BSNL JTO cheat sheet

Nyquist rate for a noiseless channel: C = 2B log2(M) bit/s, where B is bandwidth in Hz and M is number of signal levels; Shannon capacity for a noisy channel: C = B log2(1 + S/N).

Free-space path loss in dB: FSPL = 32.44 + 20log10(d_km) + 20log10(f_MHz); loss rises 6 dB per doubling of distance or frequency.

Optical fiber windows: 850 nm (multimode LAN), 1310 nm (zero dispersion in standard single-mode), 1550 nm (lowest attenuation, ~0.2 dB/km, used with EDFA).

PCM chain is sampling, quantization, encoding; bit rate = fs x n where fs >= 2 x highest frequency and n = log2(levels). For 4 kHz voice at 8 kHz and 8 bits, rate = 64 kbit/s.

OSI layers 1-7: Physical, Data Link, Network, Transport, Session, Presentation, Application; IP and routing live in layer 3, TCP/UDP in layer 4, MAC switching in layer 2.

IPv4 private ranges: 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16; loopback 127.0.0.0/8; link-local 169.254.0.0/16; APIPA indicates failed DHCP.

Subnet host count = 2^h - 2, where h is the number of host bits; prefix /26 on IPv4 leaves 6 host bits, giving 62 usable hosts per subnet.

GPON downstream uses 1490 nm and upstream 1310 nm with 1550 nm for video overlay; split ratios commonly 1:32 or 1:64 over a 20 km reach.

Ideal op-amp: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth; virtual short (V+ = V-) holds only under negative feedback.

Inverting amplifier gain = -Rf/Rin; non-inverting gain = 1 + Rf/Rin; integrator uses a capacitor in the feedback path, differentiator a capacitor at the input.

BJT regions: cutoff (both junctions off), active (BE forward, BC reverse, used for amplification), saturation (both forward, used as a switch); VBE ~ 0.7 V for silicon.

MOSFET saturation condition: VDS > VGS - VTH; drain current in saturation is (1/2)kn'(W/L)(VGS - VTH)^2, ignoring channel-length modulation.

AM: total power Pt = Pc(1 + m^2/2); sideband power = Pc m^2/2; efficiency = m^2/(2 + m^2), maximum 33.3 percent at m = 1.

FM: Carson's rule gives bandwidth BW = 2(df + fm); modulation index beta = df/fm; FM trades bandwidth for noise immunity.

Sampling theorem: fs >= 2 fmax; if violated, aliasing folds frequencies above fs/2 down to fs - f, requiring an anti-aliasing LPF before the sampler.

Logic families: CMOS has near-zero static power but dynamic power = C V^2 f; TTL input high threshold ~2.0 V, output low ~0.2 V; noise margin = VOH(min) - VIH(min).

TCP is connection-oriented and reliable with 3-way handshake (SYN, SYN-ACK, ACK), sequencing, and congestion control; UDP is connectionless with 8-byte header and no delivery guarantee.

TCP and UDP port ranges: well-known 0-1023, registered 1024-49151, dynamic/ephemeral 49152-65535; HTTP 80, HTTPS 443, DNS 53, SMTP 25, SSH 22.

Binary search runs in O(log n) on sorted data; merge sort is O(n log n) in all cases; quicksort averages O(n log n) but degrades to O(n^2) on sorted input with a bad pivot.

Stack is LIFO with push/pop at one end; queue is FIFO with enqueue at rear and dequeue at front; a circular queue of size n holds at most n-1 elements if one slot distinguishes full from empty.

Normalization: 1NF removes repeating groups, 2NF removes partial dependencies on a composite key, 3NF removes transitive dependencies, BCNF requires every determinant to be a candidate key.

SQL DDL covers CREATE, ALTER, DROP; DML covers SELECT, INSERT, UPDATE, DELETE; COMMIT makes changes durable and ROLLBACK undoes an uncommitted transaction.

Deadlock needs four simultaneous conditions: mutual exclusion, hold and wait, no preemption, circular wait; breaking any one prevents deadlock.

IPv4 header is 20 bytes minimum with TTL preventing loops; ARP resolves IP to MAC within a LAN, DNS resolves names to IP, DHCP assigns addresses automatically.

Train crossing a pole takes time = train length / speed; crossing a platform of length L takes (train length + L) / speed; convert km/h to m/s by multiplying by 5/18.

Work and time: if A finishes in a days and B in b days, together they take ab/(a+b) days; combined rate is the sum of individual rates.

Simple interest = P x R x T / 100; compound interest = P(1 + R/100)^T - P; CI exceeds SI by P(R/100)^2 for two years.

Percentage change and successive change: two successive changes of a percent and b percent equal a + b + ab/100 percent overall, with signs carrying direction.

Number series and coding-decoding questions: check differences, ratios, squares/cubes, and alternating patterns before assuming a single rule; letter position A=1 to Z=26 with reverse position 27 minus position.

Blood relations and direction sense: draw a diagram; on a left turn from facing north you face west; a person facing south turning right faces west.

Average = sum / count; if every value is increased by k, the average rises by k; if every value is multiplied by k, the average is multiplied by k.

Indian telecom awareness: BSNL is a state-owned operator; TRAI regulates tariffs and spectrum use, DoT frames policy, and GSM operates in 900/1800 MHz bands in India.