The question asks for the definition of the capacity to do work. We need to recall the fundamental definitions of the given physical quantities: power, force, pressure, and energy.
Correct Option: D) energy
Find the compound interest on ₹62500 at 20% per annum, compounded half-yearly, for 1\( \frac{1}{2} \) years.
To find the compound interest when compounded half-yearly, we need to adjust the annual interest rate and the time period. The annual rate is halved, and the number of years is doubled to get the number of compounding periods. Then, we use the compound interest formula to calculate the total amount and subtract the principal to find the compound interest.
Since the interest is compounded half-yearly, the rate per compounding period will be half of the annual rate, and the number of compounding periods will be twice the number of years.
The formula for the amount when compounded is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]Compound Interest is the difference between the Amount and the Principal.
\[ \text{CI} = A - P \]\[ \text{CI} = 83187.5 - 62500 \]\[ \text{CI} = 20687.5 \]D) ₹20,687.5 is the correct compound interest calculated.
This is an analogy question. We need to identify the relationship between the first pair of words ('Explore' and 'Discover') and then find a word that shares the same relationship with 'Walk'.
D) Ramble
To 'ramble' means to walk aimlessly for pleasure. It describes a specific manner or style of walking, often without a particular destination, similar to how 'discover' is a specific outcome of 'explore'. While 'walk' is a general action, 'ramble' specifies a type of walking. It fits the pattern of a more specific or consequential action related to the general one.
The question asks to identify which of the given actions is NOT voluntary. Voluntary actions are those that are performed consciously and are under the control of our will. Involuntary actions, on the other hand, occur automatically without conscious thought or control.
Correct Option: B) Beating of heart — The beating of the heart is an involuntary action, meaning it occurs automatically without conscious control. It is regulated by the autonomic nervous system and cardiac muscle.
To hear a distinct echo, there must be a minimum time interval between the original sound and the reflected sound. This minimum time is determined by the persistence of hearing in the human ear and the speed of sound.
B) 0.1 second — This is the minimum time required for the human ear to distinguish between two separate sounds, which is essential for perceiving a distinct echo.
To find the number when a certain percentage of it is known, we can set up a simple algebraic equation. We are given that 32% of an unknown number is 80. We will represent the unknown number with a variable and then solve for it.
Correct Option: B) 250
The question asks to identify the first Indian basketball player to be drafted into the National Basketball Association (NBA). This requires knowledge of prominent Indian basketball players and their careers, specifically their entry into the NBA draft.
Correct Option: A) Satnam Singh Bhamara
Satnam Singh Bhamara made history in 2015 when he was drafted by the Dallas Mavericks as the 52nd overall pick in the NBA draft. This marked the first time an Indian-born player was drafted into the National Basketball Association.
The question asks to identify the scientist who proposed the periodic law based on atomic masses. This requires knowledge of the historical development of the periodic table and the contributions of key scientists.
B) Mendeleev
Dmitri Mendeleev formulated the Periodic Law, which states that "the properties of the elements are the periodic function of their atomic masses." He used this law to arrange the known elements into his periodic table and even predicted the properties of undiscovered elements.
To find the other number, we can use the fundamental property of multiplication: if the product of two numbers and one of the numbers are known, the other number can be found by dividing the product by the known number.
D) 16 is the correct answer because when 40 is divided by 2.50, the result is 16.
If tan α = \(\sqrt{2}\) - 1, then the value of tan α - cot α = ?
The problem asks us to find the value of \(\tan \alpha - \cot \alpha\) given that \(\tan \alpha = \sqrt{2} - 1\). We can use the reciprocal identity \(\cot \alpha = \frac{1}{\tan \alpha}\) to express \(\cot \alpha\) in terms of \(\tan \alpha\) and then substitute the given value.
We are given the value of \(\tan \alpha\):
\[ \tan \alpha = \sqrt{2} - 1 \]Recall the reciprocal identity for \(\cot \alpha\):
\[ \cot \alpha = \frac{1}{\tan \alpha} \]Substitute the given value of \(\tan \alpha\) into the identity to find \(\cot \alpha\):
\[ \cot \alpha = \frac{1}{\sqrt{2} - 1} \]To simplify the expression for \(\cot \alpha\), we rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{2} + 1\):
\[ \cot \alpha = \frac{1}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} \]\[ \cot \alpha = \frac{\sqrt{2} + 1}{(\sqrt{2})^2 - (1)^2} \]\[ \cot \alpha = \frac{\sqrt{2} + 1}{2 - 1} \]\[ \cot \alpha = \frac{\sqrt{2} + 1}{1} \]\[ \cot \alpha = \sqrt{2} + 1 \]Now, we need to find the value of \(\tan \alpha - \cot \alpha\). Substitute the values we found for \(\tan \alpha\) and \(\cot \alpha\):
\[ \tan \alpha - \cot \alpha = (\sqrt{2} - 1) - (\sqrt{2} + 1) \]\[ \tan \alpha - \cot \alpha = \sqrt{2} - 1 - \sqrt{2} - 1 \]Combine like terms:
\[ \tan \alpha - \cot \alpha = (\sqrt{2} - \sqrt{2}) + (-1 - 1) \]\[ \tan \alpha - \cot \alpha = 0 + (-2) \]\[ \tan \alpha - \cot \alpha = -2 \]C) -2 is the correct answer.