The question asks for the approximate pH of milk of magnesia. Milk of magnesia is a common antacid, and its pH value indicates its basicity. We need to recall the typical pH range for antacids or specifically for magnesium hydroxide solutions.
A) 10.4 — Milk of magnesia is a suspension of magnesium hydroxide, which is a weak base. Its pH is typically around 10.0 to 10.5, making 10.4 a very accurate approximation.
To determine Prince's final direction from the starting point, we will trace his path step-by-step, considering each movement and turn. We'll visualize the directions (North, South, East, West) and plot his journey to find his final position relative to his starting point.
To find his direction from Point A, we need to consider the net displacement. From A, he went 6 km South, then 4 km West, and then another 6 km South.
Therefore, his final position (P3) is 12 km South and 4 km West of his starting point (A).
A point that is both South and West of another point is in the South-west direction.
Correct Option: B) South-west
It is found that during dispersion of white light by a glass prism, the more a colour component is bent, the more is the refractive index of the glass for that colour component. If μB, μY and μG are refractive indices for blue, yellow and green lights, respectively, then which of the following relations between them is correct?
μY > μG > μB
μY = μG = μB
μG > μB > μY
μB > μG > μY
The problem describes the dispersion of white light through a glass prism and states a relationship: the more a color component is bent, the higher the refractive index of the glass for that color. We need to determine the correct order of refractive indices for blue, yellow, and green light based on their bending during dispersion.
Understand Dispersion: When white light passes through a prism, it splits into its constituent colors (VIBGYOR - Violet, Indigo, Blue, Green, Yellow, Orange, Red). This phenomenon is called dispersion.
Relate Bending to Wavelength: The extent to which a color component is bent depends on its wavelength. Colors with shorter wavelengths are bent more, and colors with longer wavelengths are bent less. The order of wavelengths from shortest to longest is Violet < Indigo < Blue < Green < Yellow < Orange < Red.
Apply the Given Condition: The question states, "the more a colour component is bent, the more is the refractive index of the glass for that colour component."
Determine Bending Order for Given Colors: From the VIBGYOR spectrum, Blue light has the shortest wavelength among blue, green, and yellow. Therefore, blue light is bent the most. Yellow light has the longest wavelength among the three, so it is bent the least. Green light is in between.
So, the order of bending (from most to least) is: Blue > Green > Yellow.
Determine Refractive Index Order: Based on the given condition (more bending = higher refractive index), the order of refractive indices will be the same as the order of bending:
\[ \mu_B > \mu_G > \mu_Y \]D) \( \mu_B > \mu_G > \mu_Y \) is correct because blue light is bent the most (due to its shorter wavelength), followed by green, and then yellow (which is bent the least). According to the problem statement, greater bending implies a greater refractive index.
The question asks for the year in which the Panchayats (Extension to the Scheduled Areas) Act (PESA Act) was passed in India. This is a factual question related to Indian polity and governance, specifically concerning the empowerment of tribal communities.
B) 1996 — The Panchayats (Extension to the Scheduled Areas) Act (PESA Act) was passed by the Indian Parliament in 1996.
To find the image distance for a convex mirror, we use the mirror formula, which relates the focal length of the mirror to the object distance and image distance. We must also pay attention to the sign conventions for convex mirrors.
Correct Option: A) 6 cm — The calculation using the mirror formula and appropriate sign conventions yields an image distance of +6 cm, meaning the image is formed 6 cm behind the mirror.
The problem requires us to find the correct interchange of signs and numbers that makes the given equation \(9 - 11 \times 24 = 75\) mathematically correct. We will test each option by performing the specified interchanges and then evaluating the resulting equation.
Let's evaluate each option:
A) When \(\times\) and \(-\) are interchanged, and 9 and 11 are interchanged, the equation becomes \(11 \times 9 - 24 = 75\). Evaluating the left side gives \(99 - 24 = 75\), which matches the right side. Thus, this option makes the equation correct.
The question asks about the change in heat produced when the resistance of a conductor is doubled. We need to use Joule's Law of Heating, which relates heat produced to current, resistance, and time. We will consider two scenarios: one where the current is kept constant and another where the voltage is kept constant.
where \(I\) is the current flowing through the conductor, \(R\) is the resistance of the conductor, and \(t\) is the time for which the current flows.
In this scenario, the heat produced doubles.
If the resistance (\(R\)) is doubled, the new resistance \(R' = 2R\). The new heat produced \(H'\) would be:
\[ H' = \frac{V^2}{2R} t = \frac{1}{2} \left(\frac{V^2}{R} t\right) = \frac{1}{2} H \]In this scenario, the heat produced is halved.
A) Two times. Assuming the current (\(I\)) flowing through the conductor remains constant, if the resistance (\(R\)) is doubled, the heat produced (\(H = I^2 R t\)) will also double. This is the most common interpretation in such questions unless a constant voltage source is explicitly mentioned.
The question asks to identify which of the four Vedas contains the maximum number of verses. This requires knowledge of the structure and content of the principal Vedas.
A) Rig Veda — The Rig Veda is the largest and oldest of the four Vedas, consisting of approximately 10,600 verses organized into 10 Mandalas (books).
The question asks to identify the process by which plants obtain their carbon and energy requirements. We need to evaluate each option based on its role in plant physiology.
D) Photosynthesis — This process uses carbon dioxide from the atmosphere and light energy to synthesize organic compounds (sugars), thereby fulfilling both the carbon and energy requirements of the plant.
How many cubic cm of water can a hemispherical container of radius 7 cm hold (rounded off to 2 decimal places) (use π = \( \frac{22}{7} \))?
To find the amount of water a hemispherical container can hold, we need to calculate its volume. The formula for the volume of a hemisphere will be used, and the given radius and value of \(\pi\) will be substituted into the formula.
The volume of a sphere is given by \(V_{\text{sphere}} = \frac{4}{3} \pi r^3\). A hemisphere is half of a sphere, so its volume is:
\[ V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \]Thus, the hemispherical container can hold approximately \(718.67\) cubic cm of water.
Correct Option: D) 718.67