All questions of August Week 3 for Class 10 Exam

In India, the Gulf of Kachchh, provides ideal conditions for utilising tidal energy. A 900 mw tidal energy power plant is set up here by the National Hydropower Corporation.

The sources of energy which are exhaustible and being produced continuously in nature are called nonconventional energy or renewable sources of energy. atomic energy is the only option.

Due to the alpha decay of thorium and uranium, monazite contains a significant amount of helium, which can be extracted by heating. Monazite is an important ore for thorium, lanthanum, and cerium. It is often found in placer deposits. India, Madagascar, and South Africa have large deposits of monazite sands.

Rat-hole mining is a primitive and hazardous method of mining for coal, with tunnels that are only 3-4 feet in diameter (hence, rat-hole), leading to pits ranging from 5-100 sq. mt deep.

Mumbai high

The central nervous system (CNS), consisting of the brain and spinal cord, is the main coordinating center of the body. It receives information from all parts of the body, integrates it, and sends messages to muscles to control voluntary actions such as writing, talking, and moving. The peripheral nervous system facilitates communication between the CNS and other body parts but does not serve as the main control center.

Distance between two point is

Let's call the two given vertices A and B, with coordinates (3, 2) and (x, y) respectively.

Since a parallelogram has opposite sides that are parallel, we can find the coordinates of the other two vertices by applying the same translation to points A and B.

To find the translation, we can subtract the x-coordinate of point A from the x-coordinate of point B, and subtract the y-coordinate of point A from the y-coordinate of point B:

x - 3 = 3 - 3 = 0
y - 2 = 2 - 2 = 0

So the translation is (0, 0).

To find the coordinates of the other two vertices, we can add the translation to points A and B:

Point A + translation = (3, 2) + (0, 0) = (3, 2)
Point B + translation = (x, y) + (0, 0) = (x, y)

Therefore, the other two vertices of the parallelogram are (3, 2) and (x, y).

To determine the value of k, we need to check if the three given points (3, 2), (4, k), and (5, 3) are collinear. Two points are collinear if the slope between them is the same as the slope between any other two points on the line.

Calculating the slope between (3, 2) and (4, k):
The slope formula is given by:

m = (y2 - y1) / (x2 - x1)

Using the coordinates (3, 2) and (4, k), we have:

m = (k - 2) / (4 - 3)
m = (k - 2) / 1
m = k - 2

Calculating the slope between (4, k) and (5, 3):
Using the coordinates (4, k) and (5, 3), we have:

m = (3 - k) / (5 - 4)
m = (3 - k) / 1
m = 3 - k

Since the two slopes are equal, we can equate them:

k - 2 = 3 - k

Solving this equation for k:

2k = 5

k = 5/2

Therefore, the value of k is 5/2, which corresponds to option C.

Odisha is the largest bauxite producing state accounting for more than half of the total production of India.The main bauxite belt is in kalahandi  and Koraput districts.

B

Let A(-2, 2)
B(8, -2)
C(-4, -3)
distance
AB=√(x2-x1) ²+(y2-y1) ²
=√(8+2) ²+(-2-2) ²=√100+16=√116
BC=√(-4-8) ²+(-3+2) ²=√144+1=√145
AC=√(-4+2) ²+(-3-2) ²=√4+25=√29
from the above
AB²=(√116) ²=116
BC²=(√145) ²=145
AC²=(√29) ²=29
AB²+AC²=BC²=145units
hence, by Converse of Pythagoras theorem
ABC is a right triangle
and hence,
A, B, C are the vertices of a right ∆
hence, option (C) is correct

- Gypsum is formed as a result of evaporation.
- Minerals are formed in various forms in the earth and they normally are formed in layers or beds through the sedimentary rocks.

Finding the Incentre of a Triangle

To find the incentre of a triangle, we need to find the point where the angle bisectors of the triangle meet. The angle bisectors are the lines that divide the angles of the triangle into two equal parts. The incentre is the intersection of these angle bisectors and is equidistant from all three sides of the triangle.

Given Triangle

The triangle in the question has sides along the lines x = 0, y = 0 and x/6 y/8 = 1. Let's first plot these lines on a graph to get a visual representation of the triangle.

We can see that the triangle is a right-angled triangle with vertices at (0, 0), (6, 0) and (0, 8). Now, let's find the equation of the angle bisectors of this triangle.

Finding the Equation of Angle Bisectors

To find the equation of the angle bisectors, we need to first find the equations of the two lines that form each angle. We can then find the midpoint of these lines and the slope of the angle bisector. Finally, we can use the point-slope form of a line to find the equation of the angle bisector.

Let's start with the angle formed by sides (0, 0) to (6, 0) and (0, 8). The equation of the line joining these two points is y = -3/4x + 8. Now, let's find the equation of the line perpendicular to this line that passes through the midpoint of the line segment joining (0, 0) and (6, 0).

The midpoint of the line segment joining (0, 0) and (6, 0) is (3, 0). The slope of the line joining (0, 0) and (6, 0) is 0. Therefore, the slope of the line perpendicular to this line is undefined (since it is a vertical line). The equation of the line passing through (3, 0) with undefined slope is x = 3.

Using the same method, we can find the equation of the angle bisector of the angle formed by sides (0, 0) to (0, 8) and (6, 0). The equation of the line joining these two points is y = 8/6x = 4/3x. The midpoint of the line segment joining (0, 0) and (0, 8) is (0, 4). The slope of the line joining (0, 0) and (0, 8) is undefined. Therefore, the slope of the line perpendicular to this line is 0. The equation of the line passing through (0, 4) with slope 0 is y = 4.

Intersection of Angle Bisectors

Now that we have the equations of the two angle bisectors, we can find their intersection point, which is the incentre of the triangle. The intersection point is the solution to the system of equations:

x = 3

y = 4

y = 4

The solution to this system of equations is (3, 4), which is option (c). Therefore, the incentre of the triangle whose sides are along the lines x = 0, y = 0 and x/6 y/8 = 1 is

Involuntary Actions Controlled by the Medulla
The medulla oblongata is a crucial part of the hindbrain, responsible for regulating several vital involuntary actions essential for survival.
Regulation of Respiration
- The medulla plays a key role in controlling the rhythm and rate of breathing.
- It contains respiratory centers that send signals to the diaphragm and intercostal muscles, facilitating inhalation and exhalation.
- It responds to changes in carbon dioxide and oxygen levels in the blood, ensuring the body's respiratory needs are met.
Other Functions of the Medulla
- While respiration is a primary function, the medulla also regulates:
- Heart rate: It influences cardiac function by controlling the autonomic nervous system.
- Blood pressure: It helps in maintaining blood pressure through vasomotor control.
- Reflex actions: The medulla is involved in reflexes such as coughing, sneezing, and swallowing.
Why Other Options Are Incorrect
- Control of Posture and Balance: This function is primarily managed by the cerebellum, which coordinates muscle movements and maintains balance.
- Precision of Voluntary Actions: The motor cortex and basal ganglia are responsible for the precision and coordination of voluntary movements, not the medulla.
- Reflex Movements of Head, Neck, and Trunk: While the medulla does play a role in some reflex actions, it is not the primary center for all reflex movements of the head, neck, and trunk, which involve different neural pathways.
Conclusion
In summary, the medulla oblongata’s primary involuntary action is the regulation of respiration, making option 'A' the correct answer. Its role in maintaining vital functions is essential for life.