The problem asks us to find the missing term in an analogy based on letter clusters. We need to identify the pattern or rule that transforms the first letter cluster (RAMA) into the second (MARA), and then apply the same rule to the third letter cluster (SITA) to find the missing fourth term.
Correct Option: D) TISA
The question asks about the function of growth hormones. Growth hormones, also known as plant growth regulators or phytohormones, are chemical substances that influence plant growth and development. Their effects can vary depending on their concentration, the specific plant species, and the developmental stage of the plant.
B) sometimes as growth promoters and sometimes as growth inhibitors. This option correctly reflects the nuanced and concentration-dependent roles of plant growth hormones, where the same hormone can promote growth at one concentration and inhibit it at another, or promote one aspect of growth while inhibiting another.
To find the least number to be added to 435 to make it a perfect square, we need to find the smallest perfect square greater than 435. This can be done by finding the square root of 435 and then considering the next integer's square.
We need to estimate the square root of 435. Let's test some integers:
Since \(20^2 = 400\) and \(21^2 = 441\), we know that 435 lies between the perfect squares of 400 and 441.
The number 435 is not a perfect square. The next perfect square after 400 is 441.
To make 435 a perfect square (specifically, 441), we need to add the difference between 441 and 435.
\[ \text{Number to be added} = 441 - 435 \]\[ \text{Number to be added} = 6 \]The least number to be added to 435 to make it a perfect square is 6.
Correct Option: C) 6
This is a blood relations question. We need to decode the relationship described by Y to determine how Y is related to X. We will break down the statement "X is the son of the only son of my mother" step by step, starting from the end of the statement relative to Y.
Let's consider the case where Y is female. If Y is female, "the only son of my mother" would be Y's brother. In that case, "X is the son of Y's brother", meaning X is Y's nephew. This would make Y X's aunt. However, "father" is an option, and "aunt" is not. The phrasing "only son of my mother" strongly implies that the speaker (Y) is that son if Y is male, or that the speaker is referring to their brother if Y is female. Given the options, the most direct and common interpretation in such puzzles is that Y is male and is referring to himself.
Correct Option: C) Father
The problem involves calculating averages. We are given the overall average of four numbers and the average of two of those numbers. We need to find the average of the remaining two numbers. The key concept is that the sum of numbers is equal to their average multiplied by the count of numbers.
The overall average of A, B, C, and D is 16. There are 4 numbers.
\[ \text{Sum of (A, B, C, D)} = \text{Overall Average} \times \text{Number of terms} \]\[ \text{Sum of (A, B, C, D)} = 16 \times 4 = 64 \]The average of A and B is 9.5. There are 2 numbers.
\[ \text{Sum of (A, B)} = \text{Average of (A, B)} \times \text{Number of terms} \]\[ \text{Sum of (A, B)} = 9.5 \times 2 = 19 \]The sum of C and D can be found by subtracting the sum of A and B from the total sum of A, B, C, and D.
\[ \text{Sum of (C, D)} = \text{Sum of (A, B, C, D)} - \text{Sum of (A, B)} \]\[ \text{Sum of (C, D)} = 64 - 19 = 45 \]Now that we have the sum of C and D, and we know there are 2 numbers, we can find their average.
\[ \text{Average of (C, D)} = \frac{\text{Sum of (C, D)}}{\text{Number of terms}} \]\[ \text{Average of (C, D)} = \frac{45}{2} = 22.5 \]B) 22.5 is the correct average of C and D.
The question asks to identify the permanent tissue responsible for making a plant hard and stiff. This requires knowledge of the different types of plant permanent tissues and their primary functions.
Correct Option: B) Sclerenchyma is the permanent tissue that makes a plant hard and stiff. Its cells have thick, lignified secondary walls, providing significant mechanical strength and rigidity to plant parts like stems, leaf veins, and seed coats.
To determine the condition for a quadratic equation to have no real solutions, we need to analyze its discriminant. For a quadratic equation of the form \(ax^2 + bx + c = 0\), the discriminant is given by \(\Delta = b^2 - 4ac\). If the equation has no real solutions, then the discriminant must be less than zero (\(\Delta < 0\)).
Identify coefficients: The given quadratic equation is \(x^2 + kx + k = 0\). Comparing this with the standard form \(ax^2 + bx + c = 0\), we have:
Apply the condition for no real solutions: For a quadratic equation to have no real solutions, its discriminant must be strictly less than zero.
\[ \Delta = b^2 - 4ac < 0 \]Substitute the coefficients: Substitute the values of \(a\), \(b\), and \(c\) into the discriminant inequality:
\[ k^2 - 4(1)(k) < 0 \]\[ k^2 - 4k < 0 \]Solve the inequality: To solve \(k^2 - 4k < 0\), factor out \(k\):
\[ k(k - 4) < 0 \]Determine the range for k: For the product of two terms to be negative, one term must be positive and the other must be negative. We consider two cases:
This implies \(k > 0\) and \(k < 4\). Combining these, we get \(0 < k < 4\).
This implies \(k < 0\) and \(k > 4\). This case is impossible as \(k\) cannot be both less than 0 and greater than 4 simultaneously.
Therefore, the only valid range for \(k\) is \(0 < k < 4\).
B) \(0 < k < 4\) is the correct condition for the given quadratic equation to have no real solutions.
The question asks for the term used to describe a sound of a single frequency. We need to differentiate between various terms related to sound properties.
Correct Option: C) Tone — A tone, especially a pure tone, is defined as a sound having a single, constant frequency. It is a fundamental concept in acoustics.
To find the square root of 6561, we can use a few methods: prime factorization, estimation, or the long division method. For competitive exams, a quick estimation combined with checking the last digit is often efficient, or direct calculation if the number is small enough.
D) 81 — As calculated, \(81 \times 81 = 6561\).
15th February 2018 is a Thursday. On what day will 20th April 2019 fall?
To determine the day of the week for a future date, we need to calculate the total number of odd days between the given date and the target date. Odd days are the remainder when the total number of days is divided by 7. Each odd day shifts the day of the week by one. We must also account for leap years.
The year 2018 is not a leap year (it is not divisible by 4). Therefore, it has 365 days.
Number of odd days in a normal year \( = 365 \div 7 = 52 \) weeks and \( 1 \) odd day.
So, 15th February 2019 will be one day after 15th February 2018.
Since 15th February 2018 is a Thursday, 15th February 2019 will be a Friday.
Total number of days \( = 13 + 31 + 20 = 64 \) days.
Number of odd days \( = 64 \div 7 \)
\( = 9 \) weeks and \( 1 \) odd day.
Starting from 15th February 2019 (which is a Friday), we add 1 odd day.
Friday + 1 day = Saturday.
A) Saturday is the correct answer. By calculating the odd days from the given date to the target date, we find that the day shifts by a total of 2 days (1 day for the year transition and 1 day for the months in 2019), resulting in Saturday.