When an acid reacts with a carbonate or metal hydrogencarbonate, it forms salts, carbon dioxide gas and water accordingly. Which of the following equations is correct for this chemical reaction?
Na₂CO₃(s) + HCl(aq) → 2NaCl(aq) + H₂O(l) + 2CO₂(g) + H₂O(l)
Na₂CO₃(s) + HCl(aq) → NaCl(aq) + H₂O(l) + CO₂(g)
Na₂CO₃(s) + 2HCl(aq) → 2NaCl(aq) + H₂O(l) + CO₂(g)
Na₂CO₃(s) + 2HCl(aq) → 2NaCl(aq) + 2CO₂(g)
The question asks to identify the correct balanced chemical equation for the reaction between an acid and a carbonate. The general reaction states that an acid reacting with a carbonate or metal hydrogencarbonate produces salt, carbon dioxide gas, and water. We need to check each option for correct products and proper balancing of atoms.
Correct Option: C) Na₂CO₃(s) + 2HCl(aq) → 2NaCl(aq) + H₂O(l) + CO₂(g)
The question asks which reproductive method allows for greater genetic diversity. Genetic diversity is crucial for adaptation and evolution. We need to evaluate each option based on its mechanism of reproduction and its impact on genetic variation.
Correct Option: D) Sexual reproduction allows for more diversity in breeding because it involves the fusion of gametes from two parents and genetic recombination during meiosis. This process shuffles genes, leading to offspring with unique combinations of traits, which increases genetic diversity within a population.
This problem involves the relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers. A fundamental property states that the product of two numbers is equal to the product of their LCM and HCF. We will use this property to find the unknown second number.
For any two positive integers, the product of the numbers is equal to the product of their LCM and HCF.
\[ \text{First Number} \times \text{Second Number} = \text{LCM} \times \text{HCF} \]Divide both sides of the equation by 18:
\[ x = \frac{810}{18} \]\[ x = 45 \]If the numbers are 18 and 45:
The calculated second number is consistent with the given LCM and HCF.
Correct Option: C) 45
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This rule dictates the sequence in which mathematical operations should be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
C) 18 is the correct answer because following the order of operations (BODMAS/PEMDAS) leads to this result.
The table below shows the passing percentage of four schools in four years.
| Name of school | 2012-13 | 2013-14 | 2014-15 | 2015-16 |
| PQR | 27% | 31% | 45% | 67% |
| ABC | 61% | 65% | 50% | 78% |
| DEF | 95% | 86% | 80% | 70% |
| XYZ | 92% | 82% | 78% | 71% |
The percentage of which school is increasing sequentially (gradually)?
To identify the school whose passing percentage is increasing sequentially (gradually), we need to examine the passing percentages for each school across the given years (2012-13, 2013-14, 2014-15, 2015-16) and check if the percentage consistently increases from one year to the next.
The percentage for PQR is increasing sequentially.
The percentage for ABC is not increasing sequentially as it decreased from 2013-14 to 2014-15.
The percentage for DEF is not increasing sequentially as it decreased from 2012-13 to 2013-14.
The percentage for XYZ is not increasing sequentially as it decreased from 2012-13 to 2013-14.
Based on this analysis, only school PQR shows a consistent increase in its passing percentage over the given years.
D) PQR is the correct option because its passing percentages are 27%, 31%, 45%, and 67%, which show a continuous increase over the years 2012-13, 2013-14, 2014-15, and 2015-16, respectively.
The elevation angle of the tower is 30° from the 18 m high top of a platform. If the height of the tower is 78 m, then what is the distance of the tower from the platform?
60 m
20\(\sqrt{3}\) m
70\(\sqrt{3}\) m
60\(\sqrt{3}\) m
This problem involves trigonometry, specifically the tangent function, to find the horizontal distance between the platform and the tower. We will use the given heights and the angle of elevation to form a right-angled triangle and solve for the unknown side.
D) \(60\sqrt{3}\) m is the correct distance of the tower from the platform.
The problem requires us to find the correct sequence of mathematical operators (-, +, ×, ÷) that, when substituted into the given equation, yields a result of 5. We will test each option by replacing the '?' symbols with the operators provided in that option and then evaluating the expression following the order of operations (PEMDAS/BODMAS).
The given equation is: \(((120 ? 110) ? 5) ? 10 = 5\).
Substitute the operators: \(((120 - 110) \div 5) \div 10\)
Since \(0.2 \neq 5\), Option A is incorrect.
Substitute the operators: \(((120 + 110) \div 5) \times 10\)
Since \(460 \neq 5\), Option B is incorrect.
Substitute the operators: \(((120 - 110) + 5) + 10\)
Since \(25 \neq 5\), Option C is incorrect.
Substitute the operators: \(((120 - 110) \times 5) \div 10\)
Since \(5 = 5\), Option D is correct.
Correct Option: D) -, ×, ÷
The question asks to identify the scheme that provides piped water supply to villages using solar energy. This requires knowledge of various government initiatives related to water supply and renewable energy in rural areas.
Correct Option: A) Swajal Scheme
The Swajal Scheme, launched by the Ministry of Drinking Water and Sanitation (now part of the Ministry of Jal Shakti), aims to provide villages with their own sustainable source of clean drinking water. A key feature of this scheme is the use of solar energy to power the water supply systems, ensuring a reliable and environmentally friendly solution for piped water delivery to households in rural areas.
The question asks to identify the author of the ancient Indian epic, the Ramayana. This is a direct factual recall question related to Indian history and literature.
Correct Option: B) Valmiki is traditionally revered as the author of the epic Ramayana. He is known as the 'Adi Kavi' (first poet) and the Ramayana is considered the 'Adi Kavya' (first epic).
The question asks to identify the plant tissue responsible for storing nutrients and water in stems and roots. We need to recall the primary functions of different plant tissues.
Correct Option: A) Parenchyma tissues are widely distributed in plants and are primarily responsible for the storage of food (like starch, fats, and proteins) and water. They constitute the ground tissue in stems and roots, where these storage functions are crucial.