The given series consists of terms, each having a number, a letter, another number, and another letter. We need to identify the pattern for each component (first number, first letter, second number, second letter) separately to find the next term.
Correct Option: C) 13M12L
We are given information about three numbers: their mean, range, and a relationship between the middle number and the sum of the other two. We need to find the largest of these three numbers. We will set up a system of equations based on the given information and solve for the three numbers.
Let the three numbers be \(x, y, z\) in ascending order, so \(x < y < z\).
Mean of the three numbers:
The mean is given as 38. So,
Range of the data:
The range is the difference between the largest and the smallest number. Since we ordered them \(x < y < z\), the largest number is \(z\) and the smallest is \(x\). The range is given as 31. So,
Relationship for the middle number:
The middle number (\(y\)) is 20 less than the sum of the other two numbers (\(x + z\)). So,
Solve the system of equations:
We have three equations:
Add Equation 1 and Equation 3:
\[ (x + y + z) + (x - y + z) = 114 + 20 \]\[ 2x + 2z = 134 \]\[ x + z = 67 \quad \text{(Equation 4)} \]Now we have a simpler system with Equation 2 and Equation 4:
Add these two equations:
\[ (z - x) + (z + x) = 31 + 67 \]\[ 2z = 98 \]\[ z = \frac{98}{2} \]\[ z = 49 \]Substitute the value of \(z\) into Equation 4 to find \(x\):
\[ x + 49 = 67 \]\[ x = 67 - 49 \]\[ x = 18 \]Substitute the values of \(x\) and \(z\) into Equation 1 to find \(y\):
\[ 18 + y + 49 = 114 \]\[ y + 67 = 114 \]\[ y = 114 - 67 \]\[ y = 47 \]The three numbers are \(x=18\), \(y=47\), and \(z=49\). Let's check if they satisfy all conditions:
The largest number among these three is \(z = 49\).
B) 49 is the largest number among the three.
The question asks about the type of soil found in the fertile Gangetic plain. This requires knowledge of the major soil types in India and their geographical distribution.
Correct Option: C) Alluvial soil is formed by the deposition of sediments by rivers. The Gangetic plain is a vast riverine plain, making alluvial soil its predominant and highly fertile soil type.
This is an analogy question where you need to identify the relationship between the first pair of words and then find a word that shares the same relationship with the third word.
Correct Option: C) Curve. "True" and "False" are antonyms. Similarly, "Straight" and "Curve" are antonyms.
The question asks to identify a public sector industry from the given options. A public sector industry is one where the government owns a majority stake (typically 51% or more) and controls its operations. We need to evaluate each option based on this definition.
B) SAIL (Steel Authority of India Limited) is a Maharatna Public Sector Undertaking (PSU) and is owned by the Government of India. Therefore, it is a public sector industry.
To find the ratio \(b:c\) from the given ratios \(a:b\) and \(a:c\), we need to make the common term 'a' equal in both ratios. Once 'a' is the same, we can directly compare 'b' and 'c'.
Given the first ratio:
\[ a : b = 4 : 5 \]This can be written as:
\[ \frac{a}{b} = \frac{4}{5} \]Given the second ratio:
\[ a : c = 3 : 4 \]This can be written as:
\[ \frac{a}{c} = \frac{3}{4} \]To combine these ratios, we need to make the value of 'a' the same in both. The current values for 'a' are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12.
Adjust the first ratio so that 'a' becomes 12:
\[ a : b = 4 : 5 \]Multiply both parts of the ratio by 3:
\[ (4 \times 3) : (5 \times 3) = 12 : 15 \]So, \(a : b = 12 : 15\).
Adjust the second ratio so that 'a' becomes 12:
\[ a : c = 3 : 4 \]Multiply both parts of the ratio by 4:
\[ (3 \times 4) : (4 \times 4) = 12 : 16 \]So, \(a : c = 12 : 16\).
Now we have:
\[ a : b = 12 : 15 \] \[ a : c = 12 : 16 \]Since 'a' is the same (12) in both equivalent ratios, we can directly compare 'b' and 'c'.
\[ b : c = 15 : 16 \]A) 15 : 16 is the correct ratio for \(b:c\).
The problem describes a particle moving under a constant magnitude force that is always perpendicular to its velocity. We need to determine which physical quantity remains constant under these conditions. This scenario is characteristic of uniform circular motion or motion where the force only changes the direction of velocity, not its magnitude.
Recall the definition of power delivered by a force:
\[ P = \vec{F} \cdot \vec{v} \]The problem states that the force \(\vec{F}\) is always perpendicular to the velocity \(\vec{v}\). This means the angle between \(\vec{F}\) and \(\vec{v}\) is \(90^\circ\).
Substitute this into the power equation:
\[ P = |\vec{F}| |\vec{v}| \cos(90^\circ) \]Since \(\cos(90^\circ) = 0\), the power delivered by the force is zero:
\[ P = 0 \]According to the work-energy theorem, the net work done on a particle is equal to the change in its kinetic energy. Power is the rate of doing work, so if power is zero, the rate of change of kinetic energy is zero.
\[ P = \frac{dK}{dt} \]Since \(P=0\), it implies \(\frac{dK}{dt} = 0\). This means the kinetic energy \(K\) of the particle is constant.
Kinetic energy is given by \(K = \frac{1}{2}mv^2\). Since \(m\) (mass) is constant and \(K\) is constant, the magnitude of the velocity (speed) \(v\) must also be constant.
B) Its kinetic energy is constant. As derived, when the force is always perpendicular to the velocity, the power delivered by the force is zero, which means the kinetic energy of the particle remains constant.
The question asks for the launch date of the Pradhan Mantri Ujjwala Yojana (PMUY). This is a factual question requiring knowledge of important government schemes and their timelines.
Correct Option: D) May 2016
The value of Avogadro constant is _______.
6.023 × 1023
6.022 × 1021
6.022 × 1022
6.022 × 1024
The question asks for the value of Avogadro's constant. This is a fundamental constant in chemistry and physics, representing the number of constituent particles (atoms, molecules, ions, etc.) per mole of a substance. Its value is internationally defined and widely used in calculations involving moles and quantities of substances.
A) 6.023 × 1023. This is the standard and most widely accepted value for Avogadro's constant, representing the number of particles in one mole of a substance.