The question asks to identify the author of the influential book 'Systema Naturae'. This requires knowledge of famous botanists and their contributions to taxonomy.
Correct Option: D) Carl Linnaeus
Carl Linnaeus (1707–1778) was a Swedish botanist, zoologist, and physician who formalized binomial nomenclature, the modern system of naming organisms. He is often called the "father of modern taxonomy." His most important work, 'Systema Naturae', first published in 1735, introduced his hierarchical classification system and binomial names for species.
The problem provides a linear equation with two variables, \(x\) and \(y\), and the value of one variable, \(x\). To find the value of the other variable, \(y\), we need to substitute the given value of \(x\) into the equation and then solve the resulting linear equation for \(y\).
The given equation is:
\[ 4x - 3y = 9 \]We are given that \(x = 6\). Substitute this value into the equation:
\[ 4(6) - 3y = 9 \]Multiply the numbers:
\[ 24 - 3y = 9 \]Subtract 24 from both sides of the equation:
\[ -3y = 9 - 24 \]\[ -3y = -15 \]Divide both sides by -3:
\[ y = \frac{-15}{-3} \]\[ y = 5 \]Thus, the value of \(y\) is 5.
Correct Option: C) 5
This problem involves calculating the original price of an item given its present value, the depreciation rate, and the number of years it has depreciated. We will use the formula for depreciation, which is similar to the compound interest formula but with a negative rate.
The formula for depreciation is given by:
\[ P_t = P_0 \left(1 - \frac{R}{100}\right)^n \]Where:
We need to find the original purchase price (\(P_0\)).
To find \(P_0\), multiply both sides by \(\frac{125}{64}\):
\[ P_0 = 12288 \times \frac{125}{64} \]First, divide 12288 by 64:
\[ \frac{12288}{64} = 192 \]So, the purchase price 3 years ago was ₹24,000.
A) ₹24,000 is the correct answer, as calculated above.
The question asks to identify which of the given countries is NOT a permanent member of the United Nations Security Council (UNSC). This requires knowledge of the permanent members of the UNSC.
B) Japan is not a permanent member of the United Nations Security Council. Japan is a significant contributor to the UN budget and has often sought a permanent seat, but it currently serves as an elected non-permanent member periodically.
The problem asks for the sum of the cubes of the first four natural numbers. This can be solved by first identifying the first four natural numbers, then calculating the cube of each, and finally summing these cubes. Alternatively, one can use the formula for the sum of the cubes of the first \(n\) natural numbers.
Identify the first four natural numbers:
Natural numbers are positive integers starting from 1. So, the first four natural numbers are 1, 2, 3, and 4.
Calculate the cube of each number:
Sum the cubes:
Add the calculated cubes together:
\[ 1 + 8 + 27 + 64 = 100 \]Alternative Method (using formula):
The sum of the cubes of the first \(n\) natural numbers is given by the formula:
\[ S_n = \left[ \frac{n(n+1)}{2} \right]^2 \]For the first four natural numbers, \(n=4\). Substitute \(n=4\) into the formula:
\[ S_4 = \left[ \frac{4(4+1)}{2} \right]^2 \]\[ S_4 = \left[ \frac{4 \times 5}{2} \right]^2 \]\[ S_4 = \left[ \frac{20}{2} \right]^2 \]\[ S_4 = [10]^2 \]\[ S_4 = 100 \]Both methods yield the same result.
D) 100 is the correct sum of the cubes of the first four natural numbers.
The question asks for the district in Uttarakhand where the Kedarnath temple is located. This requires knowledge of the geographical locations of important religious sites in India, specifically in Uttarakhand.
Correct Option: B) Rudraprayag
The question asks about the continent over which the largest ozone holes were observed in 2020. This requires knowledge of the typical location and conditions for ozone depletion.
B) Antarctica — The largest and most persistent ozone holes are consistently observed over Antarctica due to unique meteorological conditions that facilitate severe ozone depletion. The 2020 ozone hole was notably large and deep over this continent.
The question asks about the function of the keyboard shortcut 'Ctrl + E' in Microsoft Word 2016. This is a common shortcut used for text formatting.
D) Selected text is centre aligned. In Microsoft Word, pressing 'Ctrl + E' is the keyboard shortcut used to center-align the selected text or the current paragraph. This means the text will be positioned equally distant from the left and right margins.
If (1 − cosP)(1 + cosP) = \( \frac{3}{4} \) and P is an acute angle, then find the value of secP.
\(\frac{\sqrt{7}}{2}\)
\( \frac{1}{2} \)
2
\(\frac{\sqrt{2}}{7}\)
The problem provides an equation involving \(\cos P\) and asks for the value of \(\sec P\). We can use the algebraic identity \((a-b)(a+b) = a^2 - b^2\) and the trigonometric identity \(\sin^2 P + \cos^2 P = 1\) to find the value of \(\cos P\). Once \(\cos P\) is known, \(\sec P\) can be found using the reciprocal relationship \(\sec P = \frac{1}{\cos P}\).
We are given the equation \((1 - \cos P)(1 + \cos P) = \frac{3}{4}\).
Using the algebraic identity \((a-b)(a+b) = a^2 - b^2\), where \(a=1\) and \(b=\cos P\), we get:
\[ 1^2 - (\cos P)^2 = \frac{3}{4} \] \[ 1 - \cos^2 P = \frac{3}{4} \]Recall the fundamental trigonometric identity: \(\sin^2 P + \cos^2 P = 1\).
From this, we can write \(\sin^2 P = 1 - \cos^2 P\).
Substitute this into the simplified equation:
\[ \sin^2 P = \frac{3}{4} \]Alternatively, we can directly solve for \(\cos^2 P\) from \(1 - \cos^2 P = \frac{3}{4}\):
\[ \cos^2 P = 1 - \frac{3}{4} \] \[ \cos^2 P = \frac{4 - 3}{4} \] \[ \cos^2 P = \frac{1}{4} \]Taking the square root of both sides:
\[ \cos P = \pm\sqrt{\frac{1}{4}} \] \[ \cos P = \pm\frac{1}{2} \]Since P is an acute angle (meaning \(0^\circ < P < 90^\circ\)), \(\cos P\) must be positive.
Therefore, \(\cos P = \frac{1}{2}\).
The secant function is the reciprocal of the cosine function:
\[ \sec P = \frac{1}{\cos P} \]Substitute the value of \(\cos P\):
\[ \sec P = \frac{1}{\frac{1}{2}} \] \[ \sec P = 2 \]Correct Option: C) 2
The question asks for the specific process used to create a thick oxide layer on aluminium. This is a direct recall question related to material science and surface treatment techniques.
Correct Option: A) Anodising is the electrochemical process of making a thick, protective oxide layer on aluminium. This layer enhances corrosion resistance, wear resistance, and can also be dyed for decorative purposes.