Calculate the relative molecular mass of CO2.
To calculate the relative molecular mass of a compound, we need to sum the relative atomic masses of all the atoms present in its chemical formula. For CO₂, we need the relative atomic masses of Carbon (C) and Oxygen (O).
Correct Option: B) 44 u
The question asks to identify the part of the brain responsible for controlling involuntary activities such as coughing and sneezing. This requires knowledge of the functions of different parts of the human brain, specifically those involved in regulating vital and reflex actions.
Correct Option: A) The Medulla oblongata (or simply Medulla) is a vital part of the brainstem that controls several involuntary functions, including respiration, heart rate, blood pressure, and reflex actions such as coughing, sneezing, swallowing, and vomiting. These actions are essential for the body's survival and occur without conscious effort.
We are given ratios of present ages for X and Y, and Y and Z. We are also given a ratio of ages for X and Y two years ago. We need to find the sum of their present ages. The strategy is to use the given ratios to establish relationships between the ages, form an equation using the past age ratio, solve for a common variable, and then calculate the present ages and their sum.
Let the present ages of X, Y, and Z be \(X\), \(Y\), and \(Z\) respectively.
From the first statement, the ratio of the present ages of X and Y is 3 : 8.
\[ \frac{X}{Y} = \frac{3}{8} \implies X = \frac{3}{8}Y \quad \text{(Equation 1)} \]From the second statement, the ratio of the present ages of Y and Z is 4 : 5.
\[ \frac{Y}{Z} = \frac{4}{5} \implies Z = \frac{5}{4}Y \quad \text{(Equation 2)} \]Two years ago, the age of X was \((X-2)\) and the age of Y was \((Y-2)\). The ratio of their ages two years ago was 1 : 3.
\[ \frac{X-2}{Y-2} = \frac{1}{3} \]Substitute Equation 1 into the ratio from two years ago:
\[ \frac{\frac{3}{8}Y - 2}{Y - 2} = \frac{1}{3} \]Cross-multiply and solve for \(Y\):
\[ 3 \left( \frac{3}{8}Y - 2 \right) = 1(Y - 2) \] \[ \frac{9}{8}Y - 6 = Y - 2 \] \[ \frac{9}{8}Y - Y = 6 - 2 \] \[ \frac{9Y - 8Y}{8} = 4 \] \[ \frac{Y}{8} = 4 \] \[ Y = 32 \text{ years} \]Now that we have \(Y\), we can find \(X\) using Equation 1:
\[ X = \frac{3}{8}Y = \frac{3}{8}(32) = 3 \times 4 = 12 \text{ years} \]And find \(Z\) using Equation 2:
\[ Z = \frac{5}{4}Y = \frac{5}{4}(32) = 5 \times 8 = 40 \text{ years} \]The present ages are \(X=12\), \(Y=32\), and \(Z=40\).
The sum of their present ages is:
\[ X + Y + Z = 12 + 32 + 40 = 84 \text{ years} \]D) The sum of the present ages of X, Y, and Z is 84 years, which matches our calculation.
The numerical value of the area of a square is equal to half the numerical value of each of its diagonals. What is the numerical value of diagonal?
To solve this problem, we need to relate the area of a square to its diagonal. We will set up an equation based on the given condition and solve for the diagonal's numerical value.
Define variables:
Let \(a\) be the side length of the square.
Let \(d\) be the length of the diagonal of the square.
Formulas for area and diagonal of a square:
The area of a square is given by \(A = a^2\).
The diagonal of a square can be found using the Pythagorean theorem. For a square with side \(a\), the diagonal \(d\) is the hypotenuse of a right-angled triangle with two sides of length \(a\).
\[ d^2 = a^2 + a^2 \]\[ d^2 = 2a^2 \]\[ d = \sqrt{2}a \]From this, we can express \(a\) in terms of \(d\):\[ a = \frac{d}{\sqrt{2}} \]Express area in terms of diagonal:
Substitute the expression for \(a\) into the area formula:
\[ A = a^2 = \left(\frac{d}{\sqrt{2}}\right)^2 \]\[ A = \frac{d^2}{2} \]Set up the equation based on the given condition:
The problem states that "The numerical value of the area of a square is equal to half the numerical value of each of its diagonals."
So, \(A = \frac{1}{2}d\).
Solve for the diagonal \(d\):
Equate the two expressions for \(A\):
\[ \frac{d^2}{2} = \frac{1}{2}d \]Simplify the equation:
Multiply both sides by 2:
\[ d^2 = d \]Solve for \(d\):
Rearrange the equation:
\[ d^2 - d = 0 \]\[ d(d - 1) = 0 \]This gives two possible solutions for \(d\):\[ d = 0 \quad \text{or} \quad d - 1 = 0 \]\[ d = 0 \quad \text{or} \quad d = 1 \]Since a diagonal cannot have a length of 0 (it would not be a square), we take the non-zero solution.Therefore, \(d = 1\).
Correct Option: C) 1
The numerical value of the diagonal is 1.
This compound is sometimes added to the food for quick cooking. It is a mild non-corrosive alkali. The reaction given below shows the action of its formation. Name this compound.
NaCl + H2O + CO2 + NH3 =?
Sodium Hydrogen Carbonate
Ammonium Carbonate
Sodium Carbonate
Ammonium Chloride
The question describes a compound used for quick cooking and as a mild non-corrosive alkali, and provides a chemical reaction for its formation. We need to identify the product of this reaction, which is the Solvay process, and match it with the given options.
A) Sodium Hydrogen Carbonate — As derived from the Solvay process, the primary product that fits the description of a mild, non-corrosive alkali used for quick cooking is Sodium Hydrogen Carbonate (\(\text{NaHCO}_3\)), also known as baking soda.
To find the perimeter of a rhombus, we first need to determine the length of its side. We can use the property that the diagonals of a rhombus bisect each other at right angles. This forms four right-angled triangles within the rhombus. By applying the Pythagorean theorem to one of these triangles, we can find the length of a side, and then calculate the perimeter.
Understand the properties of a rhombus: A rhombus is a quadrilateral where all four sides are equal in length. Its diagonals bisect each other at right angles.
Identify the given information: The lengths of the diagonals are 16 cm and 12 cm.
Determine the half-lengths of the diagonals: Since the diagonals bisect each other, their half-lengths will be:
Form a right-angled triangle: When the diagonals intersect, they form four congruent right-angled triangles. The legs of each right-angled triangle are the half-lengths of the diagonals (8 cm and 6 cm), and the hypotenuse is the side of the rhombus.
Apply the Pythagorean theorem: Let 's' be the length of the side of the rhombus. According to the Pythagorean theorem:
\[ s^2 = (\text{half } d_1)^2 + (\text{half } d_2)^2 \]\[ s^2 = (8 \text{ cm})^2 + (6 \text{ cm})^2 \]\[ s^2 = 64 \text{ cm}^2 + 36 \text{ cm}^2 \]\[ s^2 = 100 \text{ cm}^2 \]\[ s = \sqrt{100 \text{ cm}^2} \]\[ s = 10 \text{ cm} \]Calculate the perimeter: Since all four sides of a rhombus are equal, the perimeter (P) is \(4 \times s\).
\[ P = 4 \times 10 \text{ cm} \]\[ P = 40 \text{ cm} \]D) 40 cm is the correct perimeter of the rhombus.
The chemical formula of Quick Lime (Kalichuna) is ______.
The question asks for the chemical formula of Quick Lime, also known as Kalichuna. This requires knowledge of common chemical names and their corresponding formulas.
Correct Option: D) \(\text{CaO}\) is the chemical formula for Quick Lime (calcium oxide).
The question asks to identify the incorrect statement about matter. We need to evaluate each option based on the fundamental properties of matter.
C) There is no attraction force between particles of matter — This statement is incorrect because attractive forces (intermolecular or interatomic) exist between particles of matter, which are responsible for holding them together and determining their physical state and properties.
In the formula M = hi / ho, what do M, hi and ho represent?
M – Mass, hi – Height of reflection, ho – Height of object
M – Magnification, hi – Height of object, ho – Height of reflection
M – Magnification, hi – Height of reflection, ho – Height of object
M – Mass, hi – Height of object, ho – Height of reflection
The question asks to identify the terms represented by M, \(h_i\), and \(h_o\) in the given formula \(M = h_i / h_o\). This formula is standard in optics, specifically for calculating magnification.
C) M – Magnification, \(h_i\) – Height of reflection, \(h_o\) – Height of object. This option correctly identifies M as Magnification, \(h_i\) as the height of the image (often referred to as 'reflection' in a general sense, though 'image' is more precise), and \(h_o\) as the height of the object.