The question asks about the scientist who first proposed that every eighth element exhibits similar properties to the first. This concept is famously known as the 'Law of Octaves' in the history of the periodic classification of elements. We need to identify the scientist associated with this specific law.
A) Newlands ā John Newlands proposed the Law of Octaves, stating that when elements are arranged in increasing order of their atomic masses, the properties of every eighth element are similar to those of the first.
The question asks to identify the largest group of animals among the given options. This requires knowledge of animal classification and the relative diversity of different phyla.
Arthropoda is by far the largest phylum in the animal kingdom, accounting for over 80% of all known animal species. This phylum includes insects, arachnids, crustaceans, and myriapods, which inhabit nearly all environments on Earth.
Correct Option: B) Arthropoda ā The phylum Arthropoda is the largest phylum in the animal kingdom, both in terms of number of species and individuals. It includes insects, arachnids, crustaceans, and myriapods. More than 80% of all known animal species belong to this phylum.
To determine the value of \(k\) for which a system of two linear equations has no solution, we need to recall the condition for inconsistency. For a system of linear equations in two variables, \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\), there is no solution if the ratio of the coefficients of \(x\) and \(y\) are equal, but this ratio is not equal to the ratio of the constant terms. That is, \[\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\].
Correct Option: A) -12.5
If sinā“A − cosā“A = 1 then \( \frac{A}{2} \) in degrees is (0 < A ≤ 90°)
The problem asks us to find the value of \( \frac{A}{2} \) in degrees, given the trigonometric equation \( \sin^4 A - \cos^4 A = 1 \) and the condition \( 0 < A \le 90^\circ \). We will use algebraic factorization and fundamental trigonometric identities to solve for \( A \) and then calculate \( \frac{A}{2} \).
Factorize the given equation:
The given equation is \( \sin^4 A - \cos^4 A = 1 \). This can be treated as a difference of squares, \( (x^2)^2 - (y^2)^2 = (x^2 - y^2)(x^2 + y^2) \), where \( x = \sin A \) and \( y = \cos A \).
\[ (\sin^2 A - \cos^2 A)(\sin^2 A + \cos^2 A) = 1 \]Apply the Pythagorean identity:
We know that the fundamental trigonometric identity is \( \sin^2 A + \cos^2 A = 1 \).
Substitute this into the equation from Step 1:
\[ (\sin^2 A - \cos^2 A)(1) = 1 \]\[ \sin^2 A - \cos^2 A = 1 \]Express in terms of a single trigonometric function:
We can use the identity \( \sin^2 A = 1 - \cos^2 A \) to express the equation solely in terms of \( \cos A \):
\[ (1 - \cos^2 A) - \cos^2 A = 1 \]\[ 1 - 2\cos^2 A = 1 \]Solve for \( \cos A \):
Subtract 1 from both sides:
\[ -2\cos^2 A = 0 \]\[ \cos^2 A = 0 \]\[ \cos A = 0 \]Find the value of \( A \):
For \( 0 < A \le 90^\circ \), the angle \( A \) for which \( \cos A = 0 \) is \( 90^\circ \).
\[ A = 90^\circ \]Calculate \( \frac{A}{2} \):
Now, substitute the value of \( A \) to find \( \frac{A}{2} \):
\[ \frac{A}{2} = \frac{90^\circ}{2} = 45^\circ \]D) \( 45 \) is the correct answer. The value of \( \frac{A}{2} \) is \( 45^\circ \).
The question describes a two-step chemical process: first, the burning of a magnesium ribbon, and second, the dissolution of the product in water. We need to identify the final product formed when the ash from burning magnesium dissolves in water.
A) Magnesium Hydroxide is the correct answer because magnesium oxide (the product of burning magnesium) reacts with water to form magnesium hydroxide.
The question asks us to find a related word based on an analogy. We need to identify the relationship between the first pair of words (Nation : History) and then apply the same relationship to the second pair (Man : ___?).
Therefore, just as history records the life and events of a nation, a biography records the life and events of a man.
Correct Option: D) Biography
To determine the work done by the force of gravity, we need to use the formula for work done, which is the product of force, displacement, and the cosine of the angle between them. When an object is raised, the displacement is upwards, but the force of gravity acts downwards. This opposition in direction results in negative work done by gravity.
Correct Option: B) ā200 J
The question asks to identify the group of crop plants that are propagated vegetatively. Vegetative propagation is a form of asexual reproduction in plants where new plants are grown from vegetative parts like stems, roots, or leaves, rather than from seeds.
Correct Option: A) sugarcane, potato and banana
The question asks to identify the global company with which India became the first country to partner for Disaster Response Management. This is a factual question related to international collaborations in technology and disaster management.
B) Facebook. India was indeed the first country to partner with Facebook (now Meta) on its Disaster Response Management program, specifically utilizing its "Disaster Maps" to aid in disaster relief efforts. This partnership was announced in 2018.
To find the pass marks, we need to calculate the specified percentage of the total marks. The problem states that 34% is required to pass a test, and the total marks for the test are 40. We need to find what 34% of 40 is.
Identify the given information:
Convert the percentage to a decimal or fraction:
To calculate a percentage of a number, we first convert the percentage into its decimal equivalent by dividing by 100, or use it as a fraction \[\frac{\text{percentage}}{100}\].
\[ 34\% = \frac{34}{100} \]Calculate the pass marks:
Multiply the total marks by the passing percentage (in fraction or decimal form).
\[ \text{Pass Marks} = \frac{34}{100} \times 40 \] \[ \text{Pass Marks} = 0.34 \times 40 \] \[ \text{Pass Marks} = 13.6 \]Compare with the given options:
The calculated pass marks are 13.6, which matches option D.
Correct Option: D) 13.6
The pass marks are 34% of 40, which is calculated as \(0.34 \times 40 = 13.6\).