The question asks to identify the year of the Delhi Durbar where King George V announced the transfer of India's capital from Calcutta to Delhi. This requires knowledge of significant historical events during the British Raj in India.
C) 1911 — The Delhi Durbar of 1911 was the occasion where King George V announced the transfer of the capital from Calcutta to Delhi.
India with its area of 3.28 million km² accounts for 2.4 per cent of the world’s land surface area and stands as the ______ largest country in the world.
The question asks to identify India's rank in terms of land area among the world's countries, given its area and percentage of the world's land surface. This is a factual question related to world geography.
The seven largest countries in the world by area are:
Based on this list, India is the seventh-largest country in the world by land area.
B) seventh – India is indeed the seventh-largest country in the world by land area, with an area of approximately 3.28 million km², accounting for about 2.4% of the world's total land surface area.
The question asks to identify the type of coastal plains that the western coastal plains of India exemplify. This requires knowledge of the geomorphological characteristics of India's coastal regions.
C) submerged — The Western Coastal Plains are considered an example of submerged coastal plains due to their geological history and the presence of natural harbors and estuaries, indicating a sinking of the land relative to sea level.
This problem involves analyzing logical statements and conclusions, a common type of question in competitive exams. We will use Venn diagrams or logical deductions to determine which conclusions logically follow from the given statements.
C) Neither conclusion (I) nor (II) follows.
As determined in the step-by-step analysis, neither Conclusion I ("Some Grasses are Clouds") nor Conclusion II ("All Picnics are Rains") can be logically derived from the given statements. There are possible scenarios (Venn diagram arrangements) where the statements are true but both conclusions are false.
This is a logical reasoning problem involving the arrangement of boxes in a stack. We need to deduce the exact position of each box based on the given clues and then identify the box at the sixth position from the bottom.
Correct Option: B) M
In a certain code language, ‘ARMOR’ is written as ‘CVOST’ and ‘GLAND’ is written as ‘IPCRF’. How will ‘FARMS’ be written in that language?
The problem is a coding-decoding question. We need to identify the pattern or rule used to transform the given words and then apply that rule to the target word.
The pattern observed is an alternating addition of +2 and +3 to the alphabetical position of each letter.
The pattern holds true for the second word as well.
So, 'FARMS' will be coded as 'HDTPU'.
A) HDTPU is the correct option, as derived from applying the +2, +3, +2, +3, +2 pattern to the letters of 'FARMS'.
My derivation for FARMS is: F(+2)=H, A(+3)=D, R(+2)=T, M(+3)=P, S(+2)=U. So the result is HDTPU.
Let's re-check the provided options against HDTPU:
It seems there was a mismatch between my initial analysis of the provided correct option and the actual options. Option D is HDTPU, which is what I derived. Let me correct the explanation to reflect that D is the correct option, assuming the derivation is correct.
Revisiting the provided correct answer 'A' and the derived answer 'HDTPU'.
If 'A' (HETQU) is the correct answer, then the pattern applied to 'FARMS' would be:
This would mean the pattern is +2, +4, +2, +4, +2. Let's check if this pattern applies to the given examples:
'ARMOR' to 'CVOST' (using +2, +4, +2, +4, +2)
This pattern (+2, +4, +2, +4, +2) works for 'ARMOR'!
'GLAND' to 'IPCRF' (using +2, +4, +2, +4, +2)
This pattern (+2, +4, +2, +4, +2) also works for 'GLAND'!
Therefore, the correct pattern is indeed +2, +4, +2, +4, +2, and my initial pattern identification (+2, +3, +2, +3, +2) was incorrect. I apologize for the error in the initial pattern detection.
Let's re-derive 'FARMS' using the correct pattern (+2, +4, +2, +4, +2):
So, 'FARMS' will be coded as 'HETQU'.
A) HETQU is the correct option, as derived from applying the +2, +4, +2, +4, +2 pattern to the letters of 'FARMS'.
This problem involves the mirror formula and magnification for a concave mirror. We are given the object size, image size, and object distance. We need to find the principal focus (focal length) of the mirror. We will use the magnification formula to find the image distance and then substitute both object and image distances into the mirror formula to calculate the focal length.
Identify the given values and sign conventions:
Calculate the magnification (m):
The magnification formula is given by:
\[ m = \frac{h_i}{h_o} = -\frac{v}{u} \]Substitute the values of \(h_i\) and \(h_o\):
\[ m = \frac{-30.0 \text{ m}}{10.0 \text{ m}} = -3 \]Calculate the image distance (v):
Using the magnification formula \(m = -\frac{v}{u}\):
\[ -3 = -\frac{v}{-20.0 \text{ m}} \] \[ -3 = \frac{v}{20.0 \text{ m}} \] \[ v = -3 \times 20.0 \text{ m} \] \[ v = -60.0 \text{ m} \]The negative sign for \(v\) confirms that the real image is formed in front of the mirror.
Apply the mirror formula to find the focal length (f):
The mirror formula is:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]Substitute the values of \(u\) and \(v\):
\[ \frac{1}{f} = \frac{1}{-60.0 \text{ m}} + \frac{1}{-20.0 \text{ m}} \] \[ \frac{1}{f} = -\frac{1}{60.0 \text{ m}} - \frac{1}{20.0 \text{ m}} \]Find a common denominator (60):
\[ \frac{1}{f} = -\frac{1}{60.0 \text{ m}} - \frac{3}{60.0 \text{ m}} \] \[ \frac{1}{f} = -\frac{1+3}{60.0 \text{ m}} \] \[ \frac{1}{f} = -\frac{4}{60.0 \text{ m}} \] \[ \frac{1}{f} = -\frac{1}{15.0 \text{ m}} \]Therefore, the focal length \(f\) is:
\[ f = -15.0 \text{ m} \]The negative sign indicates that it is a concave mirror, which is consistent with the problem statement.
Correct Option: B) The principal focus of the mirror is at \(-15.0 \text{ m}\). This matches our calculated focal length, where the negative sign correctly indicates a concave mirror.
The question asks to identify the historical place associated with the birth of Jesus Christ. This requires knowledge of biblical history and geography.
Correct Option: D) Bethlehem is universally recognized as the birthplace of Jesus Christ according to Christian tradition and biblical texts (Matthew 2:1, Luke 2:4-7). The Church of the Nativity in Bethlehem is built over the grotto believed to be his birthplace.
3 right circular cylinders having the same base radius r cm and the same height h cm are placed one upon the other, to form another right cylinder whose radius of base is also r cm. The total surface area in cm2 of this new right cylindrical solid so formed is:
The problem asks for the total surface area of a new right cylindrical solid formed by stacking three identical right circular cylinders. We need to calculate the dimensions of the new cylinder and then apply the formula for the total surface area of a cylinder.
Identify the dimensions of the individual cylinders:
Each small cylinder has a base radius of \(r\) cm and a height of \(h\) cm.
Determine the dimensions of the new cylindrical solid:
When three identical cylinders are placed one upon the other, the radius of the base of the new solid remains the same as the individual cylinders, i.e., \(R = r\) cm.
The height of the new solid will be the sum of the heights of the three individual cylinders, i.e., \(H = h + h + h = 3h\) cm.
Recall the formula for the total surface area of a cylinder:
The total surface area (TSA) of a cylinder with radius \(R\) and height \(H\) is given by the formula:
Substitute the dimensions of the new solid into the formula:
Substitute \(R = r\) and \(H = 3h\) into the formula:
State the final total surface area:
The total surface area of the new right cylindrical solid is \(6\pi rh + 2\pi r^2\) cm\(^2\).
B) \(6\pi rh+2\pi r^2\)
This matches our calculated total surface area for the new cylindrical solid.
When four quantities \(a, b, c, d\) are in proportion, it means that the ratio of the first two is equal to the ratio of the last two. Mathematically, this is expressed as \(a : b :: c : d\) or \[\frac{a}{b} = \frac{c}{d}\]. We will substitute the given value of \(x\) into the expressions to find the numerical values of the first three terms and then use the proportion property to solve for \(y\).
First, identify the four terms given in proportion:
Substitute the given value \(x = 5\) into the first three terms:
Since the terms are in proportion, we can write the relationship as:
\[ \frac{\text{Term 1}}{\text{Term 2}} = \frac{\text{Term 3}}{\text{Term 4}} \]Substitute the calculated values into the proportion:
\[ \frac{40}{39} = \frac{30}{y} \]Now, solve for \(y\) by cross-multiplication:
\[ 40 \times y = 39 \times 30 \] \[ 40y = 1170 \]Divide by 40 to find the value of \(y\):
\[ y = \frac{1170}{40} \] \[ y = \frac{117}{4} \]Perform the division:
\[ y = 29.25 \]D) The calculated value of \(y\) is \(29.25\).