The question asks to identify the author of the book "Gita Rahasya", which is a philosophical interpretation of the Bhagavad Gita. This is a direct factual question related to prominent figures of the Indian independence movement and their literary contributions.
B) Bal Gangadhar Tilak wrote the book "Gita Rahasya". He penned this influential philosophical treatise during his imprisonment in Mandalay, Burma. The book is a comprehensive analysis of the Bhagavad Gita, advocating for the philosophy of Karma Yoga, which emphasizes the importance of selfless action.
The question asks to identify the state of matter for which the Meissner effect is a defining characteristic. We need to recall the properties of different states of matter, particularly those related to magnetism and conductivity, to determine which one exhibits the Meissner effect.
Correct Option: D) Superconducting state — The Meissner effect is the complete expulsion of magnetic field lines from the interior of a superconductor when it transitions to the superconducting state. This perfect diamagnetism is a hallmark of superconductivity, alongside zero electrical resistance.
This is a logical reasoning problem involving arrangement. We need to deduce the floor on which each person lives based on the given clues and then determine the number of people between O and M.
Correct Option: D) Two
This problem requires us to apply a set of given symbol interchanges to a mathematical expression and then evaluate the modified expression following the order of operations (BODMAS/PEMDAS).
First, perform multiplication and division from left to right.
Substitute these values back into the equation:
\[ 612 - 54 + 104 = ? \]Next, perform addition and subtraction from left to right.
Correct Option: A) 662
The question asks to identify the film that won the 2025 Golden Globe Award for Best Motion Picture – Non-English Language. This requires knowledge of recent international film awards.
Correct Option: C) Emilia Pérez won the 2025 Golden Globe Award for Best Motion Picture – Non-English Language. This French musical crime comedy film, directed by Jacques Audiard, was a significant winner at the awards ceremony.
The question asks to identify the specific day in December 2024 that honours Dr. B.R. Ambedkar's contribution to social justice. This requires knowledge of important dates associated with Dr. Ambedkar.
Correct Option: A) Mahaparinirvan Diwas is observed on December 6th every year to commemorate the death anniversary of Dr. B.R. Ambedkar. This day honours his immense contributions to social justice, equality, and the drafting of the Indian Constitution.
The given series is a decreasing sequence of numbers. We need to find the pattern of subtraction between consecutive terms to predict the next number in the series.
Identify the given series: 601, 600, 597, 592, 585, ?
Calculate the difference between consecutive terms:
Difference between the 1st and 2nd term: \(601 - 600 = 1\)
Difference between the 2nd and 3rd term: \(600 - 597 = 3\)
Difference between the 3rd and 4th term: \(597 - 592 = 5\)
Difference between the 4th and 5th term: \(592 - 585 = 7\)
Observe the pattern of the differences: 1, 3, 5, 7. This is a sequence of consecutive odd numbers.
Following this pattern, the next difference should be the next odd number after 7, which is 9.
Subtract this next difference from the last term of the given series to find the missing number:
\[ 585 - 9 = 576 \]Therefore, the missing number in the series is 576.
Correct Option: A) 576
If the ratio of two numbers is 3 : 16 and the product of their LCM and their HCF is 432, then the sum of the reciprocals of the LCM and the HCF is:
\( \frac{49}{151} \)
\( \frac{49}{145} \)
\( \frac{49}{144} \)
\( \frac{49}{159} \)
We are given the ratio of two numbers and the product of their LCM and HCF. We need to find the sum of the reciprocals of the LCM and HCF. We will use the fundamental property that for any two numbers, the product of the numbers is equal to the product of their LCM and HCF.
Let the two numbers be \(a\) and \(b\). Given that their ratio is \(3:16\), we can write them as \(a = 3x\) and \(b = 16x\) for some common factor \(x\).
We know the property: Product of two numbers = Product of their LCM and HCF.
So, \(a \times b = \text{LCM} \times \text{HCF}\).
We are given that the product of their LCM and HCF is 432.
Therefore, \(a \times b = 432\).
Substitute the expressions for \(a\) and \(b\) into the equation:
\[ (3x) \times (16x) = 432 \]\[ 48x^2 = 432 \]Solve for \(x^2\):
\[ x^2 = \frac{432}{48} \]\[ x^2 = 9 \]Solve for \(x\):
\[ x = \sqrt{9} \]\[ x = 3 \quad (\text{since numbers are positive}) \]Now find the two numbers:
\[ a = 3x = 3 \times 3 = 9 \]\[ b = 16x = 16 \times 3 = 48 \]Next, calculate the HCF and LCM of 9 and 48.
Prime factorization of 9: \(3^2\)
Prime factorization of 48: \(2^4 \times 3\)
The HCF (Highest Common Factor) is the product of the lowest powers of common prime factors:
\( \text{HCF}(9, 48) = 3^1 = 3 \)
The LCM (Least Common Multiple) is the product of the highest powers of all prime factors:
\( \text{LCM}(9, 48) = 2^4 \times 3^2 = 16 \times 9 = 144 \)
Verify the given condition: Product of LCM and HCF = \(144 \times 3 = 432\). This matches the given information.
Finally, we need to find the sum of the reciprocals of the LCM and the HCF:
\[ \frac{1}{\text{LCM}} + \frac{1}{\text{HCF}} = \frac{1}{144} + \frac{1}{3} \]To add these fractions, find a common denominator, which is 144:
\[ \frac{1}{144} + \frac{1 \times 48}{3 \times 48} = \frac{1}{144} + \frac{48}{144} \]\[ = \frac{1 + 48}{144} = \frac{49}{144} \]C) \( \frac{49}{144} \) is the correct answer, as calculated above.
This question tests the understanding of the geometric properties of a rhombus, specifically concerning its diagonals. We need to recall the definitions and characteristics of a rhombus and its diagonals to identify the correct statement.
B) The diagonals of a rhombus are not equal, intersect at right angles and bisect each other. This statement accurately describes all three key properties of the diagonals of a rhombus: they are generally not equal, they always intersect at 90 degrees, and they always bisect each other.
The problem asks us to find the breadth of a cuboid tank given its capacity (volume), length, and depth. We need to convert the capacity from litres to cubic meters and then use the formula for the volume of a cuboid.
We know that \(1000\) litres is equal to \(1\) cubic meter.
\[ 1 \text{ m}^3 = 1000 \text{ litres} \]Therefore, to convert litres to cubic meters, we divide by \(1000\).Given capacity = \(70,000\) litres.
\[ \text{Capacity in m}^3 = \frac{70,000}{1000} \text{ m}^3 = 70 \text{ m}^3 \]The volume of a cuboid is given by the product of its length, breadth, and depth.
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Depth} \]Given:
So, the equation becomes:
\[ 70 = 4 \times B \times 10 \]Simplify the right side of the equation:
\[ 70 = 40 \times B \]To find \(B\), divide both sides by \(40\):\[ B = \frac{70}{40} \]\[ B = \frac{7}{4} \]\[ B = 1.75 \text{ m} \]A) 1.75 m — This is the correct breadth calculated from the given volume, length, and depth.