The voltages across three resistances R₁, R₂ and R₃ connected in series are V₁, V₂ and V₃, respectively. What is the net voltage V across them if I represents the net current flowing through them?
\(V=\frac{1}{V_1}+\frac{1}{V_2}+\frac{1}{V_3}\)
\(V=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)
V = V₁ + V₂ + V₃
V = R₁ + R₂ + R₃
This question tests the fundamental concept of voltage distribution in a series circuit. When resistances are connected in series, the total voltage across the combination is the sum of the individual voltages across each resistance.
Correct Option: C) V = V₁ + V₂ + V₃. This option correctly states that the total voltage across series resistances is the sum of the individual voltages across each resistance, which is a direct application of Kirchhoff's Voltage Law.
The question asks for the best practice in biological waste disposal. Biological waste, also known as biomedical waste or biohazard waste, contains infectious materials that can pose a risk to human health and the environment. Therefore, the disposal method must effectively neutralize these hazards.
Correct Option: A) incineration is considered the best practice for biological waste disposal because it effectively destroys pathogens and reduces the volume of hazardous materials, minimizing risks to public health and the environment.
The question asks to identify the true statements regarding an incandescent filament bulb. We need to evaluate each statement based on the principles of how incandescent bulbs work.
Based on the evaluation:
Comparing with the options, option B includes (b) and (e) which are definitively true. Let's re-examine (a). While nichrome is not the primary material, the question asks what 'can be made of'. Tungsten is definitely used. If we interpret 'can be made of' to include any material that could theoretically function, then nichrome has high resistance and melting point, but its light emission characteristics are not as good as tungsten for visible light. However, in the context of competitive exams, tungsten is the key material for incandescent filaments. Given that (b) and (e) are unequivocally true, and (c) and (d) are unequivocally false, Option B is the most plausible choice, implying (a) is considered true because tungsten is mentioned.
B) (a), (b), (e)
The question asks to identify the apex governing body for air sports in India as of 2022. This requires knowledge of recent developments and organizational structures related to sports governance in India.
A) Air Sports Federation of India. The Air Sports Federation of India (ASFI) was established as the apex governing body for air sports in India under the National Air Sports Policy (NASP 2022), launched by the Ministry of Civil Aviation in June 2022. Its role is to regulate, promote, and develop air sports across the country.
To find the roots of a quadratic equation of the form \(ax^2 + bx + c = 0\), we can use either factorization, completing the square, or the quadratic formula. In this case, factorization is a straightforward method.
Identify the quadratic equation:
The given quadratic equation is \(x^2 - 6x + 5 = 0\).
Factorize the quadratic expression:
We need to find two numbers that multiply to \(+5\) (the constant term) and add up to \(-6\) (the coefficient of the \(x\) term).
The pairs of factors for \(5\) are \((1, 5)\) and \((-1, -5)\).
Let's check their sums:
\(1 + 5 = 6\)
\(-1 + (-5) = -6\)
The numbers are \(-1\) and \(-5\).
Rewrite the middle term:
Rewrite \(-6x\) as \(-x - 5x\):
\[x^2 - x - 5x + 5 = 0\]
Group terms and factor:
Group the terms and factor out common factors:
\[x(x - 1) - 5(x - 1) = 0\]
Now, factor out the common binomial factor \((x - 1)\):
\[(x - 1)(x - 5) = 0\]
Solve for x:
For the product of two factors to be zero, at least one of the factors must be zero.
So, either \(x - 1 = 0\) or \(x - 5 = 0\).
If \(x - 1 = 0\), then \(x = 1\).
If \(x - 5 = 0\), then \(x = 5\).
Thus, the roots of the equation are \(1\) and \(5\).
A) 5, 1 — This option correctly lists the roots of the quadratic equation \(x^2 - 6x + 5 = 0\) as \(5\) and \(1\).
The question asks about the recommendations of the Karve Committee, constituted in 1955. This committee is significant in the context of India's post-independence economic planning, particularly concerning rural development and industrialization strategy.
A) The Karve Committee (1955) was specifically constituted to advise on the promotion of small-scale industries for the purpose of rural development. Its recommendations were crucial in shaping India's industrial policy, emphasizing the role of village and small-scale industries in creating employment and ensuring a more equitable distribution of economic benefits.
The question asks us to evaluate two arguments in relation to a statement: "Eating frozen foods is advantageous." We need to determine if each argument strengthens or weakens the statement.
A) II weakens while I strengthens the statement. This option accurately reflects our analysis: Argument I provides an advantage (strengthening the statement) and Argument II provides a disadvantage (weakening the statement).
If ‘+’ means ‘−’, ‘−’ means ‘+’, ‘×’ means ‘÷’, and ‘÷’ means ‘×’, what will come in place of the question mark (?) in the following equation?
15 − 3 + 7 ÷ 6 × 3 = ?
This problem involves substituting given symbol meanings into an equation and then solving it using the BODMAS/PEMDAS rule (Order of Operations).
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Operations are performed from left to right for division/multiplication and for addition/subtraction.
First, perform multiplication and division from left to right:
\[ 15 + 3 - (7 \times 6) \div 3 = ? \] \[ 15 + 3 - 42 \div 3 = ? \] \[ 15 + 3 - (42 \div 3) = ? \] \[ 15 + 3 - 14 = ? \]Next, perform addition and subtraction from left to right:
\[ (15 + 3) - 14 = ? \] \[ 18 - 14 = ? \] \[ 4 = ? \]Correct Option: C) 4
This question involves inequalities, a common topic in reasoning sections of competitive exams. We need to analyze the given statement, which is a chain of inequalities, and determine which of the given conclusions logically follows from it. We will evaluate each option based on the relationships established in the main statement.
From the statement, we have \(W = E\) and \(E \geq D\). Combining these two, we can conclude that \(W \geq D\).
From the statement, we have \(Y = P\) and \(P \leq K\). This implies \(Y \leq K\). The conclusion \(K \leq Y\) is the opposite and therefore incorrect.
From the statement, we have \(N > W\) and \(W = E\). Combining these, we get \(N > E\). The conclusion \(N < E\) is the opposite and therefore incorrect.
From the statement, we have \(N > W\) and \(W = E\) and \(E \geq D\). This chain implies \(N > W = E \geq D\), which means \(N > D\). The conclusion \(D > N\) is the opposite and therefore incorrect.
A) W \(\geq\) D — This conclusion is true because from the given statement, we have \(W = E\) and \(E \geq D\). Therefore, by substitution, \(W \geq D\).
Select the option that represents the letters that, when placed from left to right in the same sequence in the blanks below, will complete the letter series.
M N Q _ _ M N _ _ M N P _ _ O P