To find the speed of the train, we need to determine its length first. When a train crosses a platform, the total distance covered is the sum of the train's length and the platform's length. Since the speed of the train is constant, we can set up two equations based on the given information and solve for the train's length and then its speed.
Let the length of the train be \(L_T\) meters and its speed be \(S\) m/s.
When the train crosses a platform, the distance covered is the sum of the train's length and the platform's length. We know that \(\text{Distance} = \text{Speed} \times \text{Time}\).
Case 1: Crossing a 110 m long platform in 13.5 seconds.
The total distance covered is \(L_T + 110\) meters.
So, we have the equation:
Case 2: Crossing a 205 m long platform in 18.25 seconds.
The total distance covered is \(L_T + 205\) meters.
So, we have the equation:
Now we have a system of two linear equations. We can solve for \(L_T\) and \(S\). Subtract Equation 1 from Equation 2:
\[ (L_T + 205) - (L_T + 110) = (S \times 18.25) - (S \times 13.5) \]\[ 205 - 110 = S \times (18.25 - 13.5) \]\[ 95 = S \times 4.75 \]Solve for \(S\):
\[ S = \frac{95}{4.75} \]\[ S = \frac{9500}{475} \]\[ S = 20 \text{ m/s} \]The speed is in m/s, but the options are in km/h. To convert m/s to km/h, multiply by \(\frac{18}{5}\):
\[ \text{Speed in km/h} = 20 \times \frac{18}{5} \]\[ \text{Speed in km/h} = 4 \times 18 \]\[ \text{Speed in km/h} = 72 \text{ km/h} \]Correct Option: A) 72 km/h
A cistern can be filled by two pipes A and B in 4 hours and 6 hours respectively. When full, the tank can be emptied by a third pipe C in 8 hours. If all pipes are turned on at the same time, the cistern will be full in
\( \frac{40}{7} \) hours
\( \frac{24}{7} \) hours
\( \frac{16}{7} \) hours
\( \frac{31}{7} \) hours
This problem involves calculating the combined work rate of multiple pipes filling and emptying a cistern. We will determine the individual filling/emptying rates per hour and then combine them to find the net rate. Finally, we will use the net rate to find the total time required to fill the cistern.
Correct Option: B) \( \frac{24}{7} \) hours
To determine Aadiya's final direction with respect to her initial position, we need to visualize her movements. We can represent her path using a coordinate system or by drawing a simple diagram based on standard cardinal directions (North, South, East, West).
Correct Option: B) North-West
The question asks to identify the plant whose body is not differentiated into true roots, stems, and leaves. This refers to the most primitive plant groups, specifically algae, which have a thalloid body structure.
D) Spirogyra — Spirogyra is a filamentous green alga. Algae are characterized by a simple, undifferentiated plant body called a thallus, which lacks true roots, stems, and leaves. They are aquatic and absorb nutrients directly from the water.
This question tests logical reasoning and the ability to identify implicit assumptions in a given statement. An assumption is something taken for granted or accepted as true without proof. When someone makes a statement, their underlying reasons or expectations often form the implicit assumptions.
Correct Option: A) Both I and II are implicit.
The question asks to identify the Central Government's initiative aimed at bringing the masses into the formal banking system. This refers to a specific financial inclusion scheme launched in India.
B) Jan Dhan Yojana — The Pradhan Mantri Jan-Dhan Yojana (PMJDY) is indeed the national mission for financial inclusion launched by the Central Government in August 2014. Its objective is to ensure access to financial services, namely, basic savings bank accounts, access to credit, remittance facility, insurance, and pension, in an affordable manner.
The question asks about who released commemorative coins for the Nabakalebara festival in March 2018. This is a factual question related to a specific event and requires knowledge of who holds the authority to release such coins and who was in that position at the time.
Correct Option: D) The President of India. In March 2018, the then President of India, Ram Nath Kovind, released the commemorative coins of Rs 1,000 and Rs 10 on the occasion of the Nabakalebara festival in Puri, Odisha. The President, as the head of state, frequently performs such ceremonial duties involving national cultural or religious significance.
To solve this problem, we need to perform addition and subtraction of decimal numbers. The key is to align the decimal points correctly when adding or subtracting, and then perform the operations step-by-step.
The numbers to be added are \(4\), \(4.44\), \(44.4\), \(4.04\), and \(444\).
It's helpful to write all numbers with the same number of decimal places for clarity, adding zeros where necessary.
\[ \begin{array}{r} 4.00 \\ 4.44 \\ 44.40 \\ 4.04 \\ + \quad 444.00 \\ \hline 506.88 \end{array} \]So, the sum of the positive numbers is \(506.88\).
Now, subtract \(20\) from the sum obtained in the previous step.
\[ 506.88 - 20 = 486.88 \]Let's re-add carefully:
Adding the hundredths column: \(0 + 4 + 0 + 4 + 0 = 8\). So, \(0.08\).
Adding the tenths column: \(0 + 4 + 4 + 0 + 0 = 8\). So, \(0.8\).
Adding the units column: \(4 + 4 + 4 + 4 + 4 = 20\). Write down \(0\), carry over \(2\).
Adding the tens column: \(0 + 0 + 4 + 0 + 4 + \text{carry over } 2 = 10\). Write down \(0\), carry over \(1\).
Adding the hundreds column: \(0 + 0 + 0 + 0 + 4 + \text{carry over } 1 = 5\).
So, the sum is \(500.88\).
Now, subtract \(20\):
\[ 500.88 - 20 = 480.88 \]A) \(480.88\) is the correct result after performing the addition and subtraction accurately.
In which group of the modern periodic table are halogens placed?
The question asks to identify the group number in the modern periodic table where halogens are located. This requires knowledge of the periodic table's structure and the classification of elements.
Correct Option: D) 17 th
Halogens (Fluorine, Chlorine, Bromine, Iodine, Astatine) are located in Group 17 of the modern periodic table. They are highly reactive non-metals with 7 valence electrons.
This question tests knowledge of significant appointments in public sector undertakings, which is a common topic in current affairs for competitive exams. The key is to recall the specific appointment mentioned and the organization associated with it.
Correct Option: B) Security Printing and Minting Corporation of India Limited (SPMCIL)
S. Selvakumar, an IAS officer of the 1997 batch, was appointed as the Chairman and Managing Director of Security Printing and Minting Corporation of India Limited (SPMCIL) with effect from January 16, 2018. SPMCIL is a Mini Ratna Category-I Central Public Sector Enterprise that manufactures security products like currency notes, coins, postage stamps, and other security documents.