The question asks to identify the key difference between a pulmonary vein and other veins in the human circulatory system. This requires understanding the basic function of veins and the specific role of the pulmonary circulation.
Correct Option: A) Pulmonary vein carries oxygenated blood
What will be the value of elasticity of demand (eD) if the demand curve has a shape of rectangular hyperbola?
\(\left|e_D\right|\) = Above 0 but less than 1
\(\left|e_D\right|\) = 1
\(\left|e_D\right|\) = 0
\(\left|e_D\right|\) = Always remains above 1
The question asks for the value of the elasticity of demand (\(e_D\)) when the demand curve is a rectangular hyperbola. We need to recall the properties of a rectangular hyperbola in the context of demand curves and its relationship with elasticity.
B) \(\left|e_D\right|\) = 1. A demand curve that is a rectangular hyperbola signifies that the total expenditure on the good remains constant regardless of the price changes. This is the defining characteristic of unit elastic demand, where the percentage change in quantity demanded is exactly equal to the percentage change in price.
If P, F and C represent the pole, principal focus and centre of curvature, respectively, of a concave mirror, then PC is equal to:
The question asks for the relationship between the distance from the pole to the center of curvature (PC) and the distance from the pole to the principal focus (PF) for a concave mirror. This relationship is a fundamental property of spherical mirrors.
C) 2PF — As derived, the distance from the pole to the center of curvature (PC) is twice the focal length (PF).
To find the smallest four-digit number exactly divisible by 24, 40, and 56, we need to find the Least Common Multiple (LCM) of these numbers. Once we have the LCM, we'll find the smallest multiple of the LCM that is a four-digit number.
The LCM is found by taking the highest power of all prime factors present in the numbers.
\[ \text{LCM}(24, 40, 56) = 2^3 \times 3^1 \times 5^1 \times 7^1 \]\[ \text{LCM} = 8 \times 3 \times 5 \times 7 \]\[ \text{LCM} = 24 \times 35 \]\[ \text{LCM} = 840 \]The smallest four-digit number is 1000. We need to find the smallest multiple of 840 that is greater than or equal to 1000.
Let the required number be \(N\). We know that \(N = k \times 840\) for some integer \(k\).
If \(k=1\), \(N = 1 \times 840 = 840\), which is a three-digit number.
If \(k=2\), \(N = 2 \times 840 = 1680\), which is a four-digit number.
Since 1680 is the first multiple of 840 that is a four-digit number, it is the smallest such number.
Correct Option: B) 1680
Two resistors, A of 10 Ω and B of 20 Ω, are connected in series with a battery of 6 V. If V₁ and V₂ are the potential drops across A and B and I₁ and I₂ are the currents through them, respectively, then \( \frac{V_1}{V_2} \) and \( \frac{I_1}{I_2} \) are respectively
\( \frac{1}{2} \) and \( \frac{1}{2} \)
2 and \( \frac{1}{2} \)
\( \frac{1}{2} \) and 1
2 and 1
This problem involves resistors connected in series. We need to apply the fundamental principles of series circuits: current remains the same through all components, and voltage divides across components in proportion to their resistance. Ohm's Law will be used to calculate potential drops.
In a series circuit, the current flowing through each resistor is the same. Therefore, \(I_1 = I_2 = I_{\text{total}}\).
From this, we can directly find the ratio \( \frac{I_1}{I_2} \).
\[ \frac{I_1}{I_2} = \frac{I_{\text{total}}}{I_{\text{total}}} = 1 \]According to Ohm's Law, \(V = IR\). Since the current \(I\) is the same for both resistors:
Now, we can find the ratio of the potential drops:
\[ \frac{V_1}{V_2} = \frac{I_{\text{total}} \times R_A}{I_{\text{total}} \times R_B} = \frac{R_A}{R_B} \]\[ \frac{V_1}{V_2} = \frac{10 \, \Omega}{20 \, \Omega} = \frac{1}{2} \]So, \[\frac{V_1}{V_2} = \frac{1}{2}\] and \( \frac{I_1}{I_2} = 1 \).
C) \( \frac{1}{2} \) and 1
As calculated, the ratio of potential drops \( \frac{V_1}{V_2} \) is \( \frac{1}{2} \) and the ratio of currents \( \frac{I_1}{I_2} \) is 1.
The question asks for the common method used to balance chemical equations. Balancing a chemical equation involves ensuring that the number of atoms of each element on the reactant side is equal to the number of atoms of the same element on the product side, in accordance with the Law of Conservation of Mass. This is typically achieved by adjusting the stoichiometric coefficients in front of the chemical formulas.
A) hit and trial method — This is the most common and fundamental method used by students and chemists to balance chemical equations, especially for simpler reactions. It involves systematically adjusting coefficients until the number of atoms of each element is equal on both sides of the equation.
This problem is based on mathematical operations and their symbolic representation. We need to substitute the given symbols with their corresponding mathematical operations and then solve the expression following the order of operations (BODMAS/PEMDAS).
@ means 'multiplication' (\(\times\))% means 'subtraction' (\(-\))\( means 'addition' (\(+\))& means 'division' (\(\div\))The given expression is 28 & 7 @ 8 % 6 \) 4.
Substituting the operations, it becomes:
\[ 28 \div 7 \times 8 - 6 + 4 \]BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, perform Division and Multiplication from left to right.
Perform division:
\[ 28 \div 7 = 4 \]Perform subtraction:
\[ 32 - 6 = 26 \]B) 30 is the correct answer after performing the operations in the correct order.
To determine the direction of the school from Bheema's house, we need to trace Bheema's path step-by-step and visualize the final position relative to the starting point. We will use standard cardinal directions (North, South, East, West) and their combinations.
C) South-west. The final position of the school is 35 m to the west and 50 m to the south of his house, placing it in the South-west direction.
The question asks about the specific script in which Hindi is recognized as the official language of India according to Article 343(1) of the Constitution. This requires direct knowledge of the constitutional provisions regarding official languages.
Correct Option: D) Devanagari
Article 343(1) of the Constitution of India explicitly states: "The official language of the Union shall be Hindi in Devanagari script." This makes Devanagari the correct answer.