The question asks for the origin of the Brahmaputra River. To answer this, we need to recall the geographical origins of major Indian rivers.
Correct Option: D) Lake Manasarovar is the correct answer. The Brahmaputra River originates near Lake Manasarovar in the Himalayas, specifically from the Angsi Glacier.
A, B and C can complete a task in 10, 15 and 18 days respectively. In how many days will all of them complete the same task working together?
To solve this problem, we need to determine the individual work rates of A, B, and C. The work rate is the reciprocal of the time taken to complete the task. Once we have their individual work rates, we can add them to find their combined work rate. The reciprocal of the combined work rate will give us the total time taken for all three to complete the task together.
Calculate individual work rates:
Calculate combined work rate:
When A, B, and C work together, their combined one day's work is the sum of their individual one day's work:
\[ \text{Combined one day's work} = \frac{1}{10} + \frac{1}{15} + \frac{1}{18} \]Find a common denominator (LCM) for 10, 15, and 18:
The least common multiple (LCM) of 10, 15, and 18 is 90.
Add the fractions:
\[ \text{Combined one day's work} = \frac{9}{90} + \frac{6}{90} + \frac{5}{90} \] \[ \text{Combined one day's work} = \frac{9 + 6 + 5}{90} = \frac{20}{90} \] \[ \text{Combined one day's work} = \frac{2}{9} \]Calculate total time taken:
If their combined one day's work is \( \frac{2}{9} \) of the task, then the total time taken to complete the task together is the reciprocal of this rate:
\[ \text{Time taken} = \frac{1}{\text{Combined one day's work}} = \frac{1}{\frac{2}{9}} = \frac{9}{2} \text{ days} \]Correct Option: B) \( \frac{9}{2} \)
The total time taken for A, B, and C to complete the task together is \( \frac{9}{2} \) days, which is equal to 4.5 days.
Assuming A = 1, B = 2 and so on … Z = 26, find the value of the following expression.
\( \left(I^{2} - C^{2} \times \frac{P}{R}\right) + 8 \)
The problem requires us to substitute the numerical values of the given letters into the expression and then perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).
Given the mapping A = 1, B = 2, ..., Z = 26, we find the values for the letters in the expression:
The given expression is \( \left(I^{2} - C^{2} \times \frac{P}{R}\right) + 8 \).
Substitute the numerical values:
\[ \left(9^{2} - 3^{2} \times \frac{16}{18}\right) + 8 \]First, calculate the squares:
\[ 9^2 = 81 \] \[ 3^2 = 9 \]The expression becomes:
\[ \left(81 - 9 \times \frac{16}{18}\right) + 8 \]Next, simplify the fraction \(\frac{16}{18}\) by dividing both numerator and denominator by 2:
\[ \frac{16}{18} = \frac{8}{9} \]Now, perform the multiplication inside the parentheses:
\[ 9 \times \frac{8}{9} = 8 \]So, the expression inside the parentheses becomes:
\[ (81 - 8) = 73 \]Now, add 8 to the result from the parentheses:
\[ 73 + 8 = 81 \]Correct Option: C) 81
This problem involves calculating the combined work rate of two taps, one filling and one emptying. We will determine the individual rates of filling and emptying, then find the net rate when both are open. Finally, we will use the net rate to calculate the total time required to fill the tank.
Tap A fills the tank in 40 minutes. So, in 1 minute, Tap A fills \(\frac{1}{40}\) of the tank.
\[ \text{Rate of Tap A} = \frac{1}{40} \text{ tank/min} \]Tap B empties the tank in 60 minutes. So, in 1 minute, Tap B empties \(\frac{1}{60}\) of the tank.
\[ \text{Rate of Tap B} = \frac{1}{60} \text{ tank/min} \]Since Tap A fills and Tap B empties, their effects are opposite. The net rate is the difference between the filling rate and the emptying rate.
\[ \text{Net Rate} = \text{Rate of Tap A} - \text{Rate of Tap B} \] \[ \text{Net Rate} = \frac{1}{40} - \frac{1}{60} \]To subtract these fractions, find a common denominator, which is 120.
\[ \text{Net Rate} = \frac{3}{120} - \frac{2}{120} \] \[ \text{Net Rate} = \frac{3 - 2}{120} = \frac{1}{120} \text{ tank/min} \]If the net rate is \(\frac{1}{120}\) of the tank per minute, it means it takes 120 minutes to fill the entire tank.
\[ \text{Time} = \frac{1}{\text{Net Rate}} \] \[ \text{Time} = \frac{1}{\frac{1}{120}} = 120 \text{ minutes} \]Correct Option: A) 120 min
The question asks to identify the eye condition when a person has difficulty seeing distant objects clearly and how it can be corrected. This relates to common refractive errors of the human eye and their optical corrections.
A) Myopia, using concave lens. This option correctly identifies the condition (Myopia) and its appropriate correction (concave lens).
The problem requires us to calculate the perimeter of a square whose area is equal to the area of a given trapezium. First, we will calculate the area of the trapezium using the formula for the area of a trapezium. Then, we will equate this area to the area of a square to find the side length of the square. Finally, we will calculate the perimeter of the square.
The question asks to identify the group of plants that lack a vascular system. A vascular system in plants consists of xylem and phloem, which are responsible for transporting water, nutrients, and food throughout the plant. Understanding the basic classification of plants based on the presence or absence of these tissues is key to answering this question.
Correct Option: A) bryophytes are non-vascular plants, meaning they lack xylem and phloem for water and nutrient transport. They are typically small and live in moist environments.
The question asks to identify the recipient of the Padma Vibhushan in the Art-Acting-Theatre category for the year 2019. This requires knowledge of the Padma Awards recipients for that specific year and category.
Correct Option: A) Balwant Moreshwar Purandare was awarded the Padma Vibhushan in 2019 for his contributions to Art-Theatre. He is a renowned historian and author, particularly known for his work on Chhatrapati Shivaji Maharaj, which he presented through various theatrical forms.
The question asks for the correct term for a single-celled fertilized egg. This is a fundamental concept in human reproduction and developmental biology. We need to identify the term that specifically refers to the initial stage after fertilization.
D) zygote — A zygote is the correct term for a single-celled fertilized egg. It is the first diploid cell formed after the fusion of male and female gametes during sexual reproduction.
What will be the value of θ if
\(\sqrt{3}\) tan 2θ - 3 = 0?
To find the value of \(\theta\), we need to solve the given trigonometric equation \(\sqrt{3}\) tan \(2\theta\) - 3 = 0. We will isolate the \(\tan(2\theta)\) term and then use the known values of trigonometric ratios for standard angles.
The given equation is:
\[ \sqrt{3} \tan 2\theta - 3 = 0 \]
Add 3 to both sides of the equation:
\[ \sqrt{3} \tan 2\theta = 3 \]
Divide both sides by \(\sqrt{3}\):
\[ \tan 2\theta = \frac{3}{\sqrt{3}} \]
To simplify the right-hand side, we can rationalize the denominator or recognize that \(3 = \sqrt{3} \times \sqrt{3}\):
\[ \tan 2\theta = \frac{\sqrt{3} \times \sqrt{3}}{\sqrt{3}} \]
\[ \tan 2\theta = \sqrt{3} \]
We know that \(\tan 60^\circ = \sqrt{3}\). Therefore,
\[ 2\theta = 60^\circ \]
Divide by 2:
\[ \theta = \frac{60^\circ}{2} \]
\[ \theta = 30^\circ \]
Correct Option: C) 30°