A stick of length one meter is broken at two locations at distances of $b1$ and $b2$ from the origin ($0$), as shown in the figure. Note that $0 < b1 < b2 < 1$. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces? Note: All lengths are in meter. The figure shown is representative. !image(https://uadmin.udsfgecw.tech/file/download/public/public:8ad6b863-badc-4187-9995-6f98c4487ae6.png)

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT? !image(https://uadmin.udsfgecw.tech/file/download/public/public:dad65623-6a09-4ce1-9067-10d8ad0b46db.png)

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is $20\%$ of the consulting fee, if the fee is up to ₹ $5,00,000$. For higher fees, the overhead is ₹ $1,00,000$ plus $10\%$ of the amount by which the fee exceeds ₹ $5,00,000$. The government charges a Goods and Services Tax of $18\%$ on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than ₹ $10,00,000$, what is the maximum consulting fee that the employee can charge?

Two identical sheets $A$ and $B$, of dimensions $24 \text{ cm} \times 16 \text{ cm}$, can be folded into half using two distinct operations, $FO1$ or $FO2$. In $FO1$, the axis of folding remains parallel to the initial long edge, and in $FO2$, the axis of folding remains parallel to the initial short edge. If sheet $A$ is folded twice using $FO1$, and sheet $B$ is folded twice using $FO2$, the ratio of the perimeters of the final shapes of $A$ and $B$ is

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by $Vi = 10\sin(100\pi t)$, where time $t$ is in seconds. image needed to be inserted here The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is . $6.67$ c 1 0 0 numerical Electrical and Electronic Engineering Analog and Digital Electronics The diode is forward biased when $Vi > 5V$. Given: $10\sin(100\pi t)>5$ $\sin(100\pi t)>0.5$ The conduction angle is from $30^\circ$ to $150^\circ$. Conduction angle: $150^\circ-30^\circ=120^\circ$ Fraction of one cycle: $\frac{120}{360}=\frac{1}{3}$ Input frequency: $100\pi=2\pi f$ $f=50Hz$ Time period: $T=\frac{1}{50}=20ms$ Diode forward bias duration: $\frac{1}{3}\times20=6.67ms$

(url)In the circuit shown below, the AND gate has a propagation delay of $1$ ns. The edge-triggered flip-flops have a set-up time of $2$ ns, a hold-time of $0$ ns, and a clock-to-Q delay of $2$ ns. The maximum clock frequency (in MHz, rounded off to the nearest integer) such that there are no setup violations is . !image(https://uadmin.udsfgecw.tech/file/download/public/public:42c3616d-a884-433c-87a2-64f0a88b3a7b.jpg)

An ideal p-n junction germanium diode has a reverse saturation current of $10\mu A$ at $300K$. The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of $100mA$ at $300K$ is . (Consider the Boltzmann constant $kB = 1.38 \times 10^{-23}J/K$ and the charge of an electron $e = 1.6 \times 10^{-19}C$)

A $50\Omega$ lossless transmission line is terminated with a load $ZL$ of $(50-j75)\Omega$. If the average incident power on the line is $10mW$, then the average power delivered to the load (in mW, rounded off to one decimal place) is .

Two resistors are connected in a circuit loop of area $5m^2$, as shown in the figure below. The circuit loop is placed on the x-y plane. image needed to be inserted here When a time-varying magnetic flux, with flux-density $B(t)=0.5t$ (in Tesla), is applied along the positive z-axis, the magnitude of current $I$ (in Amperes, rounded off to two decimal places) in the loop is .

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II. Group-I: Abuse $\rightarrow$ Insult $\rightarrow$ Ridicule Group-II: \\\\\\\\\\ $\rightarrow$ Praise $\rightarrow$ Appreciate

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. Over time, such adaptations lead to significant evolutionary changes with the potential to shape the development of new species. Q. In natural world, organisms constantly adapt to their environments in response to challenges and opportunities. R. This process of adaptation is driven by the principle of natural selection, where favorable traits increase an organism's chances of survival and reproduction. S. As environments change, organisms that can adapt their behavior, structure and physiology to such changes are more likely to survive.