The question asks about the head of a Municipal Corporation under normal circumstances. This requires knowledge of the structure and leadership roles within urban local self-government bodies in India.
D) The Mayor is the political and ceremonial head of the Municipal Corporation. He/She presides over the meetings of the Corporation and is responsible for its overall functioning in a leadership capacity.
The question asks to identify the specific Article of the Indian Constitution that declares Hindi as the official language of the Union. This requires knowledge of the constitutional provisions related to official languages.
Correct Option: D) Article 343 explicitly states that Hindi in Devanagari script shall be the official language of the Union.
The area of a rhombus can be calculated using the lengths of its diagonals. The formula for the area of a rhombus is half the product of its diagonals.
Correct Option: D) 48
To determine the day of the week on 29 January 2021, given that 26 January 2018 is a Friday, we need to calculate the total number of odd days between these two dates. Odd days are the remainder when the total number of days is divided by 7. Each year contributes 1 odd day, and a leap year contributes 2 odd days.
The year 2018 is not a leap year (it is not divisible by 4). So, it has 365 days.
Number of odd days \( = 365 \pmod{7} = 1 \).
The year 2019 is not a leap year. So, it has 365 days.
Number of odd days \( = 365 \pmod{7} = 1 \).
The year 2020 is a leap year (it is divisible by 4). So, it has 366 days.
Number of odd days \( = 366 \pmod{7} = 2 \).
Total odd days \( = 1 + 1 + 2 = 4 \).
Since 26 January 2018 is a Friday, 26 January 2021 will be Friday + 4 days.
Friday + 4 days = Tuesday.
We need to find the day for 29 January 2021. We know 26 January 2021 is a Tuesday.
A) Friday
As calculated, 29 January 2021 will be a Friday.
Simplify the following expression:
\(\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}\)
To simplify the given trigonometric expression, we will combine the two fractions by finding a common denominator. Then, we will use the fundamental trigonometric identity \(\sin^2 A + \cos^2 A = 1\) to further simplify the numerator and finally express the result in terms of basic trigonometric ratios.
The given expression is:
\[ \frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A} \]Find a common denominator, which is \((1+\sin A)(\cos A)\). Combine the fractions:
\[ \frac{\cos A \cdot \cos A + (1+\sin A) \cdot (1+\sin A)}{(1+\sin A)(\cos A)} \]Simplify the numerator:
\[ \frac{\cos^2 A + (1+\sin A)^2}{(1+\sin A)(\cos A)} \]Expand \((1+\sin A)^2\) using the formula \((a+b)^2 = a^2 + 2ab + b^2\):
\[ (1+\sin A)^2 = 1^2 + 2(1)(\sin A) + \sin^2 A = 1 + 2\sin A + \sin^2 A \]Substitute this back into the numerator:
\[ \frac{\cos^2 A + 1 + 2\sin A + \sin^2 A}{(1+\sin A)(\cos A)} \]Rearrange the terms in the numerator and use the identity \(\sin^2 A + \cos^2 A = 1\):
\[ \frac{(\sin^2 A + \cos^2 A) + 1 + 2\sin A}{(1+\sin A)(\cos A)} \]\[ \frac{1 + 1 + 2\sin A}{(1+\sin A)(\cos A)} \]\[ \frac{2 + 2\sin A}{(1+\sin A)(\cos A)} \]Factor out 2 from the numerator:
\[ \frac{2(1 + \sin A)}{(1+\sin A)(\cos A)} \]Cancel out the common term \((1+\sin A)\) from the numerator and the denominator:
\[ \frac{2}{\cos A} \]Recall that \(\frac{1}{\cos A} = \sec A\). Therefore, the expression simplifies to:
\[ 2\sec A \]A) 2 sec A is the correct simplification of the given expression.
The electronic configuration of an element describes the distribution of electrons in its atomic orbitals. The numbers in the configuration (e.g., 2, 8, 4) represent the number of electrons in successive electron shells (K, L, M, etc.). The sum of these numbers gives the total number of electrons in a neutral atom, which is equal to its atomic number.
Correct Option: C) Si
To find the selling price after successive discounts, we first calculate the price after the first discount, and then apply the second discount to this new price. Alternatively, we can use a direct formula for successive discounts.
C) Rs 316.80 is the selling price of the article after successive discounts.
This problem involves setting up and solving a system of linear equations based on the given age relationships. We will define variables for the present ages of Ritesh and Mohit, form equations from the given conditions, and then solve for Mohit's present age.
Define variables for present ages:
Let Ritesh's present age be \(R\) years.
Let Mohit's present age be \(M\) years.
Formulate the first equation from the first condition:
"Ritesh is 12 years older than Mohit."
\[ R = M + 12 \quad \text{(Equation 1)} \]Determine their ages 17 years ago:
Ritesh's age 17 years ago was \(R - 17\) years.
Mohit's age 17 years ago was \(M - 17\) years.
Formulate the second equation from the second condition:
"17 years ago, Ritesh’s age was four times of Mohit’s age."
\[ R - 17 = 4(M - 17) \quad \text{(Equation 2)} \]Solve the system of equations:
Substitute Equation 1 into Equation 2:
\[ (M + 12) - 17 = 4(M - 17) \]\[ M - 5 = 4M - 68 \]Isolate \(M\):
Add 68 to both sides:
\[ M - 5 + 68 = 4M \]\[ M + 63 = 4M \]Subtract \(M\) from both sides:
\[ 63 = 4M - M \]\[ 63 = 3M \]Divide by 3:
\[ M = \frac{63}{3} \]\[ M = 21 \]Thus, Mohit's present age is 21 years.
C) 21
To find the approximate value, we will first round off each number in the given equation to the nearest whole number. Then, we will perform the operations (multiplication, addition, and subtraction) following the order of operations (BODMAS/PEMDAS).
The original equation is \(12.99 - 3.02 + 11.89 \times 9.19 = ?\)
After rounding, it becomes:
\[ 13 - 3 + 12 \times 9 = ? \]A) 118 is the closest approximate value.
The question asks to identify the animal where sex determination is NOT genetically controlled. This means we need to find an animal whose sex is determined by environmental factors rather than chromosomes.
D) Snails — Many snail species exhibit environmental sex determination or sequential hermaphroditism, where sex is influenced by factors other than genetics at conception, such as age, size, or environmental cues.