This problem involves ordering six boys based on their age using given relational statements. We will deduce the relative positions of each boy from the statements and then identify the eldest.
Order: _ > Q > _ > _ > _ > _
There are 4 boys younger than Q (positions 3, 4, 5, 6) and 1 boy elder than Q (position 1).
Therefore, T is the eldest.
B) T is the eldest among them, as deduced from the combined statements.
To find the next number in the series, we need to identify the pattern or rule governing the sequence. We will examine the differences between consecutive terms to see if a consistent arithmetic or other progression exists.
The differences are 4, 8, 12, 16. This is an arithmetic progression where each subsequent difference increases by 4. So, the next difference should be \(16 + 4 = 20\).
To find the next number, add the identified next difference to the last term of the given series:
\[ \text{Next term} = \text{Last term} + \text{Next difference} \]\[ \text{Next term} = 48 + 20 \]\[ \text{Next term} = 68 \]B) 68 is the correct answer because following the established pattern of differences (4, 8, 12, 16, 20), the next number in the series is \(48 + 20 = 68\).
The question asks us to find the word that completes the analogy. We need to identify the relationship between the first pair of words (Bank : Loan) and then apply the same relationship to the third word (Court) to find the fourth word.
Correct Option: D) Judgement
The question asks for the source of the motto "Satyameva Jayate" inscribed on the State Emblem of India. This requires knowledge of ancient Indian scriptures, specifically the Upanishads.
Correct Option: A) Mundaka Upanishad is the correct source for the quote 'Satyameva Jayate'.
The question asks to identify the recipient of the Bal Shakti Puraskar 2019 in the social service category for environmental contributions, specifically the youngest among the awardees. This requires knowledge of the award recipients for that specific year.
Eiha Dixit, from Meerut, Uttar Pradesh, received the Bal Shakti Puraskar 2019 for her efforts in planting saplings and encouraging others to do so, contributing significantly to environmental protection. She was the youngest among the awardees that year.
Correct Option: C) Eiha Dixit — She received the Bal Shakti Puraskar 2019 in the field of social service for her contribution to the environment and was the youngest among all the award recipients.
If x : y = 3 : 5, then the value of \(\frac{5x-3y}{10x+6y}\) is:
The problem provides a ratio between two variables, \(x\) and \(y\), and asks us to find the value of an algebraic expression involving \(x\) and \(y\). We can solve this by expressing one variable in terms of the other using the given ratio, or by assuming \(x\) and \(y\) are multiples of the ratio terms and substituting these into the expression.
Understand the given ratio: We are given that \(x : y = 3 : 5\). This can be written as a fraction:
\[ \frac{x}{y} = \frac{3}{5} \]Express one variable in terms of the other: From the ratio, we can write \(x = 3k\) and \(y = 5k\) for some constant \(k\). Alternatively, we can express \(x\) in terms of \(y\):
\[ x = \frac{3}{5}y \]Substitute into the expression: Now, substitute \(x = \frac{3}{5}y\) into the given expression \(\frac{5x-3y}{10x+6y}\):
\[ \frac{5\left(\frac{3}{5}y\right) - 3y}{10\left(\frac{3}{5}y\right) + 6y} \]Simplify the expression: Perform the multiplications in the numerator and denominator:
Numerator: \(5 \times \frac{3}{5}y - 3y = 3y - 3y = 0\)
Denominator: \(10 \times \frac{3}{5}y + 6y = 2 \times 3y + 6y = 6y + 6y = 12y\)
So the expression becomes:
\[ \frac{0}{12y} \]Final Calculation: Assuming \(y \neq 0\) (if \(y=0\), then \(x\) would also be \(0\), making the ratio undefined and the original expression \(0/0\), which is an indeterminate form; however, in such problems, it's generally assumed that the denominator does not become zero unless specified), any fraction with a numerator of \(0\) and a non-zero denominator is \(0\).
\[ \frac{0}{12y} = 0 \]C) 0
This is a logical reasoning question based on statements and conclusions. We need to evaluate each conclusion based strictly on the information provided in the statements, without introducing outside knowledge or assumptions.
D) Only conclusion 2 follows.
Conclusion 2 is a logical deduction. If someone is fond of an adventurous sport, it implies they have an adventurous nature or are an adventurous person. Conclusion 1 is an overgeneralization; liking one adventurous sport does not mean liking all of them.
The question asks to identify the decade during which India experienced a negative population growth rate. This requires knowledge of historical demographic trends in India, specifically the period known as the "Great Divide" in Indian demography.
B) 1911-1921 — This decade is known as the period of "Great Divide" in India's demographic history because it was the only decade when the population registered a negative growth rate, mainly due to the devastating impact of the 1918 influenza pandemic and other factors like famines.
To find the value of \(k\), we need to use the formula for the centroid of a triangle. The centroid of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is given by the coordinates \[\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)\]. We will equate the given centroid coordinates with this formula to solve for \(k\).
Let the given points be:
The given centroid is \((k, 1)\).
The coordinates of the centroid \((G_x, G_y)\) are given by:
\[ G_x = \frac{x_1 + x_2 + x_3}{3} \] \[ G_y = \frac{y_1 + y_2 + y_3}{3} \]Substitute the x-coordinates of the vertices into the formula:
\[ k = \frac{3 + (-7) + 10}{3} \] \[ k = \frac{3 - 7 + 10}{3} \] \[ k = \frac{-4 + 10}{3} \] \[ k = \frac{6}{3} \] \[ k = 2 \]Substitute the y-coordinates of the vertices into the formula to ensure consistency:
\[ 1 = \frac{5 + 4 + (-6)}{3} \] \[ 1 = \frac{9 - 6}{3} \] \[ 1 = \frac{3}{3} \] \[ 1 = 1 \]This confirms our calculations are consistent with the given centroid y-coordinate.
Correct Option: A) 2
To arrange the Indian presidents in descending order of their tenure, we need to recall the tenure period for each president listed in the options. Then, we will compare these tenures and order them from longest to shortest.
Both Giani Zail Singh and Neelam Sanjiva Reddy served full 5-year terms. When tenures are equal, the order among them doesn't strictly matter for "descending order of tenure" unless a tie-breaking rule (like chronological order) is specified, which is not the case here. However, in competitive exams, if two tenures are identical, their relative order might be based on their chronological succession or simply grouped together. Since both served 5 years, they will come first.
After them, Fakhruddin Ali Ahmed (approx. 2 years 6 months) had a longer tenure than Dr. Zakir Hussain (approx. 1 year 11 months).
So the order is: Giani Zail Singh (D) / Neelam Sanjiva Reddy (B) > Fakhruddin Ali Ahmed (A) > Dr. Zakir Hussain (C).
Looking at the options, the one that places D and B first, followed by A and C, is the correct choice.
B) D, B, A, C is the correct arrangement. Both Giani Zail Singh (D) and Neelam Sanjiva Reddy (B) served full 5-year terms. Fakhruddin Ali Ahmed (A) served for about 2.5 years, and Dr. Zakir Hussain (C) served for just under 2 years.