BEL Probationary Engineer flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thevenin equivalent circuit

Any linear two-terminal network can be replaced by a single voltage source V_th in series with a resistance R_th, where V_th is the open-circuit voltage and R_th is the resistance seen looking back with all independent sources deactivated.

BJT current gain relation

In a bipolar junction transistor, beta = I_C/I_B and alpha = I_C/I_E. The two are related by alpha = beta/(1+beta) and beta = alpha/(1−alpha).

Simply supported beam central load

For a simply supported beam of span L carrying a central point load W, the maximum bending moment is WL/4 at midspan and the maximum deflection is WL³/(48EI).

De Morgan's laws

In Boolean algebra, the complement of a product equals the sum of the complements: (A·B)' = A' + B', and the complement of a sum equals the product of the complements: (A+B)' = A'·B'.

Thermal stress in constrained bar

When a bar is fully constrained and its temperature changes by ΔT, the induced thermal stress is σ = E·α·ΔT, where E is Young's modulus and α is the coefficient of thermal expansion.

Terzaghi bearing capacity equation

For a strip footing, ultimate bearing capacity is q_u = cN_c + qN_q + 0.5γBN_γ, where c is cohesion, q is surcharge, γ is soil unit weight, B is width, and N factors depend on friction angle.

Quicksort complexity

Quicksort has average-case time complexity O(n log n) and worst-case O(n²), which occurs when the pivot repeatedly splits the array into highly unbalanced partitions. Its space complexity is O(log n) on average.

Laplace transform of sine

The Laplace transform of sin(ωt) is ω/(s²+ω²), valid for s > 0. The transform of cos(ωt) is s/(s²+ω²). These are standard results used in solving linear differential equations.

Integration by parts formula

The integration by parts rule is ∫u dv = uv − ∫v du. It is used when the integrand is a product of two functions, choosing u by the LIATE preference order.

Eigenvalue condition

A scalar λ is an eigenvalue of a square matrix A if there exists a nonzero vector x such that Ax = λx. Equivalently, λ satisfies the characteristic equation det(A − λI) = 0.

Bayes' theorem

Bayes' theorem states P(A|B) = P(B|A)·P(A)/P(B), where P(B) > 0. It updates the prior probability P(A) using the likelihood P(B|A) to obtain the posterior P(A|B).

Binomial distribution mean and variance

For a binomial distribution with n independent trials and success probability p, the mean is np and the variance is np(1−p). The standard deviation is the square root of np(1−p).

First law of thermodynamics

The first law states ΔU = Q − W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system. Energy is conserved.

Successive percentage change

If a quantity changes by a% and then by b%, the net percentage change is a + b + (ab/100) percent. A 10% increase followed by a 10% decrease gives a net 1% decrease.

Compound interest two-year difference

For two years at rate R percent per annum, the difference between compound interest and simple interest on principal P is P(R/100)². This equals the interest earned on the first year's interest.

Average speed equal distances

When equal distances are covered at speeds u and v, the average speed for the whole journey is 2uv/(u+v), which is the harmonic mean of the two speeds, not their arithmetic mean.

Time and work combined rate

If A alone completes a job in x days and B alone in y days, working together they complete it in xy/(x+y) days. This follows from adding their work rates 1/x and 1/y.

Combinations formula

The number of ways to choose r objects from n distinct objects without regard to order is nCr = n!/[r!(n−r)!]. For permutations where order matters, nPr = n!/(n−r)!.

Number of polygon diagonals

An n-sided polygon has n(n−3)/2 diagonals. This is obtained by noting each vertex connects to n−3 non-adjacent vertices, and each diagonal is counted twice.

Clock hands angle formula

The angle between the hour and minute hands at H hours and M minutes is |30H − 5.5M| degrees. If the result exceeds 180, subtract it from 360 to get the smaller angle.

Syllogism conclusion rule

From 'All A are B' and 'All B are C', it validly follows that 'All A are C'. A 'Some' statement cannot be converted to 'All', and 'No A is B' converts to 'No B is A'.

Circular seating arrangements

The number of ways to seat n distinct people around a circular table is (n−1)!. If clockwise and anticlockwise arrangements are considered identical, as in a necklace, the count is (n−1)!/2.

Blood relation direction terms

In blood relation puzzles, 'maternal' refers to the mother's side (maternal uncle = mother's brother) and 'paternal' to the father's side (paternal aunt = father's sister). Drawing a family tree prevents errors.

Direction sense net displacement

After a series of right-angle turns, the net displacement from the starting point is found by summing displacements along north–south and east–west axes, then applying Pythagoras to the two totals.

Subject-verb agreement with either-or

With 'either…or' and 'neither…nor', the verb agrees with the subject nearer to it. Example: 'Neither the manager nor the workers were present.' A singular nearer subject takes a singular verb.

Present perfect tense use

The present perfect (has/have + past participle) describes a past action with present relevance or an action continuing to now. The past perfect (had + past participle) marks the earlier of two past events.

Active to passive transformation

To convert active to passive, make the object the new subject, use be + past participle of the verb, and place the original subject after 'by'. Example: 'She wrote a letter' becomes 'A letter was written by her'.

One of the plural noun rule

In the pattern 'one of the + plural noun', the verb is singular because the subject is 'one'. Example: 'One of the boys is absent.' 'Each' and 'every' also take singular verbs.

Bite the bullet idiom

'To bite the bullet' means to endure a difficult or unpleasant situation with courage and without complaint. It is often used when facing an unavoidable hardship.

BEL establishment and headquarters

Bharat Electronics Limited is a Government of India defence electronics enterprise established in 1954 under the Ministry of Defence. Its headquarters is in Bengaluru, Karnataka.

Indian Constitution adoption dates

The Constitution of India was adopted by the Constituent Assembly on 26 November 1949 and came into force on 26 January 1950. Fundamental Rights are contained in Part III, Articles 12 to 35.

Chandrayaan-3 landing

ISRO launched Chandrayaan-3 in July 2023. Its Vikram lander successfully touched down near the lunar south pole on 23 August 2023, making India the first country to land in that region.

Repo rate definition

The repo rate is the interest rate at which the Reserve Bank of India lends short-term funds to commercial banks against government securities. It is a key monetary policy tool to control inflation and liquidity.