Pointing to the man receiving the award, Sunny said, "He is the brother of my uncle's daughter." How is the man related to Sunny?
This is a blood relation problem. We need to trace the relationships mentioned in the statement to determine how the man receiving the award is related to Sunny.
Correct Option: A) Cousin
Read the statements and select one conclusion from the given alternatives.
Statement:
At the book fair, one author's books are displayed to the public. The prices of books are too high for a common man
Conclusions:
I. Layman only buys books from the exhibition
II. Expensive painting is usually displayed at the art gallery.
Only I follow
Only II follows
Both I and II follow
Neither I nor II follow
The problem requires us to analyze a given statement and determine which of the provided conclusions logically follows from it. This is a question of logical deduction. We must only use the information given in the statement and not introduce outside knowledge or assumptions.
D) Neither I nor II follow
As analyzed above, both conclusions introduce information or make claims that are not supported by the original statement. Therefore, neither of them logically follows.
The problem asks us to decode a word based on a given coding pattern. We need to identify the rule by which "PARIS" is coded as "QBSJT" and then apply the same rule to code "LONDON".
D) MPOEPO — This matches our derived coded word by applying the +1 shift rule to each letter of "LONDON".
The problem asks us to find the standard deviation given the variance of a data set. We need to recall the fundamental relationship between variance and standard deviation in statistics.
Variance (\(\sigma^2\)) is a measure of how spread out a set of data is from its mean. It is calculated as the average of the squared differences from the mean.
Standard Deviation (\(\sigma\)) is the square root of the variance. It measures the average amount of variability or dispersion around the mean, and it is expressed in the same units as the data itself.
The standard deviation is the positive square root of the variance.
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} \]Given that the variance of the data set is 361.
Let \(\sigma^2\) be the variance and \(\sigma\) be the standard deviation.
\[ \sigma^2 = 361 \]\[ \sigma = \sqrt{361} \]We need to find the number that, when multiplied by itself, equals 361.
We know that \(10^2 = 100\) and \(20^2 = 400\). So the number must be between 10 and 20.
Let's check numbers ending in 9 or 1 (since \(9 \times 9 = 81\) ends in 1).
Try 19:
\[ 19 \times 19 = 361 \]Therefore, the standard deviation is 19.
B) 19 is the correct answer because the standard deviation is the positive square root of the variance, and \(\sqrt{361} = 19\).
15 men can make a toy in 20 days. How many days will 8 men take to make it?
This is a problem of inverse proportionality. The number of men and the number of days required to complete a fixed amount of work are inversely proportional. This means if the number of men decreases, the number of days will increase, and vice versa. We can use the formula \(M_1 D_1 = M_2 D_2\), where \(M\) represents the number of men and \(D\) represents the number of days.
So, 8 men will take 37.5 days to make the toy.
Correct Option: B) 37.5
The question asks to identify the recipient of the Hridaynath Mangeshkar Award in 2015 for their contribution to Indian music. This is a factual question related to awards and honors in the field of arts, specifically music.
Correct Option: D) AR Rahman was selected for the Hridaynath Mangeshkar Award 2015 for his significant contributions to Indian music. He is an internationally renowned music composer, singer, and music producer.
If cot x = \(\frac{5}{12}\), then sin x + cos x = ?
\(\frac{31}{17}\)
\(\frac{27}{13}\)
\(\frac{13}{17}\)
\(\frac{17}{13}\)
The problem provides the value of \(\cot x\) and asks for the value of \(\sin x + \cos x\). We can use trigonometric identities or a right-angled triangle approach to find \(\sin x\) and \(\cos x\) from \(\cot x\), and then sum them up.
Given \(\cot x = \frac{5}{12}\). We know that \[\cot x = \frac{\text{adjacent side}}{\text{opposite side}}\] in a right-angled triangle. Let's assume a right-angled triangle where the angle is \(x\).
Let the adjacent side be \(5k\) and the opposite side be \(12k\) for some constant \(k\). We can find the hypotenuse using the Pythagorean theorem:
\[ \text{hypotenuse}^2 = (\text{opposite side})^2 + (\text{adjacent side})^2 \]\[ \text{hypotenuse}^2 = (12k)^2 + (5k)^2 \]\[ \text{hypotenuse}^2 = 144k^2 + 25k^2 \]\[ \text{hypotenuse}^2 = 169k^2 \]\[ \text{hypotenuse} = \sqrt{169k^2} = 13k \]Now we can find \(\sin x\) and \(\cos x\):
\[ \sin x = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{12k}{13k} = \frac{12}{13} \]\[ \cos x = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{5k}{13k} = \frac{5}{13} \]Finally, calculate \(\sin x + \cos x\):
\[ \sin x + \cos x = \frac{12}{13} + \frac{5}{13} \]\[ \sin x + \cos x = \frac{12+5}{13} \]\[ \sin x + \cos x = \frac{17}{13} \]D) \(\frac{17}{13}\) is the correct answer, as calculated in the step-by-step solution.
Given: If w = –2, x = 3, y = 0, and z = –\( \frac{1}{2} \), then find the value of \(x\sqrt{x+wz}\)
To find the value of the given expression, we need to substitute the provided values of the variables \(w\), \(x\), \(y\), and \(z\) into the expression and then simplify it following the order of operations.
Correct Option: C) 6
Which agency is responsible for naming planets and other celestial bodies?
International Institute for Space Law
International Astronomical Union
International Space Coordination Group
European Space Agency
The question asks to identify the international body responsible for naming celestial objects. This requires knowledge of the primary organizations involved in astronomy and space science governance.
Correct Option: B) The International Astronomical Union (IAU) is the internationally recognized authority for assigning designations and names to celestial bodies and their surface features. This includes planets, dwarf planets, small Solar System bodies (asteroids, comets), and stars, as well as features on these bodies.
What is the 99th amendment of the constitution about?
Starting GST in India.
Establishment of National Judicial Appointments Commission.
Empowering the Governor of Karnataka to take steps for the development of Hyderabad-Karnataka region.
Agreement on the land border between Bangladesh and India.
The question asks about the subject matter of the 99th Constitutional Amendment of India. To answer this, one needs to recall the key provisions and historical context of significant constitutional amendments.
Correct Option: B) Establishment of National Judicial Appointments Commission.
The 99th Constitutional Amendment Act, 2014, established the National Judicial Appointments Commission (NJAC). It sought to replace the collegium system for the appointment of judges to the Supreme Court and High Courts. However, the Supreme Court later declared the 99th Amendment and the NJAC Act unconstitutional in 2015, thereby reviving the collegium system.