This question tests the understanding of Archimedes' principle and buoyancy. A spring balance measures the apparent weight of an object. When an object is submerged in a fluid, it experiences an upward buoyant force, which reduces its apparent weight. The magnitude of this buoyant force depends on the volume of the fluid displaced by the object.
A) When the stone is completely submerged in the water in a beaker. This condition results in the maximum volume of water displaced, leading to the maximum buoyant force and thus the least apparent weight recorded by the spring balance.
To find the number of factors of 2250 whose square roots are natural numbers, we first need to find the prime factorization of 2250. Then, we identify the factors that are perfect squares. A number is a perfect square if all the exponents in its prime factorization are even. The square root of such a factor will be a natural number.
Prime Factorization of 2250:
First, we find the prime factorization of 2250:
\[ 2250 = 225 \times 10 \] \[ 225 = 15^2 = (3 \times 5)^2 = 3^2 \times 5^2 \] \[ 10 = 2 \times 5 \]So, combining these:
\[ 2250 = 2 \times 3^2 \times 5^2 \times 5 = 2^1 \times 3^2 \times 5^3 \]Identify Factors that are Perfect Squares:
Let a factor of 2250 be \( N \). For \( \sqrt{N} \) to be a natural number, \( N \) must be a perfect square. A number is a perfect square if all the exponents in its prime factorization are even.
The prime factors of 2250 are 2, 3, and 5. Any factor \( N \) of 2250 will be of the form \( 2^a \times 3^b \times 5^c \), where \( 0 \le a \le 1 \), \( 0 \le b \le 2 \), and \( 0 \le c \le 3 \).
For \( N \) to be a perfect square, \( a, b, c \) must all be even.
Count the Number of Such Factors:
We count the number of combinations of these even exponents:
The total number of factors of 2250 that are perfect squares is the product of the number of choices for each exponent:
\[ \text{Number of perfect square factors} = 1 \times 2 \times 2 = 4 \]These factors are:
All these factors have square roots that are natural numbers.
Correct Option: D) 4
There are 4 factors of 2250 whose square roots are natural numbers.
The question asks to identify the first Indian female cricketer to achieve the milestone of scoring 2000 runs in T20 International (T20I) Cricket. This requires knowledge of historical records in women's cricket.
Correct Option: B) Mithali Raj was the first Indian female cricketer to score 2000 runs in T20 International Cricket. She achieved this milestone on June 7, 2018, during the Women's Asia Cup T20 match against Sri Lanka.
To find a specific term in an Arithmetic Progression (AP), we need to know the first term and the common difference. The formula for the \(n\)-th term of an AP is given by \(a_n = a + (n-1)d\), where \(a_n\) is the \(n\)-th term, \(a\) is the first term, and \(d\) is the common difference. We need to find the seventh term, so \(n=7\).
Correct Option: B) Both statements I and II are sufficient
The question asks for the geometric term that describes three or more lines passing through the same point. We need to evaluate each option based on its definition in geometry.
D) Concurrent — Three or more lines are said to be concurrent if and only if they all pass through the same point. This point is called the point of concurrency.
This problem can be solved by visualizing the situation as a right-angled triangle. The ladder acts as the hypotenuse, the wall acts as one leg (height), and the distance of the ladder's base from the wall acts as the other leg (base). We can then apply the Pythagorean theorem to find the unknown distance.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
\[ a^2 + b^2 = c^2 \]The distance of the lower face of the ladder from the wall is 14 decimeters.
B) 14 decimeter — As calculated using the Pythagorean theorem, the distance is 14 decimeters.
This question tests the fundamental concepts of mass and weight in physics. Understanding the definitions and how they are affected by gravitational force is key to determining the correct statement.
B) The Mass of a body remains same while the Weight changes from place to place. This statement accurately reflects the definitions and properties of mass and weight.
The question asks to identify which of the given options adheres to a fundamental conservation law, specifically that it can neither be created nor destroyed. We need to evaluate each option based on its scientific definition and associated conservation principles.
Correct Option: A) Energy. The Law of Conservation of Energy is a fundamental principle in physics stating that the total energy of an isolated system remains constant; it is conserved over time. Energy can be transformed from one form to another (e.g., kinetic to potential, chemical to thermal), but it cannot be created from nothing or destroyed into nothing.
When a resistance wire is doubled on itself, its length is halved, and its cross-sectional area is doubled. We will use the formula for resistance, which relates resistance to resistivity, length, and cross-sectional area, to find the new resistance.
B) 2.00 Ω — As calculated, the new resistance of the wire is 2.00 Ω.
The question asks for the location of Sultanpur National Park. This is a factual question related to Indian geography and national parks, which requires direct knowledge.
Correct Option: C) Haryana