To determine the formula of the compound formed by elements A and B, we need to find their valencies. The valency of an element is determined by the number of electrons it needs to lose, gain, or share to achieve a stable noble gas configuration (usually an octet). Once the valencies are known, we can use the criss-cross method to write the chemical formula.
Determine the valency of element A:
The electronic configuration of element A is \(1s^2, 2s^2 2p^6, 3s^1\). The outermost shell is the 3rd shell, which contains 1 electron (\(3s^1\)). To achieve a stable octet (or duplet in the case of the first shell, but here it's the 2nd shell that would be full if the 3s electron is lost), element A will tend to lose this 1 electron. When it loses 1 electron, it forms a cation with a charge of \(+1\).
Thus, the valency of A is 1.
Determine the valency of element B:
The electronic configuration of element B is \(1s^2, 2s^2 2p^6, 3s^2 3p^4\). The outermost shell is the 3rd shell, which contains \(2 + 4 = 6\) electrons. To achieve a stable octet, element B will tend to gain 2 electrons. When it gains 2 electrons, it forms an anion with a charge of \(-2\).
Thus, the valency of B is 2.
Formulate the compound using the criss-cross method:
Element A has a valency of 1 (charge \(+1\)).
Element B has a valency of 2 (charge \(-2\)).
Using the criss-cross method, the numerical value of the valency of A becomes the subscript for B, and the numerical value of the valency of B becomes the subscript for A.
\[ \text{A}^{1+} \quad \text{B}^{2-} \]\[ \text{A}_2 \text{B}_1 \]The subscript 1 is usually omitted.Therefore, the formula of the compound is \(\text{A}_2\text{B}\).
Correct Option: B) A₂B
The question asks to identify which of the given options is NOT a hormone found in animals. To answer this, we need to recall the primary sources and functions of each substance listed.
B) Auxins are plant hormones responsible for cell elongation, apical dominance, and other growth processes in plants. They are not found in animals.
To determine which assumption is implicit, we need to analyze what must be true for the given statement to hold. An implicit assumption is something that is taken for granted or presupposed by the statement.
Correct Option: B) Only assumption II is implicit.
This problem involves rates of work, where the rate is the reciprocal of the time taken to complete a task (filling a sump). We will set up equations based on the given relationships between the times taken by the three tankers and then solve for the time taken by the first tanker.
Let the time taken by the first tanker to fill the sump be \(T_1\) hours.
The second tanker fills the sump 5 hours faster than the first tanker. So, the time taken by the second tanker is \(T_2 = T_1 - 5\) hours.
The second tanker fills the sump 4 hours slower than the third tanker. So, the time taken by the third tanker is \(T_3 = T_2 - 4 = (T_1 - 5) - 4 = T_1 - 9\) hours.
The problem states that the first two tankers operating simultaneously fill the sump in the same time during which the sump is filled by the third tanker alone. Let this time be \(T\). So, \(T = T_3\).
The rate of filling for a tanker is \(1/\text{time}\). When the first two tankers work simultaneously, their combined rate is the sum of their individual rates:
\[ \frac{1}{T_1} + \frac{1}{T_2} = \frac{1}{T} \]Since \(T = T_3\), we can write the equation as:
\[ \frac{1}{T_1} + \frac{1}{T_2} = \frac{1}{T_3} \]Substitute the expressions for \(T_2\) and \(T_3\) in terms of \(T_1\):
\[ \frac{1}{T_1} + \frac{1}{T_1 - 5} = \frac{1}{T_1 - 9} \]Combine the terms on the left side:
\[ \frac{(T_1 - 5) + T_1}{T_1 (T_1 - 5)} = \frac{1}{T_1 - 9} \] \[ \frac{2T_1 - 5}{T_1^2 - 5T_1} = \frac{1}{T_1 - 9} \]Cross-multiply:
\[ (2T_1 - 5)(T_1 - 9) = T_1^2 - 5T_1 \] \[ 2T_1^2 - 18T_1 - 5T_1 + 45 = T_1^2 - 5T_1 \] \[ 2T_1^2 - 23T_1 + 45 = T_1^2 - 5T_1 \]Rearrange the terms to form a quadratic equation:
\[ 2T_1^2 - T_1^2 - 23T_1 + 5T_1 + 45 = 0 \] \[ T_1^2 - 18T_1 + 45 = 0 \]Solve the quadratic equation by factoring. We need two numbers that multiply to 45 and add up to -18. These numbers are -3 and -15.
\[ (T_1 - 3)(T_1 - 15) = 0 \]This gives two possible values for \(T_1\): \(T_1 = 3\) or \(T_1 = 15\).
Check the validity of these solutions. If \(T_1 = 3\), then \(T_2 = T_1 - 5 = 3 - 5 = -2\) hours, which is not possible as time cannot be negative. Therefore, \(T_1 = 3\) is an invalid solution.
If \(T_1 = 15\), then:
All these times are positive, so \(T_1 = 15\) hours is a valid solution.
B) 15 hours is the time required by the first tanker.
The question asks about the central theme or inspiration behind the 2016 film 'Udta Punjab'. This requires knowledge of contemporary Indian cinema and the social issues it addresses.
Correct Option: B) Drug abuse in Punjab
To find the Marked Price (MP), we first need to calculate the Selling Price (SP) using the given Cost Price (CP) and profit percentage. Once we have the SP, we can use the discount percentage to work backward and find the MP.
The shopkeeper gains 25% on an article that costs ₹ 600.
Cost Price (CP) = ₹ 600
Profit % = 25%
The formula for Selling Price when profit is given is:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit}\%}{100}\right) \] \[ \text{SP} = 600 \times \left(1 + \frac{25}{100}\right) \] \[ \text{SP} = 600 \times \left(1 + 0.25\right) \] \[ \text{SP} = 600 \times 1.25 \] \[ \text{SP} = \text{₹ } 750 \]The shopkeeper allows a discount of 20% on the Marked Price and still sells it at SP = ₹ 750.
Discount % = 20%
The formula relating SP, MP, and Discount % is:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount}\%}{100}\right) \]We need to find MP, so we can rearrange the formula:
\[ \text{MP} = \frac{\text{SP}}{\left(1 - \frac{\text{Discount}\%}{100}\right)} \] \[ \text{MP} = \frac{750}{\left(1 - \frac{20}{100}\right)} \] \[ \text{MP} = \frac{750}{\left(1 - 0.20\right)} \] \[ \text{MP} = \frac{750}{0.80} \] \[ \text{MP} = 937.50 \]So, the Marked Price is ₹ 937.50.
Correct Option: A) ₹ 937.50
The question asks whether children's ability to grasp ideas in school depends on their intelligence. We need to evaluate if the given statements provide sufficient information to answer this question definitively (yes or no).
A) Neither 1 nor 2 is sufficient
Both statements provide information that is tangential to the core question. Statement 1 describes a characteristic of intelligence, but not its role in learning. Statement 2 describes a correlation between socioeconomic status and performance, without linking it to intelligence or the ability to grasp ideas. Therefore, neither statement, nor both combined, can definitively answer whether a child's ability to grasp ideas depends on their intelligence.
The question asks to identify the author of the book 'Immortal India' published in 2017. This requires knowledge of contemporary Indian authors and their works.
Correct Option: B) Amish Tripathi is the author of 'Immortal India', published in 2017. The book is a collection of essays, speeches, and articles by Tripathi, offering his perspectives on various facets of Indian civilization.
The question asks to identify the Australian city that hosted the 2018 Commonwealth Games. This is a factual question related to major international sporting events. Recalling the host cities of recent Commonwealth Games is key to answering this.
B) Gold Coast — The city of Gold Coast in Queensland, Australia, was indeed the host city for the 2018 Commonwealth Games.
The question asks to identify which statement is NOT a property of bases. We need to recall the characteristic properties of bases and compare them with the given options.
B) They turn blue litmus red. This statement describes a property of acids, not bases. Bases turn red litmus blue.