To solve this problem, we need to compare the original positions of the letters in the given word with their positions after arranging them in alphabetical order. We will list the original word and its positions, then sort the letters alphabetically and list their new positions, and finally count how many letters retain their original position.
Therefore, only one letter's position remains unchanged.
Correct Option: D) One
This problem involves tracking movements in different directions. We can solve it by breaking down Ravi's journey into components along the North-South and East-West axes. We will assign positive values for North and East movements and negative values for South and West movements.
Therefore, Ravi is 30 m South from point A.
Correct Option: B) 30 m, South
This is a direction and distance problem. We need to track the movements in the East-West and North-South directions separately to find the net displacement and final direction from the starting point (restaurant) to the end point (apartment).
Correct Option: A) 423 m, South
Which of the following chemical reactions is balanced?
Zn + H₂SO₄ → ZnSO₄ + H₂
Fe + H₂O → Fe₃O₄ + H₂
Fe + 4H₂O → Fe₃O₄ + 4H₂
Mg + O₂ → MgO
To determine if a chemical reaction is balanced, we need to ensure that the number of atoms of each element on the reactant side (left side of the arrow) is equal to the number of atoms of the same element on the product side (right side of the arrow). This adheres to the Law of Conservation of Mass.
Correct Option: A) \( \text{Zn} + \text{H}_2\text{SO}_4 \rightarrow \text{ZnSO}_4 + \text{H}_2 \)
This reaction is balanced because the number of atoms of each element is the same on both sides of the equation:
The question asks to identify the process when a reactant gains oxygen. This relates to the fundamental definitions of oxidation and reduction in chemistry.
Correct Option: B) oxidation — Oxidation is defined as the gain of oxygen, loss of hydrogen, or loss of electrons by a substance.
The problem asks us to modify a given set of five three-digit numbers by adding 4 to the second digit of each number. Then, we need to count how many of these new numbers have a second digit that is exactly divisible by their third digit.
Correct Option: B) Three
To find the largest four-digit number that leaves a remainder of 4 when divided by 7, 11, and 13, we first need to find the Least Common Multiple (LCM) of 7, 11, and 13. Then, we find the largest four-digit multiple of this LCM and add the remainder 4 to it.
Find the LCM of 7, 11, and 13:
Since 7, 11, and 13 are all prime numbers, their LCM is simply their product.
\[ \text{LCM}(7, 11, 13) = 7 \times 11 \times 13 \]\[ \text{LCM}(7, 11, 13) = 77 \times 13 \]\[ \text{LCM}(7, 11, 13) = 1001 \]Identify the largest four-digit number:
The largest four-digit number is 9999.
Find the largest multiple of the LCM (1001) that is less than or equal to 9999:
Divide 9999 by 1001 to find the quotient.
\[ 9999 \div 1001 \]\[ 9999 = 1001 \times 9 + 990 \]The quotient is 9, and the remainder is 990. This means that \(1001 \times 9\) is the largest multiple of 1001 that is less than 9999.\[ 1001 \times 9 = 9009 \]Add the required remainder:
The number that leaves a remainder of 4 when divided by 7, 11, and 13 will be of the form \((\text{LCM} \times k) + 4\). In this case, it will be \(9009 + 4\).
\[ 9009 + 4 = 9013 \]B) 9013 is the largest four-digit number which when divided by 7, 11, and 13 leaves a remainder of 4 in each case.
This problem involves solving a system of linear equations based on age ratios at different points in time. We will set up equations for the ages of A and B at present, 10 years ago, and 15 years from now, and then solve for their current ages to find A's age 15 years from now.
Let the present ages of A and B be \(A_p\) and \(B_p\) respectively.
10 years ago: Their ages were \(A_p - 10\) and \(B_p - 10\). The ratio was 5:9.
\[ \frac{A_p - 10}{B_p - 10} = \frac{5}{9} \]Cross-multiplying gives:
\[ 9(A_p - 10) = 5(B_p - 10) \] \[ 9A_p - 90 = 5B_p - 50 \] \[ 9A_p - 5B_p = 40 \quad \text{(Equation 1)} \]15 years from now: Their ages will be \(A_p + 15\) and \(B_p + 15\). The ratio will be 15:17.
\[ \frac{A_p + 15}{B_p + 15} = \frac{15}{17} \]Cross-multiplying gives:
\[ 17(A_p + 15) = 15(B_p + 15) \] \[ 17A_p + 255 = 15B_p + 225 \] \[ 17A_p - 15B_p = 225 - 255 \] \[ 17A_p - 15B_p = -30 \quad \text{(Equation 2)} \]Solve the system of equations: We have two linear equations:
Equation 1: \(9A_p - 5B_p = 40\)
Equation 2: \(17A_p - 15B_p = -30\)
Multiply Equation 1 by 3 to make the coefficient of \(B_p\) the same as in Equation 2:
\[ 3 \times (9A_p - 5B_p) = 3 \times 40 \] \[ 27A_p - 15B_p = 120 \quad \text{(Equation 3)} \]Now subtract Equation 2 from Equation 3:
\[ (27A_p - 15B_p) - (17A_p - 15B_p) = 120 - (-30) \] \[ 27A_p - 15B_p - 17A_p + 15B_p = 120 + 30 \] \[ 10A_p = 150 \] \[ A_p = \frac{150}{10} \] \[ A_p = 15 \text{ years} \]So, A's present age is 15 years.
Calculate A's age 15 years from now: The question asks for A's age 15 years from now.
\[ \text{A's age (15 years from now)} = A_p + 15 \] \[ = 15 + 15 \] \[ = 30 \text{ years} \]A) 30 years is the correct answer, as calculated above.
The problem asks us to find the focal length of a convex lens given its power. We will use the fundamental relationship between the power of a lens and its focal length, paying attention to the sign convention for convex lenses.
A) +0.33 m — This is the correct focal length calculated from the given power, and the positive sign correctly indicates a convex lens.
The first Digital Food Museum in India was launched in ______ in the year 2021.
The question asks for the state where India's first Digital Food Museum was launched in 2021. This is a factual recall question related to current affairs and general knowledge about significant national initiatives.
C) Tamil Nadu — The first Digital Food Museum in India was indeed launched in Thanjavur, Tamil Nadu, in 2021. Thanjavur is known as the 'rice bowl' of Tamil Nadu and has a rich agricultural history, making it a fitting location for such a museum.