equation:
Let the new roots be \(\alpha = -8\) and \(\beta = 4\). The general form of a quadratic equation with roots \(\alpha\) and \(\beta\) is \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\).
Calculate the sum of the new roots:
\[ \text{Sum of new roots} = \alpha + \beta = -8 + 4 = -4 \]Calculate the product of the new roots:
\[ \text{Product of new roots} = \alpha \beta = (-8)(4) = -32 \]Substitute these values into the general quadratic equation form:
\[ x^2 - (-4)x + (-32) = 0 \]\[ x^2 + 4x - 32 = 0 \]Correct Option: C) x² + 4x - 32 = 0
In the given letter-cluster pairs, the first letter-cluster is related to the second letter-cluster following a certain logic. Study the given pairs carefully, and from the given options, select the pair that follows the same logic.
YVQ : TQL
WKG : RFB
The problem asks us to identify the letter-cluster pair that follows the same logical pattern as the given examples. We need to find the relationship between the letters in each cluster based on their alphabetical positions.
A) SIY : NDT
S = 19, I = 9, Y = 25
N = 14, D = 4, T = 20
S to N: \(19 - 14 = 5\)
I to D: \(9 - 4 = 5\)
Y to T: \(25 - 20 = 5\)
This pair follows the established logic.
The question describes a rule that relates the direction of magnetic field, motion of a conductor, and induced current, using the thumb, forefinger, and middle finger held perpendicular to each other. This configuration is characteristic of Fleming's rules in electromagnetism.
Correct Option: D) Fleming's right hand rule
To solve this problem, we need to compare the positions of digits in the original number with their positions after arranging the digits in descending order. We will list the original number and then the new number, aligning them to easily identify digits whose positions remain unchanged.
Original Number: \(2 \quad 5 \quad 7 \quad 3 \quad 1 \quad 6 \quad 4 \quad 0\)
Positions: \(\quad \quad \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8\)
The digits in descending order are: \(7, 6, 5, 4, 3, 2, 1, 0\).
New Number: \(7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1 \quad 0\)
Positions: \(\quad \quad \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8\)
Original Number: \(2 \quad 5 \quad 7 \quad 3 \quad 1 \quad 6 \quad 4 \quad 0\)
New Number: \(\quad \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1 \quad 0\)
Let's check each position:
Correct Option: B) One
The question asks to identify the combination of minerals that help crops withstand pests. This requires knowledge of the specific roles of various essential plant nutrients in plant defense mechanisms.
C) Potassium, Calcium and Magnesium. These three minerals are well-documented to enhance plant health, strengthen cell walls, and activate defense mechanisms, making crops more resilient to pest attacks.