The question asks for the location of the Mahatma Gandhi Marine National Park. This requires knowledge of the geographical locations of important national parks and protected areas in India.
Correct Option: B) The Mahatma Gandhi Marine National Park, also known as Wandoor National Park, is located in the Andaman and Nicobar Islands. It was established in 1983 for the protection of marine life, including corals and nesting sea turtles. It covers an area of about 281.5 square kilometers.
To find 63% of the number, we first need to determine the original number. We are given that 44% of the number is 798.6. We can set up a proportion or use algebraic equations to find the full number (100%) and then calculate 63% of that number.
Let the unknown number be \(X\).
According to the problem, 44% of \(X\) is 798.6. We can write this as an equation:
\[ 0.44 \times X = 798.6 \]To find \(X\), divide 798.6 by 0.44:
\[ X = \frac{798.6}{0.44} \]\[ X = 1815 \]Now that we have the number \(X = 1815\), we need to find 63% of this number:
\[ 63\% \text{ of } 1815 = 0.63 \times 1815 \]Perform the multiplication:
\[ 0.63 \times 1815 = 1143.45 \]Thus, 63% of the number is 1143.45.
D) 1143.45 — This is the correct calculation for 63% of the number.
The question asks about a specific appointment made in February 2021 related to a constitutional body in India. To answer this, one needs to recall current affairs and significant appointments from that period.
Correct Option: D) Vijay Sampla was appointed as the new Chairman of the National Commission for Scheduled Castes (NCSC) in February 2021.
The question gives an isosceles triangle ABC in which angle A is twice the base angle B. We need to use the property that the base angles of an isosceles triangle are equal, along with the angle sum property of a triangle, to determine angle C.
Identify the given information:
According to the question:
\[ A=2B \]Apply the property of an isosceles triangle:
In an isosceles triangle, the angles opposite the equal sides are equal.
Since B is a base angle and A is twice B, angle A is the vertex angle, while B and C are the equal base angles.
Therefore:
\[ B=C \]Apply the angle sum property of a triangle:
The sum of the three interior angles of a triangle is 180°.
\[ A+B+C=180^\circ \]Substitute A = 2B and C = B:
\[ 2B+B+B=180^\circ \] \[ 4B=180^\circ \]Calculate angle B:
Dividing both sides by 4:
\[ B=\frac{180^\circ}{4} \] \[ B=45^\circ \]Calculate angle C:
Since the base angles of an isosceles triangle are equal:
\[ C=B \] \[ C=45^\circ \]Therefore, the measure of angle C is 45°.
Correct Option: A) 45° — In an isosceles triangle, the two base angles are equal. Since angle A is twice the base angle B:
\[ A=2B,\quad C=B \]
Using the angle sum property:
\[ 2B+B+B=180^\circ \] \[ 4B=180^\circ \] \[ B=C=45^\circ \]
Hence, Option A is the correct answer.
B) 90°: This is incorrect because angle A is 90°, while the two equal base angles B and C are 45° each.
C) 33°: This is incorrect because the angle sum property gives each base angle as 45°, not 33°.
D) 30°: This is incorrect because if each base angle were 30°, angle A would be 60°, making the total angle sum only 120°, not 180°.
To find the area of the rectangle, we first need to determine its length and breadth. We are given the perimeter and a relationship between the length and breadth. We will use these two pieces of information to set up equations and solve for the dimensions, then calculate the area.
Define variables: Let the breadth of the rectangle be \(b\) meters. Given that the length is twice its breadth, the length \(l\) will be \(2b\) meters.
Use the perimeter formula: The perimeter of a rectangle is given by the formula \(P = 2(l + b)\). We are given that the perimeter \(P = 120\) m.
Substitute the expressions for \(l\) and \(b\) into the perimeter formula:
\[ 120 = 2(2b + b) \]Solve for breadth (\(b\)):
\[ 120 = 2(3b) \] \[ 120 = 6b \] \[ b = \frac{120}{6} \] \[ b = 20 \text{ m} \]Calculate length (\(l\)): Since \(l = 2b\):
\[ l = 2 \times 20 \] \[ l = 40 \text{ m} \]Calculate the area: The area of a rectangle is given by the formula \(A = l \times b\).
\[ A = 40 \text{ m} \times 20 \text{ m} \] \[ A = 800 \text{ m}^2 \]Correct Option: D) 800 m²
The calculated area of the rectangle is 800 m², which matches option D.
To find the least number that leaves a specific remainder when divided by several numbers, we first need to find the Least Common Multiple (LCM) of those numbers. Once we have the LCM, we add the common remainder to it to get the desired number.
Identify the divisors and the remainder:
The divisors are 9, 8, 10, and 12.
The remainder is 3 in each case.
Find the LCM of the divisors (9, 8, 10, 12):
We can use the prime factorization method.
To find the LCM, we take the highest power of all prime factors present in these numbers:
\[ \text{LCM}(9, 8, 10, 12) = 2^3 \times 3^2 \times 5^1 \] \[ \text{LCM} = 8 \times 9 \times 5 \] \[ \text{LCM} = 72 \times 5 \] \[ \text{LCM} = 360 \]Add the remainder to the LCM:
The least number that leaves a remainder of 3 when divided by 9, 8, 10, and 12 will be the LCM plus the remainder.
\[ \text{Required Number} = \text{LCM} + \text{Remainder} \] \[ \text{Required Number} = 360 + 3 \] \[ \text{Required Number} = 363 \]Correct Option: C) 363
When 363 is divided by 9, \(363 = 9 \times 40 + 3\). Remainder is 3.
When 363 is divided by 8, \(363 = 8 \times 45 + 3\). Remainder is 3.
When 363 is divided by 10, \(363 = 10 \times 36 + 3\). Remainder is 3.
When 363 is divided by 12, \(363 = 12 \times 30 + 3\). Remainder is 3.
To determine the sum of consecutive angles in a parallelogram, we need to recall the properties of a parallelogram, specifically regarding its parallel sides and transversal lines. Consecutive angles in a parallelogram are angles that share a common side. We will use the property of interior angles on the same side of a transversal.
D) 180° — As derived from the properties of parallel lines and transversals, consecutive angles in a parallelogram are supplementary, meaning their sum is 180°.
This question asks us to identify which assumptions are implicit in the given statement. An implicit assumption is something that must be true for the statement to make sense or be logically valid. We need to analyze each assumption in relation to the statement.
C) Neither assumption 1 nor 2 is implicit.
The question asks about the primary function of the World Trade Organization (WTO). To answer this, one needs to recall the core mandate and activities of the WTO.
Correct Option: B) global trade. The WTO's fundamental purpose is to establish and enforce rules for international trade, aiming to reduce barriers and ensure fair competition among member nations.
The question asks to identify the committee whose report recommended a three-tier Panchayati Raj System in India. This requires knowledge of the history and key committees related to Panchayati Raj institutions in India.
C) Balwant Rai Mehta Committee — This committee, constituted in 1957, is credited with recommending the three-tier Panchayati Raj system (Gram Panchayat, Panchayat Samiti, and Zila Parishad) which became the foundational structure for local self-governance in rural India.