This problem requires calculating simple interest. The formula for simple interest is \(I = \frac{P \times R \times T}{100}\), where \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time period in years.
The formula for simple interest is:
\[ I = \frac{P \times R \times T}{100} \]The interest Anita has to pay at the end of one year is ₹750.
Correct Option: D) ₹750 is the correct amount of simple interest calculated for the given principal, rate, and time.
If '÷' stands for 'addition', '+' stands for 'subtraction', '×' stands for 'division and '–' stands for 'multiplication', then which of the following equations will NOT be correct?
36 × 4 + 3 – 6 ÷ 16 = 7
36 + 4 ÷ 3 × 6 – 16 = 40
36 – 4 × 3 + 6 ÷ 16 = 60
36 ÷ 4 – 3 × 6 + 16 = 22
This problem involves symbol substitution and then evaluating mathematical expressions using the BODMAS/PEMDAS rule. We need to substitute the given symbols with their new meanings and then check each equation to find which one does not hold true.
The given symbol substitutions are:
Let's evaluate each option after substituting the symbols:
Original equation: \(36 \times 4 + 3 \text{ – } 6 \div 16 = 7\)
After substitution:
\[ 36 \div 4 - 3 \times 6 + 16 \]\[ 9 - 3 \times 6 + 16 \]\[ 9 - 18 + 16 \]\[ -9 + 16 \]\[ 7 \]Since \(7 = 7\), this equation is correct.
Original equation: \(36 + 4 \div 3 \times 6 \text{ – } 16 = 40\)
After substitution:
\[ 36 - 4 + 3 \div 6 \times 16 \]\[ 32 + 0.5 \times 16 \]\[ 32 + 8 \]\[ 40 \]Since \(40 = 40\), this equation is correct.
Original equation: \(36 \text{ – } 4 \times 3 + 6 \div 16 = 60\)
After substitution:
\[ 36 \times 4 \div 3 - 6 + 16 \]\[ 144 \div 3 - 6 + 16 \]\[ 48 - 6 + 16 \]\[ 42 + 16 \]\[ 58 \]Since \(58 \neq 60\), this equation is NOT correct.
Original equation: \(36 \div 4 \text{ – } 3 \times 6 + 16 = 22\)
After substitution:
\[ 36 + 4 \times 3 \div 6 - 16 \]\[ 36 + 12 \div 6 - 16 \]\[ 36 + 2 - 16 \]\[ 38 - 16 \]\[ 22 \]Since \(22 = 22\), this equation is correct.
C) \(36 \text{ – } 4 \times 3 + 6 \div 16 = 60\) is the equation that is NOT correct after substituting the symbols and evaluating.
The problem involves finding the number of ₹50 notes given the total amount of money, the denominations of the notes, and the ratio of the number of notes for each denomination. We will use the given ratio to express the number of notes of each denomination in terms of a common variable, then calculate the total value based on these expressions, and finally solve for the variable to find the actual number of notes.
Let the number of notes of ₹100, ₹50, and ₹10 be \(5x\), \(8x\), and \(10x\) respectively, as their ratio is given as \(5:8:10\).
Calculate the total value contributed by each denomination:
The total amount in the bag is ₹3,000. So, the sum of the values from all denominations must equal ₹3,000:
\[ 500x + 400x + 100x = 3000 \]
Combine the terms with \(x\):
\[ 1000x = 3000 \]
Solve for \(x\):
\[ x = \frac{3000}{1000} \]
\[ x = 3 \]
The question asks for the number of ₹50 notes. From step 1, the number of ₹50 notes is \(8x\).
\[ \text{Number of ₹50 notes} = 8 \times 3 = 24 \]
C) 24. As calculated, the number of ₹50 notes is 24.
The question asks about the PAHAL scheme. To answer this, one needs to recall the full form and primary objective of the PAHAL scheme, which is a significant government initiative.
Correct Option: C) Direct transfer of LPG subsidy
The problem presents a series of letter-clusters. To find the missing cluster, we need to identify the pattern in how the letters in each position change from one cluster to the next.
B) GRU is the correct option because it follows the established pattern where each letter in the cluster increments by one position in the alphabet from the corresponding letter in the previous cluster.
The question asks to identify an allotropic form of carbon from the given options. Allotropy is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of these elements. Allotropes are different structural modifications of an element.
Correct Option: C) Diamond is a crystalline allotrope of carbon. In diamond, each carbon atom is \(\text{sp}^3\) hybridized and covalently bonded to four other carbon atoms in a tetrahedral arrangement, forming a giant covalent structure. This structure accounts for its extreme hardness and high melting point.
The question asks about the acid used in the anodising process. Anodising is an electrolytic passivation process used to increase the thickness of the natural oxide layer on the surface of metal parts, most commonly aluminium. The choice of electrolyte is crucial for forming the desired oxide layer.
Correct Option: B) Dilute sulphuric acid is the most commonly used acid in the anodising process, especially for aluminium, to create a protective and decorative oxide layer.
The internal measures of a cuboidal room are 12 m × 8 m × 4 m, with the height being 4 m. Find the total cost of whitewashing all four walls along with ceiling of the room, if the cost of white washing is ₹5 per sq. m.
To find the total cost of whitewashing, we first need to calculate the total area to be whitewashed. This includes the area of the four walls and the area of the ceiling. The floor is not whitewashed. Once the total area is found, we multiply it by the given cost per square meter.
D) ₹1,280 is the correct total cost of whitewashing the four walls and the ceiling.
When 0.434343..... is converted into a fraction, then the result will be:
\( \frac{43}{100} \)
\( \frac{4.3}{0.1} \)
\( \frac{43}{9.9} \)
\( \frac{43}{99} \)
The problem asks us to convert a repeating decimal into a fraction. We can solve this by setting the repeating decimal equal to a variable, multiplying by a power of 10 to shift the repeating part, and then subtracting the original equation from the new one to eliminate the repeating digits.
Thus, the fractional equivalent of \(0.434343...\) is \( \frac{43}{99} \).
D) \( \frac{43}{99} \) is the correct conversion of the repeating decimal to a fraction.
The question asks for the year in which the Constitution of India came into force. This is a fundamental fact about Indian history and polity, crucial for competitive exams.
Correct Option: B) 1950 — The Constitution of India was adopted on November 26, 1949, but it was formally enacted and came into full force on January 26, 1950. This date marks the establishment of India as a republic.