Select the option that represents the correct lateral image of PEN
To determine the correct lateral image of the word "PEN," we need to understand how lateral inversion works. Lateral inversion flips the image horizontally, reversing the order of letters from left to right.
Correct Option: D) The option "NԐp" correctly represents the lateral inversion of "PEN."
This problem involves finding the other root of a quadratic equation when one root is given. We can use the properties of quadratic equations, specifically the relationship between the roots and the coefficients. For a quadratic equation in the form \(ax^2 + bx + c = 0\), if \(\alpha\) and \(\beta\) are the roots, then the sum of the roots is \(\alpha + \beta = -b/a\) and the product of the roots is \(\alpha \beta = c/a\).
Identify the given quadratic equation and its coefficients. The equation is \(x^2 - 24x + k = 0\).
Comparing this with the standard form \(ax^2 + bx + c = 0\), we have:
Identify the given root. One root is \(x = 2\). Let's call this root \(\alpha = 2\).
Use the property of the sum of the roots. The sum of the roots is given by \(\alpha + \beta = -b/a\).
Substitute the known values:
\[ 2 + \beta = -\frac{(-24)}{1} \]\[ 2 + \beta = 24 \]Solve for the other root, \(\beta\).
\[ \beta = 24 - 2 \]\[ \beta = 22 \]Alternatively, we could first find the value of \(k\) by substituting the given root into the equation:
\[ (2)^2 - 24(2) + k = 0 \]\[ 4 - 48 + k = 0 \]\[ -44 + k = 0 \]\[ k = 44 \]Now, the equation is \(x^2 - 24x + 44 = 0\). We can find the roots by factoring or using the quadratic formula. By factoring, we look for two numbers that multiply to 44 and add up to -24. These numbers are -2 and -22.
\[ (x - 2)(x - 22) = 0 \]Setting each factor to zero gives the roots:
\[ x - 2 = 0 \implies x = 2 \]\[ x - 22 = 0 \implies x = 22 \]Thus, the other root is \(x = 22\).
Correct Option: C) x = 22
Which of the given figure is embedded in the following option:
The task is to identify which option contains the figure embedded in the given diagram. We need to carefully compare the elements and orientation of the shapes in the options with the main diagram.
Correct Option: D) The trapezoidal shape with the correctly oriented smiley face and arrow matches the main diagram.
To determine the unit of the universal gravitational constant G, we need to recall Newton's Law of Universal Gravitation and rearrange the formula to isolate G. Then, we can substitute the standard SI units for each variable to find the unit of G.
A) Nm²/kg² is the correct unit for the universal gravitational constant G, derived directly from Newton's Law of Universal Gravitation.
The question asks to identify the person appointed as the President of the Indian National Congress in 2017. This is a factual question related to Indian political history and current affairs.
Correct Option: C) Rahul Gandhi was appointed as the President of the Indian National Congress in December 2017, succeeding Sonia Gandhi.
Which of the following is the correct match of the given figure?
To solve this question, we need to match the arrangement of shapes in the given figure with one of the options provided. The key is to observe the position and orientation of the triangle and star within the square grid.
Correct Option: A) The arrangement of the triangle and star matches the original figure.
The problem presents a coding-decoding scenario. We need to identify the pattern used to convert "EAT" into "7322" and then apply the same pattern to find the code for "URN". The pattern usually involves the alphabetical position of letters, possibly with some arithmetic operations or reversals.
Correct Option: D) 232016
Read the given passage and the two statements carefully.
What will be the total age of Mayur and Shyam?
Statements:
1. Mayur is 15 years old today.
2. Shyam is 3 years younger than Mayur.
Which of the following statements is sufficient to answer the question?
Statement 1 alone is sufficient.
Statements 1 and 2 together are sufficient.
Statements 1 and 2 together are not sufficient.
Statement 2 alone is sufficient.
The problem asks for the total age of Mayur and Shyam. We need to determine which of the given statements, alone or together, provides enough information to calculate this total age.
Correct Option: B) Statements 1 and 2 together are sufficient.
The question asks to identify the Mughal emperor during whose reign Abul Fazl and Abul Faizi were prominent poets and scholars. This requires knowledge of the prominent figures in Mughal history and their associated courts.
Correct Option: A) Abul Fazl and Abul Faizi were two of the "Nine Jewels" (Navaratnas) of Emperor Akbar's court. Abul Fazl was a historian, biographer, and chief advisor to Akbar, known for writing the Akbarnama and Ain-i-Akbari. His brother, Abul Faizi, was a celebrated poet and scholar, also a part of Akbar's court. Their intellectual contributions and close relationship with Akbar are well-documented in Mughal history.
Which of the following expresses the relationship between the given pair?
A) Elephant
B) Lion
C) Animal
To solve this problem, we need to identify the correct diagram that represents the relationship between the given pair: Elephant, Lion, and Animal. The relationship is that both Elephant and Lion are types of Animals.
Correct Option: D) The diagram correctly shows both A (Elephant) and B (Lion) as subsets of C (Animal).
