The question asks to identify an Indian river that originates from Gangotri and is significantly polluted by human activities and industries. We need to recall the origin points of the given rivers and their pollution status.
D) Ganga — The Ganga river originates from the Gangotri Glacier and is one of the most polluted rivers in India due to extensive human activities and industrial discharge along its basin.
The question asks to identify the device that operates on the principle of a force being produced on a current-carrying coil when placed in a magnetic field. This phenomenon is a direct application of the motor effect, where electrical energy is converted into mechanical energy.
C) Motor. An electric motor operates on the principle that a current-carrying conductor (coil) placed in a magnetic field experiences a force, which causes it to rotate, thereby converting electrical energy into mechanical energy.
The question asks about the characteristics of a commercial motor. We need to evaluate two statements regarding the type of magnet used and the core material.
Commercial motors, especially powerful ones, require strong and controllable magnetic fields. Electromagnets provide this advantage over permanent magnets. The strength of an electromagnet can be varied by changing the current flowing through its coil, which allows for better control over the motor's speed and torque. Permanent magnets have fixed magnetic strength, limiting the motor's performance and control. Therefore, using electromagnets is a common feature in commercial motors.
The core material inside the coils of an electromagnet plays a crucial role in enhancing the magnetic field. Soft iron is a ferromagnetic material that can be easily magnetized and demagnetized. When current flows through the coil, the soft-iron core becomes strongly magnetized, significantly increasing the magnetic field strength. When the current is switched off, soft iron quickly loses its magnetism, which is essential for the continuous rotation in a motor where the magnetic poles need to switch rapidly. Hard magnetic materials (like steel) retain magnetism, which would hinder the motor's operation. Thus, a soft-iron core is ideal for commercial motors.
Both statements describe features that are characteristic of commercial motors designed for efficiency, power, and control. Commercial motors typically use electromagnets for variable and strong magnetic fields, and these electromagnets are wound around soft-iron cores to maximize magnetic flux and allow for quick demagnetization.
Correct Option: C) Both (a) and (b)
A train overtakes two persons who are walking at 15 m/s and 35 m/s, respectively, in the same direction as that of the train in 20 seconds and 40 seconds, respectively. The length of the train is:
This problem involves relative speed. When a train overtakes a person moving in the same direction, the relative speed is the difference between the speed of the train and the speed of the person. The distance covered in this context is the length of the train itself. We will set up two equations based on the given information and solve for the length and speed of the train.
Let the length of the train be \(L\) meters and its speed be \(V\) m/s.
The first person is walking at \(v_1 = 15 \text{ m/s}\). The train overtakes this person in \(t_1 = 20 \text{ seconds}\).
Since they are moving in the same direction, the relative speed is \(V - v_1\). The distance covered is the length of the train, \(L\).
Using the formula \(\text{Distance} = \text{Speed} \times \text{Time}\), we get:
\[ L = (V - 15) \times 20 \quad \text{(Equation 1)} \]The second person is walking at \(v_2 = 35 \text{ m/s}\). The train overtakes this person in \(t_2 = 40 \text{ seconds}\).
Similarly, the relative speed is \(V - v_2\). The distance covered is \(L\).
So, we get:
\[ L = (V - 35) \times 40 \quad \text{(Equation 2)} \]Now we have two equations for \(L\). We can equate them to find \(V\):
\[ (V - 15) \times 20 = (V - 35) \times 40 \]Divide both sides by 20:
\[ V - 15 = (V - 35) \times 2 \] \[ V - 15 = 2V - 70 \]Rearrange the terms to solve for \(V\):
\[ 2V - V = 70 - 15 \] \[ V = 55 \text{ m/s} \]So, the speed of the train is \(55 \text{ m/s}\).
Substitute the value of \(V\) back into either Equation 1 or Equation 2 to find \(L\).
Using Equation 1:
\[ L = (55 - 15) \times 20 \] \[ L = 40 \times 20 \] \[ L = 800 \text{ m} \]Using Equation 2 (for verification):
\[ L = (55 - 35) \times 40 \] \[ L = 20 \times 40 \] \[ L = 800 \text{ m} \]The length of the train is \(800 \text{ m}\).
C) 800 m is the correct length of the train, as calculated from the given conditions.
A) 1000 m — This would be incorrect if there was an error in calculating the relative speeds or the time taken. For example, if the train's speed was higher or the time taken was different.
B) 900 m — This value does not satisfy both conditions simultaneously. A calculation error could lead to this option.
D) 700 m — This value is also incorrect and would result from miscalculations, such as incorrect relative speed or time values.
The question asks us to evaluate two statements regarding neutralization reactions. We need to determine if each statement accurately describes a neutralization reaction and its general representation.
Correct Option: D) Both statements are correct.
This problem involves arranging six friends (G, H, I, J, K, L) based on their relative heights. We need to deduce the height order using the given clues and identify the shortest person.
Clue 1: G is taller than only two other friends.
This means G is the 3rd shortest person. There are 6 friends, so 3 friends are taller than G and 2 friends are shorter than G. We can represent this as:
_ _ G _ _ _
Clue 2: I is shorter than only one friend.
This means I is the 2nd tallest person. Only one friend is taller than I. So, I is at the 5th position from the shortest end, or 2nd from the tallest end.
_ _ G _ I _
Clue 3: K is shorter than G but taller than J.
From clue 1, we know G is the 3rd shortest. K is shorter than G, so K must be either the 1st or 2nd shortest. K is also taller than J, which means J must be the shortest. This places J as the 1st shortest and K as the 2nd shortest.
J K G _ I _
Clue 4: H is shorter than L.
We have three friends remaining to place: H, L, and one empty slot between G and I. Since H is shorter than L, and the only remaining slots are between G and I, and the tallest position, H must be in the slot between G and I, and L must be the tallest.
J K G H I L
Final Order:
The complete order from shortest to tallest is: J < K < G < H < I < L.
Identify the shortest:
From the final order, J is the shortest among all friends.
B) J — Based on the step-by-step deduction, J is the shortest friend.
In a code language, the numbers/symbols are coded using letters as per the table given below and as per the given conditions.
| Number/ Symbol | 2 | $ | 7 | @ | 4 | # | 9 | & | 1 | ! | 3 | * |
| Code | T | D | C | R | G | B | Y | H | N | J | P | L |
Conditions:
i. If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.
ii. If the first element is an odd number and the last an even number, the first and last elements are to be coded as ‘©’.
iii. If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.
What will be the code for @ 4 # 3 * 9?
The problem requires us to decode a given sequence of symbols and numbers based on a provided coding table and a set of conditions. We need to apply the conditions sequentially to determine the final code.
D) YGBPLR is the correct code after applying the conditions.
To find a quadratic equation given its roots, we can use the relationship between the roots and the coefficients of a quadratic equation. If \(\alpha\) and \(\beta\) are the roots of a quadratic equation \(ax^2 + bx + c = 0\), then the equation can be written as \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\).
The roots are given as 7 and 12. Let \(\alpha = 7\) and \(\beta = 12\).
Sum of roots, \(\alpha + \beta = 7 + 12 = 19\).
Product of roots, \(\alpha\beta = 7 \times 12 = 84\).
The general form of a quadratic equation with roots \(\alpha\) and \(\beta\) is:
\[ x^2 - (\alpha + \beta)x + \alpha\beta = 0 \]Substitute the calculated sum and product of roots into this formula:
\[ x^2 - (19)x + 84 = 0 \] \[ x^2 - 19x + 84 = 0 \]Correct Option: D) x² – 19x + 84 = 0
The question asks to identify which process is NOT used by plants for excretion. We need to evaluate each given option against the known excretory mechanisms in plants.
Correct Option: D) Filter toxic substances through the leaves. This process is not followed by plants for excretion. Plants do not possess a filtering system analogous to animal kidneys to filter toxic substances through their leaves.
The question asks to identify the bank that organized the global hackathon "HARBINGER 2021 – Innovation for Transformation" with the theme "Smarter Digital Payments". This is a factual question related to current affairs and banking initiatives.
A) Reserve Bank of India. The Reserve Bank of India (RBI) was indeed the organizer of the global hackathon, HARBINGER 2021 – Innovation for Transformation, with the theme 'Smarter Digital Payments'. This was a significant initiative by the central bank to foster innovation in the digital payments ecosystem.