The question asks to identify the Indian Institute of Technology (IIT) that developed a robot named "HomoSEP" for cleaning septic tanks without human intervention in June 2022. This is a factual recall question related to recent technological advancements in India.
Correct Option: C) Indian Institute of Technology (IIT), Madras
Researchers at IIT Madras developed "HomoSEP", a robot designed to clean septic tanks without human intervention. This innovation aims to eliminate manual scavenging, a dangerous and undignified practice. The robot was developed in collaboration with the Safai Karamchari Andolan (SKA) and has been successfully field-tested.
The given series consists of alternating perfect squares and perfect cubes. We need to identify the pattern of these numbers and apply it to find the missing term.
This sequence of bases for the squares is \(8, 6, 4, \dots\), which is an arithmetic progression decreasing by 2 each time.
This sequence of bases for the cubes is \(7, 5, \dots\), which is an arithmetic progression decreasing by 2 each time.
The missing term is the sixth term in the series. Following the alternating pattern, it should be a cube. The base for the previous cube was 5. Decreasing by 2, the next base should be \(5 - 2 = 3\).
Therefore, the missing term is \(3^3\).
Correct Option: B) 27
The question asks to identify the river on which the famous Majuli island is located. This is a factual question related to Indian geography. We need to recall the location of Majuli and its associated river.
Correct Option: C) Brahmaputra — Majuli is a large river island in the Brahmaputra River, Assam, India. It is a well-known geographical feature and a significant cultural center.
The valency of an atom is its combining capacity, which is determined by how readily it can gain, lose, or share electrons to achieve a stable electron configuration. This stability is typically achieved when the outermost electron shell is full, often referred to as the octet rule (having 8 electrons) or the duet rule for the first shell (having 2 electrons).
B) Number of electrons in the outermost shell — The number of electrons in the outermost shell (valence electrons) dictates an atom's combining capacity, as these are the electrons involved in chemical reactions to achieve a stable electron configuration.
In a row of people, all facing north, Anil is 5th from the right end. Mona is 13th from the right end. Mona is exactly between Anil and Ritu. If Ritu is 5th from the left end of the row, how many people are there in the row?
This problem involves determining the total number of people in a row based on their positions from both ends and relative positions. We will use the given information to find the positions of Anil, Mona, and Ritu, and then use the formula for total people in a row: \(\text{Total} = \text{Position from Left} + \text{Position from Right} - 1\).
Determine Anil's position from the right:
Anil is 5th from the right end.
Determine Mona's position from the right:
Mona is 13th from the right end.
Find the number of people between Anil and Mona:
Since Anil is 5th from the right and Mona is 13th from the right, the number of people between them is:
Determine Ritu's position relative to Mona:
Mona is exactly between Anil and Ritu. This means the number of people between Anil and Mona is equal to the number of people between Mona and Ritu. So, there are 7 people between Mona and Ritu.
Determine Ritu's position from the right end:
Since Mona is 13th from the right, and there are 7 people between Mona and Ritu, Ritu's position from the right end will be:
Use Ritu's positions to find the total number of people:
We know Ritu is 5th from the left end and 21st from the right end. The total number of people in the row can be calculated using the formula:
Therefore, there are 25 people in the row.
Correct Option: C) 25
If an image formed after reflection from a mirror is virtual and highly diminished, then the position of the object and type of mirror is:
Between C and F and concave mirror
Centre of curvature and concave mirror
Infinity and concave mirror
Infinity and convex mirror
The question asks to identify the type of mirror and the object's position that results in a virtual and highly diminished image. We need to recall the image formation properties of concave and convex mirrors for different object positions.
D) Infinity and convex mirror. When an object is placed at infinity in front of a convex mirror, the rays of light coming from the object are parallel to the principal axis. After reflection, these rays appear to diverge from the principal focus (F) behind the mirror. This results in a virtual, erect, and highly diminished image formed at F.
The question asks to identify the Five-Year Plan that was also known as the 'Gadgil Yojna'. This requires knowledge of the specific names associated with India's Five-Year Plans and the key figures involved in their formulation.
Correct Option: B) The Third Five-Year Plan (1961-1966) is also known as the 'Gadgil Yojna'. Dr. D.R. Gadgil, who was the Deputy Chairman of the Planning Commission during that period, was instrumental in its formulation. This plan focused on agriculture and improving the production of wheat, but it faced significant challenges due to the Sino-Indian War (1962) and the Indo-Pakistani War (1965), leading to its failure to achieve its growth targets.
The question asks about the rule used to determine the direction of rotation of a coil in an electric motor. An electric motor works on the principle that a current-carrying conductor placed in a magnetic field experiences a force. This force causes the rotation. We need to identify the rule that relates the direction of magnetic field, current, and the resulting force/motion.
Correct Option: D) Fleming’s left hand rule
This problem deals with the fundamental concept of current flow in a series circuit. In a series circuit, the current remains the same through all components connected in series, regardless of their individual resistance values.
D) 6 amp is correct because in a series circuit, the current is the same at every point. If 6 amp flows through the 5 ohm resistor, it must also flow through the 10 ohm resistor connected in series with it.
To find the single equivalent discount for successive discounts, we can assume an original price (e.g., 100 units) and apply each discount sequentially. Alternatively, we can use a formula for successive discounts.
Assume Original Price: Let the original price of the item be \(P = 100\).
Apply the first discount (30%):
After a 30% discount, the price becomes \(100\% - 30\% = 70\%\) of the original price.
\[ \text{Price}_1 = P \times \left(1 - \frac{30}{100}\right) = 100 \times 0.70 = 70 \]Apply the second discount (20%):
This discount is applied to the new price (\(70\)). After a 20% discount, the price becomes \(100\% - 20\% = 80\%\) of the previous price.
\[ \text{Price}_2 = \text{Price}_1 \times \left(1 - \frac{20}{100}\right) = 70 \times 0.80 = 56 \]Apply the third discount (10%):
This discount is applied to the latest price (\(56\)). After a 10% discount, the price becomes \(100\% - 10\% = 90\%\) of the previous price.
\[ \text{Price}_3 = \text{Price}_2 \times \left(1 - \frac{10}{100}\right) = 56 \times 0.90 = 50.4 \]Calculate the total equivalent discount:
The final price after all discounts is \(50.4\). The original price was \(100\).
The total discount is the difference between the original price and the final price.
\[ \text{Total Discount Amount} = \text{Original Price} - \text{Final Price} = 100 - 50.4 = 49.6 \]Express as a percentage:
Since we started with 100, the total discount amount directly represents the percentage discount.
\[ \text{Equivalent Discount Percentage} = \frac{\text{Total Discount Amount}}{\text{Original Price}} \times 100\% = \frac{49.6}{100} \times 100\% = 49.6\% \]A) 49.6 % is the correct single percentage discount equivalent to three successive discounts of 30%, 20%, and 10%.