The task is to identify which of the given assumptions are implicit in the statement: "During winters, the sky is very clear at night." An implicit assumption is something that is taken for granted or presupposed by the statement, without being explicitly stated. We need to evaluate each assumption independently to see if the statement relies on it.
A) Neither assumption I nor II is implicit. As analyzed, neither the early sunset nor the occurrence of rain is a prerequisite or an underlying condition for the statement that the sky is very clear at night during winters.
Which is the smallest fraction among the options given below?
\(\frac{1981}{150}\)
\(\frac{1981}{155}\)
\(\frac{1981}{153}\)
\(\frac{1981}{152}\)
To find the smallest fraction among a set of fractions that have the same numerator, we need to compare their denominators. When the numerators are the same, the fraction with the largest denominator will be the smallest in value.
Correct Option: B) \(\frac{1981}{155}\) is the smallest fraction because it has the largest denominator among all the given options, while the numerator remains constant.
The question asks to identify one of the recipients of the Major Dhyan Chand Khel Ratna Award in 2021 from the given options. This requires knowledge of the awardees for that specific year.
Correct Option: A) Neeraj Chopra was indeed one of the recipients of the Major Dhyan Chand Khel Ratna Award in 2021 for his historic gold medal win in Javelin Throw at the Tokyo Olympics.
The question asks to identify the type of reaction to which precipitation reactions belong. We need to recall the definitions of different types of chemical reactions and specifically what characterizes a precipitation reaction.
Correct Option: B) double displacement reactions
To determine the date and day after 100 days, we need to calculate the number of remaining days in each month starting from January 2020, until we reach 100 days. We also need to find the "odd days" to determine the day of the week. Since 2020 is a leap year, February will have 29 days.
Days remaining in January 2020:
Given date is January 22, 2020. Total days in January = 31.
\[ \text{Remaining days in January} = 31 - 22 = 9 \text{ days} \]Days in February 2020:
2020 is a leap year (divisible by 4). So, February 2020 has 29 days.
Days in March 2020:
March has 31 days.
Calculate cumulative days:
We need to count 100 days from January 22.
Thus, the date will be May 1, 2020.
Calculate the day of the week:
The number of odd days is the remainder when the total number of days (100) is divided by 7.
\[ \text{Odd days} = 100 \pmod{7} \]\[ \text{Odd days} = 14 \times 7 + 2 \]\[ \text{Odd days} = 2 \]Determine the final day:
Today is Monday. After 100 days, the day will be Monday + 2 odd days.
Monday + 1 day = Tuesday
Monday + 2 days = Wednesday
So, the day will be Wednesday.
Therefore, after 100 days from January 22, 2020, it will be May 1, 2020, Wednesday.
B) 1 May 2020, Wednesday
The problem requires us to find the value of 'n' in an equation involving exponents. We will use the laws of exponents, specifically the product rule \((a^m \times a^n = a^{m+n})\) and the quotient rule \((a^m \div a^n = a^{m-n})\), to simplify both sides of the equation. Once simplified, we can equate the exponents since the bases are the same.
The LHS is \(2^{-7} \times 2^{3n+4}\). Using the product rule \(a^m \times a^n = a^{m+n}\):
\[ 2^{-7} \times 2^{3n+4} = 2^{(-7) + (3n+4)} \]\[ = 2^{-7 + 3n + 4} \]\[ = 2^{3n - 3} \]The RHS is \(2^{11} \div 2^5\). Using the quotient rule \(a^m \div a^n = a^{m-n}\):
\[ 2^{11} \div 2^5 = 2^{11 - 5} \]\[ = 2^6 \]Now we have the equation:
\[ 2^{3n - 3} = 2^6 \]Since the bases are equal, their exponents must also be equal:
\[ 3n - 3 = 6 \]Correct Option: C) The value of n is 3.
The question asks about the natural habitat of the Musk Deer. To answer this, one needs to recall the ecological preferences and geographical distribution of this species, which is typically found in specific high-altitude environments.
Correct Option: A) High alpine environments above altitudes of 2500 m. Musk deer are typically found in mountainous regions, specifically in high-altitude subalpine and alpine zones, generally above 2500 meters, where they inhabit coniferous and deciduous forests, and shrublands.
To solve this problem, we need to identify pairs of letters in the given word "PLATE" such that the number of letters between them in the word is the same as the number of letters between them in the English alphabetical order. This check must be performed in both forward and backward directions.
Correct Option: B) None
The following graph shows the earnings of Mr. Rajesh from his grocery shop, over the months. Study the graph and answer the question.
What is the respective ratio of the total earnings in May, June and July together to the total earnings in August, September and October together?
To find the respective ratio of the total earnings from May, June, and July to the total earnings from August, September, and October, we need to sum the earnings for each group of months and then calculate the ratio.
Correct Option: A) 1 : 1
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate the conclusions based on these diagrams. We need to find conclusions that logically follow from the statements.
C) Only conclusion (I) follows.