The question asks for the minimum concentration of the minority population in a catchment area (5 km radius) required for States/UTs to propose infrastructure projects under the Revised PMJVK Scheme 2022–23. This is a factual question related to government schemes and their criteria.
Correct Option: D) The Revised PMJVK Scheme 2022–23 specifies that States/UTs can propose infrastructure projects in identified areas where the concentration of the minority population is more than 25% in the catchment area (5 km radius). This threshold is crucial for the scheme's implementation.
The question asks to identify the committee that recommended constitutional recognition for local government bodies in 1989. This requires knowledge of the various committees formed to study and recommend reforms for local self-governance in India.
B) PK Thungon Committee — The P.K. Thungon Committee, constituted in 1989, was indeed instrumental in recommending constitutional recognition for local government bodies (Panchayati Raj Institutions). This recommendation paved the way for the 64th Constitutional Amendment Bill in 1989, which, although not passed, laid the groundwork for the later 73rd and 74th Constitutional Amendment Acts of 1992 that finally granted constitutional status to Panchayats and Municipalities, respectively.
To solve this problem, we need to identify pairs of numbers in the given series where the first number is even and the second number is a multiple of 3. We will scan the series from left to right, checking each number and its immediate successor against these two conditions.
Therefore, there is only 1 even number immediately followed by a multiple of 3.
D) 1 — As determined by the step-by-step analysis, only one instance (58 followed by 63) meets both criteria.
The quadratic equation which has real and equal roots \( \frac{3}{5} \) is:
x² – 30x + 3 = 0
x² – 6x + 9 = 0
25x² – 30x + 9 = 0
5x² – 6x + 9 = 0
A quadratic equation with real and equal roots implies that the discriminant is zero. Also, if a quadratic equation has equal roots, say \(\alpha\), then the equation can be written in the form \(a(x - \alpha)^2 = 0\). We are given that the equal root is \(\frac{3}{5}\).
Understand the condition for real and equal roots: For a quadratic equation \(ax^2 + bx + c = 0\), the roots are real and equal if and only if the discriminant \(D = b^2 - 4ac = 0\).
Use the given root to form the equation: If the roots are real and equal, and the root is \(x = \frac{3}{5}\), then the quadratic equation must be of the form \(k(x - \frac{3}{5})^2 = 0\) for some non-zero constant \(k\).
Expand the equation: \[ k \left(x - \frac{3}{5}\right)^2 = 0 \] \[ k \left(x^2 - 2 \cdot x \cdot \frac{3}{5} + \left(\frac{3}{5}\right)^2\right) = 0 \] \[ k \left(x^2 - \frac{6}{5}x + \frac{9}{25}\right) = 0 \]
Compare with options: We need to find an option that matches this form. Let's try to eliminate the fraction by choosing a suitable value for \(k\). If we choose \(k = 25\), we get: \[ 25 \left(x^2 - \frac{6}{5}x + \frac{9}{25}\right) = 0 \] \[ 25x^2 - 25 \cdot \frac{6}{5}x + 25 \cdot \frac{9}{25} = 0 \] \[ 25x^2 - 5 \cdot 6x + 9 = 0 \] \[ 25x^2 - 30x + 9 = 0 \] This matches option C.
Correct Option: C) \(25x^2 - 30x + 9 = 0\)
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will calculate the differences between consecutive terms to see if there's a consistent arithmetic progression, a geometric progression, or a pattern in the differences themselves.
C) 158. Based on the identified pattern where the differences between consecutive terms double each time (2, 4, 8, 16, 32), the next number in the series is \(126 + 32 = 158\).
To find the height of the cylinder, we will use the formula for the curved surface area of a cylinder. We are given the curved surface area and the base radius. We can rearrange the formula to solve for the height.
Recall the formula for the curved surface area (CSA) of a cylinder:
\[ \text{CSA} = 2 \pi r h \]where \(r\) is the base radius and \(h\) is the height of the cylinder.
Identify the given values:
Substitute the given values into the formula:
\[ 1848 = 2 \times \frac{22}{7} \times 19.6 \times h \]Simplify the equation to solve for \(h\):
First, calculate the product of the known terms:
\[ 2 \times \frac{22}{7} \times 19.6 = 44 \times \frac{19.6}{7} \] \[ = 44 \times 2.8 \] \[ = 123.2 \]Now, the equation becomes:
\[ 1848 = 123.2 \times h \]Solve for \(h\):
\[ h = \frac{1848}{123.2} \]To simplify the division, multiply the numerator and denominator by 10 to remove the decimal:
\[ h = \frac{18480}{1232} \]Perform the division:
\[ h = 15 \text{ cm} \]Correct Option: C) 15 cm
This is a statement and conclusion type of question. We need to analyze the given statement and determine which of the provided conclusions logically follow from it. The statement describes a decision by a state government to reallocate city buses for the monsoon season. We must infer the underlying reasons or implications of this decision.
Correct Option: C) Both I and II can be concluded from the given information.
The given series is a combination of two alternating sub-series or follows a specific pattern of repetition and subtraction. We need to identify this pattern to find the missing number.
Correct Option: D) 56. The series follows a pattern where each distinct number is repeated, and the next distinct number is obtained by subtracting 11 from the previous distinct number. Following this, after 56, the next number should be 56, making the sequence 67, 67, 56, 56, 45, 45, ...
The question asks about the location within a cell where the initial breakdown of glucose into pyruvate occurs. This process is known as glycolysis, a fundamental metabolic pathway.
A) Cytoplasm: Glycolysis, the process of breaking down glucose (6-carbon) into pyruvate (3-carbon), universally occurs in the cytoplasm of the cell. This is the initial stage of cellular respiration.
Refer to the following letter, number, symbol series and answer the question.
(Left) H ^ 5 T & M 4 @ 5 # 1 4 J 3 P H 9 L ! 5 2 (Right)
If all numbers are dropped from the series, which of the following will be fifth from the right?
The problem asks us to identify the fifth element from the right end of a given series after all numbers have been removed. We need to first filter out the numbers from the original series and then count from the right to find the desired element.
Therefore, the fifth element from the right after dropping all numbers is J.
A) J is the fifth element from the right in the modified series.