Dalton's atomic theory, proposed in the early 19th century, was a foundational concept in chemistry. It provided a scientific basis for understanding the composition of matter. This theory was developed by observing and interpreting experimental results, particularly those related to how substances react and combine. The key principles of his theory were directly supported by certain fundamental laws of chemistry that had been established by other scientists.
Correct Option: B) Conservation of Mass — Dalton's theory explained that atoms are neither created nor destroyed during a chemical reaction, only rearranged. This directly accounts for the Law of Conservation of Mass, which states that mass remains constant in a closed system during a chemical reaction. His theory also explained the Law of Definite Proportions, but the conservation of mass is a more fundamental aspect addressed by the non-creation/destruction of atoms.
The question asks to identify the global aluminium rolled products company acquired by Novelis Inc., a subsidiary of Hindalco, in August 2018. This is a factual question related to business acquisitions and current affairs relevant to economic news.
In August 2018, Novelis Inc., a subsidiary of Hindalco (part of the Aditya Birla Group), announced its definitive agreement to acquire Aleris Corporation. Aleris Corporation is a global leader in aluminium rolled products and is headquartered in the United States.
D) Aleris Corporation — Novelis Inc. announced the acquisition of Aleris Corporation in August 2018. Aleris is a global aluminium rolled products company headquartered in the US, fitting all the criteria mentioned in the question.
Select the option that is related to the third word on the same basis as the second word is related to the first word.
Wait : Linger ∷ Bite:
The problem asks us to find a word that shares the same relationship with "Bite" as "Linger" shares with "Wait". This is a word analogy question, so we need to identify the nature of the relationship between the first pair of words.
Correct Option: A) Gnaw
Find the value of \(\sqrt{0.7}\).
To find the square root of 0.7, we can either use a calculator (which is usually not allowed in competitive exams) or estimate its value by comparing it to perfect squares or by using the long division method for square roots. Since the options are close, a precise estimation or calculation is required.
Alternatively, one can perform long division for square roots for 0.700000:
Set up the long division for \(\sqrt{0.700000}\). We pair digits from the decimal point. So we consider 70, then 00, then 00.
0.836
_________
. | 0.70 00 00
8 | -64
-----
163| 6 00
| -4 89
-------
1666| 1 11 00
| -99 96
--------
11 04
Thus, \(\sqrt{0.7} \approx 0.836\).
D) 0.836 is the closest and most accurate value for \(\sqrt{0.7}\).
Which of the following is a reducible fraction?
\( \frac{77}{72} \)
\( \frac{105}{112} \)
\( \frac{104}{121} \)
\( \frac{5}{49} \)
To determine if a fraction is reducible, we need to check if the numerator and the denominator share any common factors other than 1. If they do, the fraction can be simplified (reduced). This involves finding the Greatest Common Divisor (GCD) of the numerator and the denominator. If \(\text{GCD}(\text{numerator}, \text{denominator}) > 1\), the fraction is reducible.
B) \( \frac{105}{112} \) is the reducible fraction because its numerator and denominator share a common factor of \(7\).
The problem is a coding-decoding question. We need to identify the pattern or rule used to transform "TRUCK" into "RPSAI" and then apply the same rule to "TOOL" to find its coded form.
The pattern is that each letter in the original word is shifted backward by 2 positions in the alphabet to get the coded letter.
C) RMMJ is the correct code for TOOL, following the identified pattern of shifting each letter two positions backward in the alphabet.
The question asks to identify the historical figure known as the 'Iron Chancellor'. This requires knowledge of prominent historical figures and their associated epithets.
Correct Option: C) Otto von Bismarck was the first Chancellor of the German Empire and is famously known as the "Iron Chancellor." He played a crucial role in the unification of Germany through a series of wars and diplomatic maneuvers, often employing a pragmatic and forceful approach to politics, which earned him this epithet.
To calculate the amount received after one year when interest is compounded quarterly, we need to use the compound interest formula. We will first determine the interest rate per compounding period and the total number of compounding periods, then apply the formula.
Since the interest is compounded quarterly, the annual rate needs to be divided by 4.
\[ i = \frac{R}{n} = \frac{0.40}{4} = 0.10 \]The total number of compounding periods is the number of years multiplied by the compounding frequency per year.
\[ N = T \times n = 1 \times 4 = 4 \]The formula for the amount \((A)\) after compound interest is:
\[ A = P \left(1 + i\right)^N \]B) Rs. 146.41 is the correct amount received after one year when Rs. 100 is invested at 40% annual interest compounded quarterly.
An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 600 J, find the height at which the object is with respect to the ground. Given g = 10 ms-2
To find the height of the object, we need to use the formula for gravitational potential energy, which relates mass, gravitational acceleration, and height. We are given the mass of the object, its potential energy, and the value of gravitational acceleration.
The potential energy (\(PE\)) of an object at a certain height (\(h\)) above the ground is given by:
\[ PE = mgh \]To find the height, we can rearrange the formula as follows:
\[ h = \frac{PE}{mg} \]A) 5 m is the correct height calculated using the potential energy formula.
This problem can be solved by setting up a system of linear equations based on the given information about the ages of Anusri and Yashomati. We will define variables for their present ages and then translate the given conditions into equations. Finally, we will solve for Yashomati's present age.
Let Anusri's present age be \(A\) years.
Let Yashomati's present age be \(Y\) years.
"Anusri is eleven years younger than Yashomati."
This means Yashomati is eleven years older than Anusri.
\[ Y = A + 11 \quad (1) \]"Fifteen years from now, Yashomati’s age will be three times Anusri’s present age."
Yashomati's age fifteen years from now will be \(Y + 15\).
Anusri's present age is \(A\).
So, we have:
\[ Y + 15 = 3A \quad (2) \]We have two equations:
1) \(Y = A + 11\)
2) \(Y + 15 = 3A\)
Substitute the expression for \(Y\) from equation (1) into equation (2):
\[ (A + 11) + 15 = 3A \]\[ A + 26 = 3A \]Subtract \(A\) from both sides:
\[ 26 = 3A - A \]\[ 26 = 2A \]\[ A = \frac{26}{2} \]\[ A = 13 \]Now that we have Anusri's present age (\(A = 13\)), substitute this value back into equation (1) to find Yashomati's present age:
\[ Y = A + 11 \]\[ Y = 13 + 11 \]\[ Y = 24 \]Therefore, Yashomati's present age is 24 years.
B) 24 years is the correct answer, as calculated from the given conditions.