To find the Least Common Multiple (LCM) of a set of numbers, we can use the prime factorization method or the division method. The LCM is the smallest positive integer that is a multiple of all the given numbers. In this case, since 20 and 60 are factors of 120, the LCM will be 120 itself.
D) 120 is the correct answer because it is the smallest number that is a multiple of 20, 120, and 60.
What is the relation between m, v, and u for a spherical mirror?
m = v × u
m = \( \frac{v}{u} \)
m = \( \frac{-v}{u} \)
m = -v × u
This question asks for the relationship between magnification (m), image distance (v), and object distance (u) for a spherical mirror. This is a fundamental formula in optics.
C) m = \( \frac{-v}{u} \) is the correct relation for linear magnification in spherical mirrors. The negative sign is crucial and indicates the orientation of the image relative to the object.
The problem requires us to transform each letter in the word HOCKEY based on whether it's a vowel or a consonant. Vowels are changed to the next letter in the alphabet, and consonants are changed to the preceding letter. After transformation, the new letters must be arranged alphabetically, and we need to find the fourth letter from the right.
The transformed letters are: G, P, B, J, F, X.
B, F, G, J, P, X
Counting from the right: X (1st), P (2nd), J (3rd), G (4th).
The fourth letter from the right is G.
B) G is the fourth letter from the right after applying the transformations and arranging alphabetically.
To calculate the compound interest, we first need to find the total amount accumulated after 3 years using the compound interest formula. Then, we subtract the principal amount from the total amount to get the compound interest.
Identify the given values:
Use the compound interest formula to find the total amount \(A\):
\[ A = P \left(1 + \frac{R}{100}\right)^T \]Substitute the given values into the formula:
\[ A = 82000 \left(1 + \frac{6}{100}\right)^3 \] \[ A = 82000 \left(1 + 0.06\right)^3 \] \[ A = 82000 (1.06)^3 \]Calculate \((1.06)^3\):
\[ (1.06)^3 = 1.06 \times 1.06 \times 1.06 = 1.191016 \]Calculate the total amount \(A\):
\[ A = 82000 \times 1.191016 \] \[ A = 97663.312 \]Calculate the compound interest (CI):
\[ \text{CI} = A - P \] \[ \text{CI} = 97663.312 - 82000 \] \[ \text{CI} = 15663.312 \]Round the compound interest to the nearest rupee:
\[ \text{CI} \approx \text{₹}15,663 \]C) ₹15,663 is the compound interest rounded to the nearest rupee.
The correct relation between the focal length of a lens and its power is:
P = \( \frac{1}{f} \)
P = \( \frac{-1}{f} \)
P ∝ f
P = f
The question asks for the correct relationship between the power of a lens and its focal length. This is a fundamental concept in optics, particularly in the study of lenses.
A) P = \( \frac{1}{f} \) is the correct relation. This formula directly defines the power of a lens as the reciprocal of its focal length, provided the focal length is in metres.
This is a linear seating arrangement puzzle. We need to deduce the positions of individuals based on the given clues and then count the total number of people. We will build the arrangement step-by-step, starting with the most definitive clues.
C) 12 is the total number of persons seated in the row based on the step-by-step arrangement.
The question asks for the formula representing Joule's heating effect. This effect describes the heat produced when an electric current flows through a conductor due to its resistance. We need to recall the fundamental formulas relating electrical power, energy, and Ohm's Law.
Correct Option: C) H = VIt
This formula directly represents the heat produced (\(H\)) when a current (\(I\)) flows through a conductor with a voltage (\(V\)) across it for a time (\(t\)). It is derived from the definition of electrical power (\(P = VI\)) and the relation between energy and power (\(H = P \times t\)).
The question asks to identify which pair of elements would have similar properties according to Newlands' Law of Octaves. This law states that when elements are arranged in increasing order of their atomic masses, the properties of every eighth element are similar to the first, much like the notes in a musical octave.
| Note | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th |
|---|---|---|---|---|---|---|---|
| Sa (do) | Li | Be | B | C | N | O | F |
| Re (re) | Na | Mg | Al | Si | P | S | Cl |
| Ga (mi) | K | Ca | Cr | Ti | Mn | Fe | Co & Ni |
Based on the arrangement, Be and Mg are an octave apart and thus would exhibit similar properties.
A) Be and Mg - According to Newlands' Law of Octaves, if we start from Beryllium (Be), the eighth element is Magnesium (Mg). Thus, they are expected to have similar properties.
To solve this problem, we first need to identify the original number. Then, we apply the given operation (adding 1 to each digit) to form a new number. Finally, we identify the fourth, fifth, and sixth digits from the left in the new number and calculate their sum.
Identify the original number: The given number is 870548362.
Apply the operation to each digit: Add 1 to each digit of the number.
The new number formed by these digits is 981659473.
Identify the fourth, fifth, and sixth digits from the left in the new number:
Calculate the sum of the fourth, fifth, and sixth digits:
\[ \text{Sum} = 6 + 5 + 9 = 20 \]C) 20 — As calculated, the sum of the fourth, fifth, and sixth digits of the modified number is 20.
This is a syllogism problem that can be solved using Venn diagrams to visualize the relationships between the categories (plums, guavas, mangoes, kiwis) described in the statements. We will draw diagrams based on the given statements and then check if the conclusions logically follow.
Correct Option: A) Neither conclusion I nor II follows