This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the statements to determine B's relation to K. We will use a step-by-step deduction process.
Correct Option: C) Father-in-law. Based on the analysis, B is the father of K's husband, making B K's father-in-law.
The question asks for the primary seat of government during Emperor Akbar's reign. This requires knowledge of Mughal history, specifically the capital cities used by Akbar.
Correct Option: D) Agra was the primary seat of government for Emperor Akbar for a significant part of his reign. He built the magnificent Agra Fort there, which served as his imperial residence and administrative center.
A circular ground of radius 7 m is surrounded by a path of width 3.5 m. Find the area of the path. (π = \( \frac{22}{7} \))
To find the area of the path surrounding a circular ground, we need to calculate the area of the larger circle (including the path) and subtract the area of the smaller circle (the ground itself). The area of a circle is given by the formula \( \pi r^2 \), where \( r \) is the radius.
Identify the radius of the circular ground (inner circle):
Given, radius of the circular ground, \( r_1 = 7 \text{ m} \).
Calculate the area of the circular ground:
Area of inner circle \( A_1 = \pi r_1^2 \)
\[ A_1 = \frac{22}{7} \times (7)^2 \]
\[ A_1 = \frac{22}{7} \times 49 \]
\[ A_1 = 22 \times 7 \]
\[ A_1 = 154 \text{ sq.m} \]
Identify the radius of the circular ground including the path (outer circle):
The path width is \( 3.5 \text{ m} \). So, the radius of the outer circle \( r_2 \) will be the radius of the ground plus the width of the path.
\[ r_2 = r_1 + \text{path width} \]
\[ r_2 = 7 + 3.5 \]
\[ r_2 = 10.5 \text{ m} \]
Calculate the area of the circular ground including the path:
Area of outer circle \( A_2 = \pi r_2^2 \)
\[ A_2 = \frac{22}{7} \times (10.5)^2 \]
\[ A_2 = \frac{22}{7} \times 110.25 \]
\[ A_2 = 22 \times 15.75 \]
\[ A_2 = 346.5 \text{ sq.m} \]
Calculate the area of the path:
The area of the path is the difference between the area of the outer circle and the area of the inner circle.
\[ \text{Area of path} = A_2 - A_1 \]
\[ \text{Area of path} = 346.5 - 154 \]
\[ \text{Area of path} = 192.5 \text{ sq.m} \]
Correct Option: C) 192.5 sq.m
P, Q and R can do a work in 10, 15 and 30 days respectively. P works daily. Q and R together join P on alternate days starting the first day. In how many days will the work be done?
6 \( \frac{1}{3} \)
6 \( \frac{3}{4} \)
6 \( \frac{1}{2} \)
6
To solve this problem, we first need to determine the individual work rates of P, Q, and R. Then, we will calculate the amount of work done in a cycle of two days, as P works daily and Q and R join P on alternate days. Finally, we will find out how many such cycles are needed to complete the total work.
Correct Option: C) 6 \( \frac{1}{2} \)
The problem presents a series of letters. To find the missing letter, we need to identify the pattern or rule governing the sequence. This typically involves looking at the alphabetical positions of the letters or the differences between consecutive letters.
Therefore, the missing letter is H.
C) H is the correct option because it follows the established pattern of decreasing alphabetical positions by 2, 3, 4, 5, and then 6.
To find the fourth proportional to three given numbers, we set up a proportion where the ratio of the first two numbers is equal to the ratio of the third number to the unknown fourth proportional. We then solve for the unknown value.
Let the given numbers be \(a = 14\), \(b = 6\), and \(c = 28\).
Let the fourth proportional be \(x\).
According to the definition of proportion, if \(a, b, c, x\) are in proportion, then the ratio of the first two terms is equal to the ratio of the last two terms. That is:
\[ \frac{a}{b} = \frac{c}{x} \]Substitute the given values into the proportion:
\[ \frac{14}{6} = \frac{28}{x} \]To solve for \(x\), cross-multiply:
\[ 14 \times x = 6 \times 28 \]Calculate the product on the right side:
\[ 14x = 168 \]Divide both sides by 14 to find \(x\):
\[ x = \frac{168}{14} \]Perform the division:
\[ x = 12 \]Thus, the fourth proportional to 14, 6, and 28 is 12.
Correct Option: A) 12
This is an analogy question based on letter positions in the English alphabet. We need to find the relationship between the first pair of letters (CD : GA) and then apply the same relationship to the second pair (PQ : ?).
Correct Option: D) TN
The question asks to identify which category of species is NOT part of the IUCN (International Union for Conservation of Nature) classification of threatened species. We need to recall the different categories used by IUCN for assessing the conservation status of species.
Correct Option: A) Harmful
The problem involves two parts: first, calculating the principal amount using simple interest, and second, calculating the compound interest on that principal with a new rate and time period. We will use the formulas for simple interest and compound interest to solve this problem.
Calculate the Principal (P) using Simple Interest:
Given:
The formula for Simple Interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R}_1 \times \text{T}_1}{100} \]Substitute the given values:
\[ 16000 = \frac{\text{P} \times 8 \times 8}{100} \] \[ 16000 = \frac{64 \text{P}}{100} \]Now, solve for P:
\[ \text{P} = \frac{16000 \times 100}{64} \] \[ \text{P} = \frac{1600000}{64} \] \[ \text{P} = 25000 \]So, the principal amount is Rs. 25,000.
Calculate the new rate of interest (\(\text{R}_2\)):
The new rate is one-fourth of the original rate:
\[ \text{R}_2 = \frac{1}{4} \times \text{R}_1 \] \[ \text{R}_2 = \frac{1}{4} \times 8\% = 2\% \text{ p.a.} \]Calculate the Compound Interest (CI):
Given:
The formula for Amount (A) with Compound Interest is:
\[ \text{A} = \text{P} \left(1 + \frac{\text{R}_2}{100}\right)^{\text{T}_2} \]Substitute the values:
\[ \text{A} = 25000 \left(1 + \frac{2}{100}\right)^2 \] \[ \text{A} = 25000 \left(1 + 0.02\right)^2 \] \[ \text{A} = 25000 \left(1.02\right)^2 \] \[ \text{A} = 25000 \times 1.0404 \] \[ \text{A} = 26010 \]Now, calculate the Compound Interest (\(\text{CI}\)):
\[ \text{CI} = \text{A} - \text{P} \] \[ \text{CI} = 26010 - 25000 \] \[ \text{CI} = 1010 \]So, the compound interest is Rs. 1,010.
C) Rs. 1,010
We need to deduce the height relationships between V, A, and D based on the given statements. We will convert each statement into an inequality and then combine them to find the overall order.
From (II) and (III), we have \(V > D\) and \(D > A\). Combining these gives us \(V > D > A\).
Now, let's check this against statement (I): \(V \ge A\). Our derived inequality \(V > D > A\) implies \(V > A\), which is consistent with \(V \ge A\).
So, the definitive order of height from tallest to shortest is \(V > D > A\).
B) A is shorter than V and D