Solution:

For two similar triangles, the ratio of their corresponding sides is equal to the ratio of their perimeters.

Given:

Sum:

Thus,

✅ Correct Answer: 50 cm

Operational Amplifier Output Rate of Change

The question asks about the maximum rate at which the output of an operational amplifier (op-amp) can change. This specific characteristic of an operational amplifier is crucial for understanding its performance, especially when dealing with rapidly changing input signals.

Slew Rate: The Key Characteristic

The term that describes the maximum rate at which an operational amplifier's output voltage can change is the Slew rate. It is typically measured in volts per microsecond (V/μs). A higher slew rate indicates that the op-amp can respond more quickly to changes in its input signal without causing distortion in the output waveform, particularly for high-frequency signals or large signal swings.

• The slew rate limits how fast the output voltage can rise or fall. If the input signal changes too rapidly for the op-amp's slew rate, the output will not be able to follow the input accurately, leading to what is known as slew-rate limiting distortion.
• It is an important parameter for applications such as audio amplifiers, video amplifiers, and data converters, where signal integrity at high frequencies or during large voltage transitions is critical.

Analyzing Other Operational Amplifier Parameters

Let's briefly look at the other options provided to understand why they do not describe the maximum rate of change of an operational amplifier's output:

• CMRR (Common-Mode Rejection Ratio):

  CMRR is a measure of an operational amplifier's ability to reject common-mode signals, which are signals present simultaneously and in phase on both input terminals. A high CMRR indicates good rejection of unwanted noise or interference that appears equally on both inputs. It is expressed as a ratio (often in decibels) and is unrelated to the speed at which the output voltage changes.

  Mathematically, CMRR is given by:

• Input offset voltage:

  The input offset voltage (V_OS​) is the differential DC voltage that must be applied between the input terminals of an operational amplifier to make the output voltage zero. Ideally, an op-amp should produce zero output when both inputs are at the same potential, but due to imperfections in the manufacturing process, a small DC voltage is often required at the input to achieve this zero output. This parameter quantifies the DC accuracy of the operational amplifier and does not relate to the maximum rate of change of the output.

Based on the definitions and functionalities of these parameters, it is clear that only the Slew rate directly quantifies the maximum rate at which an operational amplifier's output can change.

The given figure is redrawn as:

Y = AB + 1

Since 1 + Any Variable is always 1

Y = 1

Important Points

Step 1: Use the union formula

To find the magnetic force on a charged particle moving in a magnetic field, use the formula:

Let’s solve it step by step.

Given:

• Number stored = 8 (decimal)

• In binary (8-bit):

• Instruction: RAL (Rotate Accumulator Left through Carry)

• Initial CY = 0 (standard assumption unless specified)

How RAL Works

• Each bit shifts left by 1.

• Bit 7 goes to Carry.

• Carry goes to Bit 0.

First RAL

Binary before:

Shift left:

• Bit 7 → CY = 0

• CY (0) enters bit 0

Result:

Carry = 0

Second RAL

Binary before:

Rotate:

• Bit 7 → CY = 0

• CY enters bit 0

Result:

✅ Final Answer: decimal 32

Mean of the data = 30

Mean deviation about mean:

Coefficient of mean deviation:

✅ Correct Answer: 0.22

Curie: Understanding the Unit of Radioactivity

The question asks to identify what 'Curie' is a unit of. Let's explore the concept of the Curie unit and its relationship to various physical quantities.

Radioactivity: The Correct Answer

The correct answer is Radioactivity. The Curie (Ci) is a non-SI unit used to measure the activity of a radioactive substance. It was named in honor of Marie and Pierre Curie, who did pioneering research on radioactivity.

• One Curie (1 Ci) is defined as the activity of a quantity of any radioactive material in which the number of disintegrations per second is equal to the number of disintegrations per second of one gram of radium-226.

Why Other Options are Incorrect

Let's briefly look at why the other options are not correct:

• Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance. Its SI unit is Kelvin (K), and other common units include Celsius (°C°C) and Fahrenheit (°F°F). The Curie is not used for temperature.
• Heat: Heat is a form of energy transfer between systems due to a temperature difference. Its SI unit is the Joule (J), and another common unit is the calorie (cal). The Curie is not a unit of heat.
• Energy: Energy is the capacity to do work. Its SI unit is the Joule (J). Other units include the electron-volt (eV) and the calorie (cal). The Curie measures radioactive activity, not energy directly. While radioactive decay releases energy, the Curie quantifies the rate of decay events, not the energy produced.

Conclusion on Curie Unit

In summary, the Curie is specifically a unit that quantifies the rate of nuclear decay events, which is known as radioactivity. It represents a large number of disintegrations per second and has been widely used in fields like nuclear medicine and radiation protection, although the Becquerel is now the preferred SI unit.

The primary architectural component in Public Key Infrastructure (PKI) that enables verifiable trust for digital identities and non-repudiation is:

✅ The secure distribution and management of cryptographic keys, including their lifecycle from issuance to revocation, through Certificate Authorities (CAs).

Certificate Authorities are the trust anchors in PKI, responsible for issuing, validating, and revoking digital certificates—thereby ensuring authenticity, integrity, and non-repudiation in electronic transactions.

When unfolded, the paper takes the shape of a rectangle with two horizontal creases, indicating the correct unfolding pattern.