The question asks to identify which of the given subjects falls under the State List as per the Seventh Schedule of the Indian Constitution. This requires knowledge of the distribution of legislative powers between the Union and State governments.
Correct Option: D) Public Health and Sanitation
Public Health and Sanitation is explicitly listed as Entry 6 in the State List of the Seventh Schedule of the Indian Constitution. This means state governments have the primary responsibility and legislative power over these matters, which are crucial for local governance and welfare.
The question asks to identify which of the given options is NOT a UNESCO World Heritage Site in India. This requires knowledge of the sites recognized by UNESCO in India.
D) Group of Monuments at Mandu, Madhya Pradesh
While Mandu is an ancient city with significant historical and architectural importance, the "Group of Monuments at Mandu, Madhya Pradesh" is not currently inscribed on the UNESCO World Heritage List. It has been on India's Tentative List for UNESCO World Heritage status since 1998, but it has not yet received the final inscription.
The question asks to identify the article of the Indian Constitution that mandates the protection of the natural environment as a fundamental duty of every citizen. This requires knowledge of the Fundamental Duties enshrined in the Constitution.
Correct Option: A) Article 51A. Article 51A lists the Fundamental Duties of citizens. Specifically, Article 51A(g) makes it a fundamental duty to protect and improve the natural environment.
The question asks to identify the state that has NOT officially recognized Jews as a religious minority. This requires knowledge of specific state government notifications regarding minority status.
B) Kerala — The state of Kerala has not officially recognized the Jewish community as a religious minority, unlike Maharashtra, Gujarat, and West Bengal.
To find the largest angle of the parallelogram, we need to use the properties of parallelograms: opposite angles are equal, and consecutive angles are supplementary (sum to 180°). We will set up an equation based on the given relationship between one angle and the smallest angle, solve for the angles, and then identify the largest one.
Let the smallest angle of the parallelogram be \(x\).
In a parallelogram, consecutive angles are supplementary. This means if one angle is \(x\), the adjacent angle must be \(180^\circ - x\). Since \(x\) is the smallest angle, \(180^\circ - x\) will be the largest angle.
The problem states that one angle of the parallelogram is \(18^\circ\) less than twice the smallest angle. This "one angle" could be either \(x\) or \(180^\circ - x\). However, since \(x\) is the smallest angle, it cannot be \(18^\circ\) less than twice itself (unless \(x=18^\circ\), which would make \(180^\circ-x = 162^\circ\), and \(2x-18 = 2(18)-18 = 18\), which means the smallest angle is equal to \(2x-18\), which is not possible as \(x\) is the smallest). Therefore, the angle referred to must be the larger angle, \(180^\circ - x\).
Set up the equation based on the given information:
\[ 180^\circ - x = 2x - 18^\circ \]Solve for \(x\):
Add \(x\) to both sides:
\[ 180^\circ = 3x - 18^\circ \]Add \(18^\circ\) to both sides:
\[ 180^\circ + 18^\circ = 3x \]\[ 198^\circ = 3x \]Divide by 3:
\[ x = \frac{198^\circ}{3} \]\[ x = 66^\circ \]So, the smallest angle is \(66^\circ\).
The largest angle is \(180^\circ - x\):
\[ \text{Largest angle} = 180^\circ - 66^\circ \]\[ \text{Largest angle} = 114^\circ \]Check the condition: Is \(114^\circ\) equal to \(2x - 18^\circ\)?
\[ 2(66^\circ) - 18^\circ = 132^\circ - 18^\circ = 114^\circ \]The condition is satisfied.
Correct Option: A) 114°
First, we will use the given simple interest information to find the principal sum of money. Once the principal is known, we will calculate the compound interest for the same sum, period, and rate.
Calculate the Principal (P) using Simple Interest:
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]Given:
Substitute the values into the formula:
\[ 50 = \frac{P \times 5 \times 2}{100} \] \[ 50 = \frac{10P}{100} \] \[ 50 = \frac{P}{10} \]Solving for P:
\[ P = 50 \times 10 = \text{₹}500 \]Calculate the Compound Interest (CI):
The formula for Amount (A) under compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]Using the principal \(P = \text{₹}500\), \(R = 5\%\), and \(T = 2\) years:
\[ A = 500 \left(1 + \frac{5}{100}\right)^2 \] \[ A = 500 \left(1 + \frac{1}{20}\right)^2 \] \[ A = 500 \left(\frac{21}{20}\right)^2 \] \[ A = 500 \times \frac{21 \times 21}{20 \times 20} \] \[ A = 500 \times \frac{441}{400} \] \[ A = \frac{5 \times 441}{4} \] \[ A = \frac{2205}{4} \] \[ A = 551.25 \]So, the Amount after 2 years is \(\text{₹}551.25\).
Now, calculate the Compound Interest (CI):
\[ \text{CI} = A - P \] \[ \text{CI} = 551.25 - 500 \] \[ \text{CI} = \text{₹}51.25 \]Correct Option: B) ₹51.25
This question asks about factors that do NOT impact a computer's general performance. We need to evaluate each option to determine its role in overall system speed and responsiveness.
Correct Option: A) Size of the Graphics Card. While the graphics processing unit (GPU) itself is important for visual output, its physical size or even the amount of VRAM (beyond what's needed for basic display) does not generally impact the computer's overall performance for typical, non-graphical tasks. For general performance, CPU, RAM, and storage speed are far more critical.
The question asks to identify the incorrect statement about Raja Ram Mohan Roy. We need to evaluate each option based on historical facts related to Raja Ram Mohan Roy's life and work.
Correct Option: D) He founded Arya Samaj.
To find the total simple interest earned over 3 years with different interest rates each year, we calculate the simple interest for each year separately and then sum them up. The principal amount remains the same for simple interest calculations each year.
The formula for simple interest is \(SI = \frac{P \times R \times T}{100}\). Here, \(T=1\) year for each calculation.
\[ SI_1 = \frac{800 \times 6 \times 1}{100} = \frac{4800}{100} = \text{₹}48 \]Total Interest = \(SI_1 + SI_2 + SI_3\)
\[ \text{Total Interest} = 48 + 64 + 80 = 192 \]The total interest earned at the end of 3 years is ₹192.
D) ₹192 — This is the sum of the simple interests calculated for each year based on the respective rates.
To find the percentage increase in the area, we first assume an initial side length for the square. Then, we calculate the original area. Next, we determine the new length and breadth after the given percentage increases and calculate the new area. Finally, we compute the percentage increase in area using the formula: \[\frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \times 100\%\].
Assume the side of the square: Let the side of the original square be \(s\). For simplicity, let's assume \(s = 10\) units.
Calculate the original area of the square: Original Area \(= s \times s = s^2\). If \(s = 10\), then Original Area \(= 10 \times 10 = 100\) square units.
Calculate the new length: The length is increased by 30%. New Length \(= s + 30\% \text{ of } s = s + 0.30s = 1.30s\). If \(s = 10\), New Length \(= 1.30 \times 10 = 13\) units.
Calculate the new breadth: The breadth is increased by 20%. New Breadth \(= s + 20\% \text{ of } s = s + 0.20s = 1.20s\). If \(s = 10\), New Breadth \(= 1.20 \times 10 = 12\) units.
Calculate the area of the resulting rectangle: New Area \(= \text{New Length} \times \text{New Breadth} = (1.30s) \times (1.20s) = 1.56s^2\). If \(s = 10\), New Area \(= 13 \times 12 = 156\) square units.
Calculate the increase in area: Increase in Area \(= \text{New Area} - \text{Original Area} = 1.56s^2 - s^2 = 0.56s^2\). If \(s = 10\), Increase in Area \(= 156 - 100 = 56\) square units.
Calculate the percentage increase in area: Percentage Increase \[= \frac{\text{Increase in Area}}{\text{Original Area}} \times 100\%\]. \[ \text{Percentage Increase} = \frac{0.56s^2}{s^2} \times 100\% = 0.56 \times 100\% = 56\% \] Using the assumed values: \[ \text{Percentage Increase} = \frac{56}{100} \times 100\% = 56\% \]
Correct Option: C) 56%