To determine the correct order of periods in terms of the number of elements, we need to recall the structure of the modern periodic table and the number of elements present in each period.
Now, let's list the number of elements for each period:
Comparing these numbers, we can establish the following order:
\(1 < 2 = 3 < 4 = 5 < 6 = 7\)
B) \(1 < 2 = 3 < 4 = 5 < 6 = 7\)
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. The key is to draw the most restrictive diagram first and then consider alternative diagrams if a conclusion is not definitively true or false.
Combining these, we get a nested structure: Singers are inside Musicians, and Musicians are inside Actors. The set of Boys is separate from Singers.
Let's visualize this:
C) Only conclusion I follows
The question asks about the components of the human excretory system. We need to identify the correct combination of organs that form this system.
Combining these components, the human excretory system consists of one pair of kidneys, one pair of ureters, a single urinary bladder, and a single urethra.
C) One pair of kidneys, one pair of ureters, single urinary bladder and single urethra. This option accurately lists all the components of the human excretory system with their correct numbers.
We are given three numbers in a specific ratio and their Least Common Multiple (LCM). We need to find their Highest Common Factor (HCF). We can represent the numbers using the HCF as a common factor and then use the property that for numbers \(a \cdot x, a \cdot y, a \cdot z\), their LCM is \(a \cdot \text{LCM}(x, y, z)\).
Let the three numbers be \(N_1, N_2, N_3\). Their ratio is given as \(4 : 5 : 7\).
Let \(H\) be the HCF of these three numbers. Then, the numbers can be expressed as multiples of \(H\):
\[ N_1 = 4H \] \[ N_2 = 5H \] \[ N_3 = 7H \]The LCM of these three numbers can be found. Since 4, 5, and 7 are pairwise coprime (they have no common factors other than 1), the LCM of \(4H, 5H, 7H\) is \(H \times \text{LCM}(4, 5, 7)\).
Calculate the LCM of 4, 5, and 7:
\[ \text{LCM}(4, 5, 7) = 4 \times 5 \times 7 = 20 \times 7 = 140 \]So, the LCM of the three numbers \(N_1, N_2, N_3\) is \(140H\).
We are given that the LCM of the numbers is 5600. Therefore, we can set up the equation:
\[ 140H = 5600 \]Solve for \(H\):
\[ H = \frac{5600}{140} \] \[ H = \frac{560}{14} \] \[ H = 40 \]Thus, the HCF of the three numbers is 40.
Correct Option: B) 40
This is a logical reasoning problem involving ordering and arrangement. We need to deduce the travel month for each of the five persons (P, Q, R, S, T) based on the given clues. We will create a table of months and fill in the persons step-by-step.
| Month | Person |
|---|---|
| January | |
| February | P |
| March | |
| April | |
| May |
| Month | Person |
|---|---|
| January | |
| February | P |
| March | |
| April | R |
| May |
| Month | Person |
|---|---|
| January | S |
| February | P |
| March | |
| April | R |
| May | Q |
| Month | Person |
|---|---|
| January | S |
| February | P |
| March | T |
| April | R |
| May | Q |
D) S travelled in January, as deduced from the given clues and step-by-step arrangement.
The problem asks us to perform an operation based on specific digits from the largest and smallest numbers in a given set of three-digit numbers. We need to identify the largest and smallest numbers first, then extract the required digits, and finally perform the addition.
A) 7 is the correct answer because, as calculated, the sum of the second digit of the largest number (2) and the third digit of the smallest number (5) is 7.
The number of valence electrons of an atom is determined by its atomic number. The atomic number represents the number of protons in the nucleus, which in a neutral atom is equal to the number of electrons. These electrons are arranged in shells around the nucleus. The outermost shell's electrons are called valence electrons.
A) 6 — An atom with atomic number 6 (Carbon) has 6 electrons. Its electron configuration is 2, 4. The outermost shell contains 4 electrons, which are its valence electrons.
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the letters of the original words into their coded forms and then apply the same rule to the target word 'CLEAR'.
Correct Option: A) EPKIB
The value of (0.1 × 0.001 × 0.0001 × 10⁶) is:
To solve this problem, we will convert all decimal numbers into fractions or powers of 10. Then, we will multiply these terms and simplify the expression to find the final value.
Convert decimals to powers of 10:
Substitute these values into the expression:
\[ (0.1 \times 0.001 \times 0.0001 \times 10^6) = (10^{-1} \times 10^{-3} \times 10^{-4} \times 10^6) \]Apply the rule of exponents \(a^m \times a^n = a^{m+n}\):
\[ 10^{(-1) + (-3) + (-4) + 6} \]Calculate the sum of the exponents:
\[ -1 - 3 - 4 + 6 = -8 + 6 = -2 \]The expression simplifies to:
\[ 10^{-2} \]Convert back to a decimal or fraction:
\[ 10^{-2} = \frac{1}{10^2} = \frac{1}{100} \]D) \( \frac{1}{100} \) is the correct answer, as derived from the step-by-step calculation.
To find the ratio of the surface areas of two spheres given the ratio of their volumes, we first need to establish the relationship between volume, radius, and surface area of a sphere. We will use the given volume ratio to find the ratio of their radii, and then use the radius ratio to find the ratio of their surface areas.
Recall the formulas for volume and surface area of a sphere:
Set up the ratio of volumes: Let the radii of the two spheres be \(r_1\) and \(r_2\), and their volumes be \(V_1\) and \(V_2\). We are given \(V_1 : V_2 = 216 : 125\).
\[ \frac{V_1}{V_2} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3 \]So, we have:
\[ \left(\frac{r_1}{r_2}\right)^3 = \frac{216}{125} \]Find the ratio of their radii: To find the ratio of radii, take the cube root of both sides:
\[ \frac{r_1}{r_2} = \sqrt[3]{\frac{216}{125}} = \frac{\sqrt[3]{216}}{\sqrt[3]{125}} = \frac{6}{5} \]So, \(r_1 : r_2 = 6 : 5\).
Set up the ratio of surface areas: Let the surface areas of the two spheres be \(A_1\) and \(A_2\).
\[ \frac{A_1}{A_2} = \frac{4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{r_2^2} = \left(\frac{r_1}{r_2}\right)^2 \]Calculate the ratio of surface areas: Substitute the ratio of radii we found:
\[ \frac{A_1}{A_2} = \left(\frac{6}{5}\right)^2 = \frac{6^2}{5^2} = \frac{36}{25} \]Thus, the ratio of their surface areas is \(36 : 25\).
Correct Option: B) 36 : 25