How many participants from India won the gold medal in the 14th International Olympiad on Astronomy and Astrophysics (IOAA) 2021?
The question asks about the number of gold medals won by Indian participants in a specific international competition. This requires factual knowledge about the results of the 14th International Olympiad on Astronomy and Astrophysics (IOAA) 2021.
C) 4 — India won 4 gold medals at the 14th International Olympiad on Astronomy and Astrophysics (IOAA) 2021. The gold medalists were S. Pranav, Prashant Singh, B. Siddharth, and G. S. Animesh.
The question asks to identify an advantage of building dams, given a list of statements where some are disadvantages. We need to evaluate each option to determine if it represents a benefit or a drawback of dam construction.
Correct Option: D) Helpful in irrigation and electricity production
Dams are multi-purpose projects designed to provide several benefits. Two of the most significant advantages are their role in irrigation, by supplying water to agricultural lands, and in generating hydroelectricity, which is a clean and renewable source of energy. These benefits contribute significantly to economic development and food security.
This problem can be solved using the fundamental relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers. The product of two numbers is always equal to the product of their HCF and LCM.
B) 217 — The calculation shows that the other number is 217.
The sum of the roots of the quadratic equation 4x2 + 7x - 21 = 0 is:
\(\frac{21}{4}\)
\(\frac{7}{4}\)
\(-\frac{7}{4}\)
\(-\frac{21}{4}\)
To find the sum of the roots of a quadratic equation, we can use the standard formula derived from the general form of a quadratic equation. The general form is \(ax^2 + bx + c = 0\), and the sum of its roots is given by \(-b/a\).
Correct Option: C) \(-\frac{7}{4}\) is the correct sum of the roots, calculated using the formula \(-b/a\).
What will come in place of A and B, respectively, in the given double displacement reaction?
A + B → AgBr + KNO3
Ag and HNO3
HBr and NaOH
AgNO3 and KBr
HBr and NaNO3
The given reaction is a double displacement reaction. In such reactions, the ions of two compounds exchange places to form two new compounds. We need to identify the reactants (A and B) that would yield the given products, silver bromide (AgBr) and potassium nitrate (KNO₃).
Correct Option: C) AgNO₃ and KBr
The problem states that four terms are in proportion. If four quantities \(a, b, c, d\) are in proportion, it means that the ratio of the first two is equal to the ratio of the last two, i.e., \(a:b = c:d\) or \[\frac{a}{b} = \frac{c}{d}\]. We are given the value of \(x\), which allows us to find the numerical values of the first three terms. Then, we can use the proportion property to solve for \(y\).
Identify the given terms and the condition:
The four terms are \(5 + x\), \(2x + 7\), \(6x + 9\), and \(y\).
They are in proportion when \(x = 2\).
Substitute \(x = 2\) into the first three terms:
First term: \(A = 5 + x = 5 + 2 = 7\)
Second term: \(B = 2x + 7 = 2(2) + 7 = 4 + 7 = 11\)
Third term: \(C = 6x + 9 = 6(2) + 9 = 12 + 9 = 21\)
Fourth term: \(D = y\)
Apply the condition of proportion:
If \(A, B, C, D\) are in proportion, then \[\frac{A}{B} = \frac{C}{D}\].
Substituting the values we found:
Solve for \(y\):
To solve for \(y\), we can cross-multiply:
Correct Option: B) The value of \(y\) is 33.
The question asks to identify the state associated with the Gosikhurd National Irrigation Project. This requires knowledge of major irrigation projects and their geographical locations in India.
The Gosikhurd National Irrigation Project is located in the state of Maharashtra. It is a multi-purpose project on the Wainganga River, aimed at providing irrigation, flood control, and power generation in the Vidarbha region of Maharashtra.
The question asks to identify the INCORRECT option among the given techniques for soil conservation. This means we need to find the option that contributes to soil degradation, rather than preventing it.
Correct Option: D) Overgrazing — Overgrazing is a significant cause of soil degradation. When animals consume too much vegetation, the protective plant cover is removed, leaving the soil exposed to wind and water erosion. This leads to loss of topsoil, reduced fertility, and desertification.
The question asks to identify an organism where sex determination is not solely genetic. This means looking for an organism where environmental factors or other non-genetic mechanisms play a role in determining sex.
Correct Option: D) Snail — Sex determination in many snail species is not solely genetic. They can be hermaphroditic, or their sex can be influenced by environmental factors or developmental changes (sequential hermaphroditism).
This problem involves setting up and solving a system of two linear equations based on the given age relationships at different points in time (six years ago and three years hence). We will define variables for the present ages of the father and daughter and then translate the given conditions into algebraic equations.
Define variables for present ages:
Let the present age of the father be \(F\) years.
Let the present age of the daughter be \(D\) years.
Formulate the first equation (six years ago):
Six years ago, the father's age was \(F - 6\).
Six years ago, the daughter's age was \(D - 6\).
According to the problem, six years ago, the father's age was six times the daughter's age:
\[ F - 6 = 6(D - 6) \]\[ F - 6 = 6D - 36 \]\[ F = 6D - 30 \quad \text{(Equation 1)} \]Formulate the second equation (three years hence):
Three years hence (from now), the father's age will be \(F + 3\).
Three years hence, the daughter's age will be \(D + 3\).
According to the problem, three years hence, the father will be thrice as old as his daughter:
\[ F + 3 = 3(D + 3) \]\[ F + 3 = 3D + 9 \]\[ F = 3D + 6 \quad \text{(Equation 2)} \]Solve the system of equations:
Now we have two equations for \(F\):
From Equation 1: \(F = 6D - 30\)
From Equation 2: \(F = 3D + 6\)
Set the expressions for \(F\) equal to each other:
\[ 6D - 30 = 3D + 6 \]Solve for \(D\):
Subtract \(3D\) from both sides:
\[ 3D - 30 = 6 \]Add \(30\) to both sides:
\[ 3D = 36 \]Divide by \(3\):
\[ D = \frac{36}{3} \]\[ D = 12 \]State the present age of the daughter:
The present age of the daughter is \(12\) years.
A) 12 years is the correct answer, as calculated from the system of equations.