The problem asks for the present worth of a future amount due at compound interest. This means we need to find the principal amount that, when compounded at a given rate for a given time, will yield the specified future amount. We will use the compound interest formula and rearrange it to solve for the principal.
The formula for the amount (A) after compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]where \(P\) is the Principal (Present Worth), \(R\) is the rate of interest per annum, and \(n\) is the number of years.To find the present worth, we need to solve for \(P\):
\[ P = \frac{A}{\left(1 + \frac{R}{100}\right)^n} \]Substitute \(A = 338\), \(R = 4\), and \(n = 2\):
\[ P = \frac{338}{\left(1 + \frac{4}{100}\right)^2} \]First, simplify the term inside the parenthesis:
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]The present worth is approximately ₹312.50.
Correct Option: D) ₹312.50
The question asks to identify the 'father of Indian Supercomputers'. This requires knowledge of prominent figures in India's computing history, specifically those associated with the development of supercomputing.
Correct Option: D) Vijay Bhatkar is widely regarded as the 'father of Indian Supercomputers'. He is best known as the architect of India's first supercomputer, PARAM 8000, which was developed by the Centre for Development of Advanced Computing (C-DAC) in 1991. His pioneering work laid the foundation for India's indigenous supercomputing capabilities.
The question asks about the fields for which Marie Curie was awarded the Nobel Prize. This requires knowledge of her historical achievements and the specific Nobel Prizes she received.
Correct Option: A) Physics and Chemistry
The question asks about the number of companies whose stocks constitute the SENSEX index of the Bombay Stock Exchange (BSE). This is a factual question related to financial markets in India.
C) 30. SENSEX is composed of 30 of the largest and most actively traded stocks on the Bombay Stock Exchange.
India's first struggle for independence started on 10th May 1857 at:
The question asks for the starting point of India's First War of Independence (also known as the Sepoy Mutiny or the Revolt of 1857) on May 10, 1857. This requires knowledge of a key historical event in modern Indian history.
Correct Option: C) Meerut
To find the number, we need to set up an equation based on the given percentage information. If 40% of an unknown number is 800, we can represent this mathematically and solve for the unknown number.
Thus, the number is 2000.
Correct Option: B) 2000
The question asks to identify which option is NOT an allotrope of Carbon. To answer this, we need to understand what an allotrope is and then evaluate each given option.
B) Carbon dioxide is a compound of carbon and oxygen, not a pure form of carbon. Therefore, it is not an allotrope of carbon.
This problem involves finding a number when its square is given. We are told that the total fees collected is ₹2,601, and that the number of students is equal to the fees paid by each student. If we let 'x' be the number of students (and also the fee per student), then the total fees collected will be \(x \times x = x^2\). We need to find the value of 'x' by calculating the square root of 2,601.
Let the number of students in the school be \(N\).
Let the fees paid by each student be \(F\).
According to the problem, the fees paid by each student and the number of students are equal. So, \(N = F\).
The total fees collected is ₹2,601.
The total fees collected can also be expressed as the product of the number of students and the fees paid by each student:
\[ \text{Total Fees} = N \times F \]Since \(N = F\), we can substitute \(F\) with \(N\) (or vice versa) into the total fees equation:
\[ 2601 = N \times N \] \[ 2601 = N^2 \]To find \(N\), we need to calculate the square root of 2,601:
\[ N = \sqrt{2601} \]We can find the square root by estimation or by prime factorization. Let's try estimation:
So, \(N = 51\).
There were 51 students in the school.
Correct Option: C) 51
The question asks for the location of the Indian National Centre for Ocean Information Services (INCOIS). This is a factual question about the headquarters of a prominent scientific institution in India. Recalling the locations of major research centers is key for competitive exams.
Correct Option: D) Hyderabad is the correct answer because the Indian National Centre for Ocean Information Services (INCOIS) is headquartered in Hyderabad, Telangana.
The question asks to identify the application for which bleaching powder is NOT used. To answer this, we need to recall the common uses and chemical properties of bleaching powder (calcium hypochlorite).
B) preparing bread — Bleaching powder is not used in the preparation of bread. Its chemical properties make it unsuitable and harmful for food items.