To find the greatest number that divides two given numbers and leaves the same remainder in each case, we first subtract the remainder from each number. The greatest number that divides the resulting differences will be the Greatest Common Divisor (GCD) of these new numbers. This GCD will be our answer.
A) 9 is the greatest number that divides 39 and 84 to leave a remainder of 3 in each case. This is because \(39 - 3 = 36\) and \(84 - 3 = 81\), and the GCD of 36 and 81 is 9.
The question asks to identify which of the given diseases does NOT spread through the air. This requires knowledge of common modes of transmission for infectious diseases.
Correct Option: C) Cholera is an acute diarrheal illness caused by the bacterium Vibrio cholerae. It is primarily transmitted through the fecal-oral route, meaning it spreads through contaminated water or food, not through airborne particles.
The question asks for the location of the headquarters of the Archaeological Survey of India (ASI). This is a factual question requiring knowledge of the administrative structure of important government bodies in India.
A) New Delhi: The Archaeological Survey of India (ASI) has its headquarters in New Delhi. It operates under the Ministry of Culture, Government of India.
When was India's first semi-high speed train Vande Bharat Express flagged off by Prime Minister Narendra Modi?
15th December 2018
15th February 2019
15th January 2019
15th March 2019
The question asks for the date when India's first semi-high speed train, Vande Bharat Express, was flagged off by Prime Minister Narendra Modi. This is a factual question related to current affairs and Indian railway history. Recalling the specific date of this significant event is key to answering correctly.
Correct Option: B) 15 th February 2019
The first Vande Bharat Express (Train 18) was flagged off by Prime Minister Narendra Modi on February 15, 2019, from New Delhi. It began its commercial service between New Delhi and Varanasi.
To find the total area of the wet surface in the cistern, we need to calculate the area of the base and the area of the four side walls that are in contact with the water. The cistern is a cuboid, and the water fills it up to a certain depth. The wet surface will consist of the bottom surface and the four vertical side surfaces up to the water level.
Convert depth to meters:
The depth of the water is given as 1 m 22 cm. We convert this to meters:
\[ \text{Depth} (h) = 1 \text{ m} + 22 \text{ cm} = 1 \text{ m} + \frac{22}{100} \text{ m} = 1 + 0.22 \text{ m} = 1.22 \text{ m} \]Identify dimensions:
Length of the cistern \((L) = 8 \text{ m}\)
Width of the cistern \((W) = 4 \text{ m}\)
Height of the water \((h) = 1.22 \text{ m}\)
Calculate the area of the base:
The base of the cistern is a rectangle with length \(L\) and width \(W\).
\[ \text{Area of base} = L \times W = 8 \text{ m} \times 4 \text{ m} = 32 \text{ m}^2 \]Calculate the area of the four wet side walls:
There are two walls of length \(L\) and height \(h\), and two walls of width \(W\) and height \(h\).
Area of two longer walls \(= 2 \times (L \times h) = 2 \times (8 \text{ m} \times 1.22 \text{ m}) = 2 \times 9.76 \text{ m}^2 = 19.52 \text{ m}^2\)
Area of two shorter walls \(= 2 \times (W \times h) = 2 \times (4 \text{ m} \times 1.22 \text{ m}) = 2 \times 4.88 \text{ m}^2 = 9.76 \text{ m}^2\)
Total area of side walls \(= 19.52 \text{ m}^2 + 9.76 \text{ m}^2 = 29.28 \text{ m}^2\)
Alternatively, the perimeter of the base multiplied by the height of the water gives the total side area:
\[ \text{Area of side walls} = 2(L+W)h = 2(8+4) \times 1.22 = 2(12) \times 1.22 = 24 \times 1.22 = 29.28 \text{ m}^2 \]Calculate the total wet surface area:
The total wet surface area is the sum of the area of the base and the area of the wet side walls.
\[ \text{Total wet surface area} = \text{Area of base} + \text{Area of side walls} \]\[ \text{Total wet surface area} = 32 \text{ m}^2 + 29.28 \text{ m}^2 = 61.28 \text{ m}^2 \]C) 61.28 m² is the correct total wet surface area, calculated by summing the area of the base and the four wet side walls.
This problem involves concepts of work and time, specifically dealing with efficiency. We are given the time taken by one person to complete a work and the relative efficiency of another person. We need to find the time taken by the second person to complete the same work. The key is to understand that efficiency is inversely proportional to the time taken to complete a certain amount of work.
Understand Kamal's work rate:
Kamal completes the work in 14 days. This means Kamal's efficiency (or work rate) is \(\frac{1}{14}\) of the work per day.
Calculate Vimal's efficiency:
Vimal is 40% more efficient than Kamal. This means Vimal's efficiency is Kamal's efficiency plus 40% of Kamal's efficiency.
Vimal's efficiency \( = \text{Kamal's efficiency} + 40\% \text{ of Kamal's efficiency}\)
Vimal's efficiency \( = \text{Kamal's efficiency} \times (1 + 0.40)\)
Vimal's efficiency \( = \text{Kamal's efficiency} \times 1.40\)
Substituting Kamal's efficiency:
\[ \text{Vimal's efficiency} = \frac{1}{14} \times 1.40 \]\[ \text{Vimal's efficiency} = \frac{1.40}{14} \]\[ \text{Vimal's efficiency} = \frac{140}{1400} \]\[ \text{Vimal's efficiency} = \frac{1}{10} \text{ of the work per day} \]Calculate the number of days Vimal takes:
If Vimal completes \(\frac{1}{10}\) of the work per day, then Vimal will take 10 days to complete the entire work.
Number of days \[= \frac{1}{\text{Vimal's efficiency}}\]
\[ \text{Number of days} = \frac{1}{\frac{1}{10}} \]\[ \text{Number of days} = 10 \text{ days} \]D) 10 days — As calculated, Vimal, being 40% more efficient, completes the work in 10 days.
If we select 3 persons randomly from a group, consisting of 4 men, 3 women and 2 boys, then the probability that 2 men are selected is:
\( \frac{5}{14} \)
\( \frac{7}{12} \)
\( \frac{3}{14} \)
\( \frac{5}{28} \)
To find the probability, we need to calculate the total number of ways to select 3 persons from the group and the number of ways to select 3 persons such that exactly 2 men are selected. We will use combinations for these calculations.
Correct Option: A) \( \frac{5}{14} \)
The question asks for the specific year when Rabindranath Tagore received the Nobel Prize in Literature for his work 'Gitanjali'. This is a factual recall question related to Indian history and literature, often tested in competitive exams.
Correct Option: D) 1913 is the correct year when Rabindranath Tagore was awarded the Nobel Prize in Literature.
What will be the interest on the amount of ₹25,000 compounded annually at the rate of 4%, 5% and 6% per annum for the first, second and third year respectively?
The problem asks for the total compound interest on an amount of ₹25,000 over three years, with different interest rates for each year. Since the interest is compounded annually, we need to calculate the amount at the end of each year and then use that as the principal for the next year's calculation.
A) ₹3,938 is the correct total compound interest calculated over the three years with varying annual rates.
The question asks about the winner of a specific international snooker tournament held in March 2019. This requires knowledge of sports current affairs from that period.
A) Matthew Selt — Matthew Selt won the 2019 Indian Open snooker tournament by defeating Lyu Haotian in the final.