National STEM Internship Exam Review Flashcards

Vocabulary and concept flashcards covering Logical Reasoning, Mathematics, and Science & Technology based on the National STEM Internship Exam transcript.

Caesar Cipher

A coding method where letters are shifted by a fixed value or reversed/mirrored.

Syllogism

A logical conclusion derived from two premises using terms like All, Some, or No.

Percentage Change Formula

$$\text{\% change} = \frac{\text{Change}}{\text{Original}} \times 100$$

Successive Percentage Change Formula

$$a + b + \frac{ab}{100}$$

Arithmetic Progression (AP)

A sequence $a, a+d, a+2d, \dots$ where $a$ is the first term and $d$ is the common difference.

AP nth Term Formula

$$T_n = a + (n-1)d$$

Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Discriminant (D)

$D = b^2 - 4ac$; used to determine the nature of roots ($D > 0$ for distinct real roots, $D = 0$ for equal roots, and $D < 0$ for no real roots).

Factor Theorem

A rule stating that $(x-a)$ is a factor of a polynomial $p(x)$ if and only if $p(a) = 0$.

SOH-CAH-TOA

A mnemonic for trigonometric ratios: $\sin(\theta) = \frac{\text{Opp}}{\text{Hyp}}$, $\cos(\theta) = \frac{\text{Adj}}{\text{Hyp}}$, and $\tan(\theta) = \frac{\text{Opp}}{\text{Adj}}$.

Fundamental Trigonometric Identity

$$\sin^2(\theta) + \cos^2(\theta) = 1$$

Velocity

A vector quantity defined as $\text{Displacement} / \text{Time}$; it includes both magnitude and direction.

Acceleration (a)

$a = \frac{v - u}{t}$; measured in units of $m/s^2$.

Newton's 1st Law (Inertia)

A body stays at rest or in uniform motion unless acted upon by a net external force.

Newton's 2nd Law

$F = ma$, where force is measured in Newtons (N), mass in kg, and acceleration in $m/s^2$.

Newton's 3rd Law

The law stating that for every action, there is an equal and opposite reaction; the principle used in rocket propulsion.

Momentum (p)

$p = mv$; a vector quantity measured in $kg \cdot m/s$.

Universal Law of Gravitation

$F = \frac{Gm_1m_2}{r^2}$ where $G = 6.67 \times 10^{-11}\,N \cdot m^2/kg^2$.

Work (W)

$W = F \times d \times \cos(\theta)$; work is zero if force is perpendicular to displacement ($\theta = 90^\circ$).

Potential Energy (PE)

$PE = mgh$, representing energy based on height.

Kinetic Energy (KE)

$KE = \frac{1}{2}mv^2$, representing energy of motion.

Power (P)

$P = \frac{W}{t}$; also expressed as $P = F \times v$. The unit is the Watt (W) or Horsepower ($1\,HP = 746\,W$).

Ohm's Law

$V = IR$; states that voltage equals current multiplied by resistance for ohmic conductors at constant temperature.

ISRO

Indian Space Research Organisation, founded in 1969 by Dr. Vikram Sarabhai, with headquarters in Bengaluru.

Chandrayaan-3

The 2023 ISRO mission that made India the first country to soft-land near the Moon's South Pole on August 23, 2023.

Pragyan

The name of the rover carried by the Vikram lander during the Chandrayaan-3 mission.

Gaganyaan

India's first crewed spaceflight mission designed to carry three Vyomanauts to a $400\,km$ orbit.

Geostationary Orbit (GEO)

An orbit at an altitude of approximately $36,000\,km$ where a satellite's period is $24\,h$, making it appear stationary.

NavIC/IRNSS

India's independent navigation satellite system, equivalent to GPS.

ESC

Electronic Speed Controller; a drone component that controls the motor rotations per minute (RPM).

Narrow AI

Artificial Intelligence designed to perform a specific task, such as voice recognition or spam filtering.

Turing Test

A test of a machine's ability to exhibit intelligent behavior indistinguishable from that of a human in conversation.

Supervised Learning

A subset of machine learning where the model is trained on labeled data consisting of both inputs and correct outputs.

Overfitting

A modeling error that occurs when a machine learning model performs perfectly on training data but poorly on unseen test data.

Degrees of Freedom (DOF)

In robotics, the number of independent joints or directions in which a robot arm can move.