The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3).
Question: The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3). Find the probability of his travelling by plane or train. Solution: let A denote the event that a company executive will travel by plane and B denote the event of him travelling by train Given : $P(A)=\frac{2}{5}, P(B)=\frac{1}{3}$ To find : Probability of a company executive will be travelling by plane or train=P(A or B) Formula used: $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$ P...
Read More →A speech signal of 3 kHz is used to modulate
Question: A speech signal of 3 kHz is used to modulate a carrier signal of frequency 1 MHz, using amplitude modulation. The frequencies of the sidebands will be (a) 1.003 MHz and 0.997 MHz (b) 3001 kHz and 2997 kHz (c) 1003 kHz and 1000 kHz (d) 1 MHz and 0.997 MHz Solution: (a) 1.003 MHz and 0.997 MHz...
Read More →A 1 KW signal is transmitted using a communication
Question: A 1 KW signal is transmitted using a communication channel which provides attenuation at the rate of 2dB per km. If the communication channel has a total length of 5 km, the power of the signal received is [gain in dB = 10 log P0/P1] (a) 900 W (b) 100 W (c) 990 W (d) 1010 W Solution: (b) 100 W...
Read More →A 100m long antenna is mounted on a 500m tall building.
Question: A 100m long antenna is mounted on a 500m tall building. The complex can become a transmission tower for waves with (a) ~ 400 m (b) ~ 25 m (c) ~ 150 m (d) ~ 2400 m Solution: (a) ~ 400 m...
Read More →Three waves A, B and C of frequencies 1600 kHz,
Question: Three waves A, B and C of frequencies 1600 kHz, 5 MHz and 60 MHz, respectively are to be transmitted from one place to another. Which of the following is the most appropriate mode of communication: (a) A is transmitted via space wave while B and C are transmitted via skywave (b) A is transmitted via ground wave, B via skywave and C via space wave (c) B and C are transmitted via ground wave while A is transmitted via skywave (d) B is transmitted via ground wave while A and C are transmi...
Read More →A, B, C are three mutually exclusive and exhaustive events associated with a random experiment.
Question: A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = (3/2) P(A) and P(C) = (1/2) P(B), find P(A). Solution: Given : A,B,C are mutually exclusive events and exhaustive events P(B) = (3/2) P(A) and P(C) = (1/2) P(B) To find : $P(A)$ Formula used: $P(A)+P(B)+P(C)=1$ For mutually exclusive events $A, B$, and $C, P(A$ and $B)=P(B$ and $C)=P(A$ and $C)=0$ Let $P(A)=x, P(B)=(3 / 2) P(A)=\frac{3}{2} x, P(C)=(1 / 2) P(B)=\frac{\frac{1}{2}}{2}...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{2}{2+\sin 2 x} d x$ Solution: Given $I=\int \frac{2}{2+\sin 2 x} d x$ We know that $\sin 2 x=2 \sin x \cos x$ $\Rightarrow \int \frac{2}{2+\sin 2 x} d x=\int \frac{2}{2+2 \sin x \cos x} d x$ $=\int \frac{1}{1+\sin x \cos x} d x$ Dividing the numerator and denominator by $\cos ^{2} x$, $\Rightarrow \int \frac{1}{1+\sin x \cos x} d x=\int \frac{\sec ^{2} x}{\sec ^{2} x+\tan x} d x$ Replacing $\sec ^{2} x$ in denominator by $1+\tan ^{2} x$, $\...
Read More →Let A and B be two mutually exclusive events of a random experiment
Question: Let A and B be two mutually exclusive events of a random experiment such that P(not A) = 0.65 and P(A or B) = 0.65, find P(B). Solution: Given : A and B are mutually exclusive events $\mathrm{P}(\operatorname{not} \mathrm{A})=\mathrm{P}\left({ }^{\bar{A}}\right)=0.65, \mathrm{P}(\mathrm{A}$ or $\mathrm{B})=0.65$ To find : P(B) Formula used : $\mathrm{P}(\mathrm{A})=1-\mathrm{P}(\bar{A})$ $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$ For mutually exclusive events $A$ and $B, P(A$ and $B)=0$ $P(A...
Read More →If A and B are two mutually exclusive events such that
Question: If A and B are two mutually exclusive events such that P(A) = (1/2) and P(B) = (1/3), find P(A or B). Solution: Given : A and B are mutually exclusive events $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}$ To find : $\mathrm{P}(\mathrm{A}$ or $\mathrm{B})$ Formula used: $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$ For mutually exclusive events $A$ and $B, P(A$ and $B)=0$ Substituting in the above formula we qet. $\mathrm{P}(\mathrm{A}$ or $\mathrm{B})=\frac{\frac{1}{2}}{2}+\frac{1}{3}-0$ $\mathrm{P}(\mat...
Read More →If A and B be two events associated with a random experiment
Question: If A and B be two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P $(A \cap B)=0.1$, find (i) $P(\bar{A} \cap B)$ (ii) $P(A \cap \bar{B})$ Solution: (i) Given : $P(A)=0.3, P(B)=0.2, P(A \cap B)=0.1$ To find $P(\bar{A} \cap B)$ Formula used: $P(\bar{A} \cap B)=\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ Substituting in the above formula we get, $P(\bar{A} \cap B)=0.2-0.1$ $P(\bar{A} \cap B)=0.1$ $P(\bar{A} \cap B)=0.1$ (ii) Given : $P(...
Read More →In the circuit, find the value of RC.
Question: In the circuit, find the value of RC. Solution: Ie = Ic + Ib IcRc + Vce + IeRe = Vcc Rib + Vbe + IeRe = Vcc Ib = 11.5/200 mA Rc + Re = 1.56 kilo ohm Rc = 560 Ohm...
Read More →For the transistor circuit shown
Question: For the transistor circuit shown in Fig.14.19, evaluate VE, RB, REgiven IC= 1 mA, VCE= 3V, VBE= 0.5 V and VCC= 12 V, = 100. Solution: Ic = Ie Rc = 7.8 kilo ohm Ic (Rc + Re) + Vce = 12 Ve = 1.2 V Vb = Ve + Vbe = 1.7 V I = 0.085 mA Rb = 108 kilo ohms...
Read More →Consider a box with three terminals on top of it:
Question: Consider a box with three terminals on top of it: Three components namely, two germanium diodes and one resistor are connected across these three terminals in some arrangement. A student performs an experiment in which any two of these three terminals are connected in the circuit shown in the figure (b). The student obtains graphs of current-voltage characteristics for an unknown combination of components between the two terminals connected in the circuit. The graphs are (i) when A is ...
Read More →If A and B are two events associated with a random experiment
Question: If A and B are two events associated with a random experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or B) = 0.5, find the values of (i) $P(A$ and $B)$ (ii) $\mathrm{P}(\mathrm{A}$ and $\overline{\mathrm{B}})$ Solution: (i) Given : P(A) = 0.25, P(A or B) = 0.5 and P(B) = 0.4 To find : P(A and B) Formula used : P(A or B) = P(A) + P(B) - P(A and B) Substituting in the above formula we get, $0.5=0.25+0.4-P(A$ and $B)$ $0.5=0.65-P(A$ and $B)$ $P(A$ and $B)=0.65-0.5$ $P(A$ and $B)=0.15$ ...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{4 \sin ^{2} x+5 \cos ^{2} x} d x$ Solution: Given I $=\int \frac{1}{4 \sin ^{2} x+5 \cos ^{2} x} d x$ Dividing the numerator and denominator of the given integrand by $\cos ^{2} x$, we get $\Rightarrow I=\int \frac{1}{4 \sin ^{2} x+5 \cos ^{2} x} d x=\int \frac{\sec ^{2} x}{4 \tan ^{2} x+5} d x$ Putting $\tan x=t$ and $\sec ^{2} x d x=d t$, we get $\Rightarrow I=\int \frac{d t}{4 t^{2}+5}=\frac{1}{4} \int \frac{d t}{t^{2}+\left(\frac{5}{...
Read More →An X-OR gate has the following truth table:
Question: An X-OR gate has the following truth table: It is represented by the following logic relation $Y=\bar{A} \cdot B+A \cdot \bar{B}$ Build this gate using AND, OR, and NOT gates. Solution: The logic relation is y =A.B + A.B...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{4 \cos ^{2} x+9 \sin ^{2} x} d x$ Solution: Given $I=\int \frac{1}{4 \cos ^{2} x+9 \sin ^{2} x} d x$ Dividing the numerator and denominator of the given integrand by $\cos ^{2} x$, we get $\Rightarrow I=\int \frac{1}{4 \cos ^{2} x+9 \sin ^{2} x} d x=\int \frac{\sec ^{2} x}{4+9 \tan ^{2} x} d x$ Putting $\tan x=t$ and $\sec ^{2} x d x=d t$, we get $\Rightarrow I=\int \frac{d t}{4+9 t^{2}}=\frac{1}{9} \int \frac{d t}{\frac{4}{9}+t^{2}}$ We...
Read More →Suppose a ‘n’-type wafer is created by doping
Question: Suppose a n-type wafer is created by doping Si crystal having 5 1028atoms/m3with 1ppm concentration of As. On the surface 200 ppm Boron is added to create the P region in this wafer. Considering ni = 1.5 1016m3, (i) Calculate the densities of the charge carriers in the n p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when the diode is reverse biased. Solution: (i) Ne = 5 1022m3 Nh = 0.45 1010m3 Nh = Na = 1 1025m3 Ne = 2.25 107m...
Read More →Assuming the ideal diode.
Question: Assuming the ideal diode. Explain the waveform. Solution: The waveform of the above circuit would be a sine wave with a dip off in the input wave....
Read More →Consider the circuit arrangement in
Question: Consider the circuit arrangement in which the input and output characteristics of NPN transistor in CE configuration Select the values of RB and RC for a transistor whose VBE = 0.7 V, so that the transistor is operating at point Q as shown in the characteristics shown in the figure (b). Given that the input impedance of the transistor is very small and VCC = VBB = 16 V, also find the voltage gain and power gain of circuit making appropriate assumptions. Solution: Vbe = 0.7V Vcc = Vbb =...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x+2}{\sqrt{x^{2}+2 x+3}}$ Solution: Given $I=\int \frac{x+2}{\sqrt{x^{2}+2 x+3}} d x$ Integral is of form $\int \frac{\mathrm{px}+\mathrm{q}}{\sqrt{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}}} \mathrm{dx}$ Writing numerator as $\mathrm{px}+\mathrm{q}=\lambda\left\{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\right)\right\}+\mu$ $\Rightarrow \mathrm{px}+\mathrm{q}=\lambda(2 \mathrm{ax}+\mathrm{b})+\mu$ $\Rightarrow ...
Read More →In the circuit shown in the figure,
Question: In the circuit shown in the figure, when the input voltage of the base resistance is 10V, Vbe is zero and Vce is also zero. Find the values of Ib, Ic and . Solution: Vi = 10 V Rb = 400 kilo ohms Vbe = 0 Vce = 0 Rc = 3 kilo ohms Ib = 25 micro ampere Rc = 10 V Ic = 3.33 mA Current gain = 133...
Read More →If each diode in the figure has a forward
Question: If each diode in the figure has a forward bias resistance of 25Ω and infinite resistance in reverse bias, what will be the values of the current I1, I2, I3 and I4? Solution: Forward bias resistance = 25 ohms Reverse biased resistance = infinity I3 = 0 Resistance in AB = 150 ohms Resistance in EF = 150 ohms AB is parallel to EF Effective resistance, R = 75 ohm Resistance R of the circuit = R = 100 ohms Current = 0.05 A I2 = 0.025 A I4 = 0.025 A Therefore, I1 = 0.05 A I2 = 0.025 A I3 = 0...
Read More →In a random experiment, let A and B be events such that P
Question: In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and $P(\bar{A})$ = 0.4. Find P(B). Solution: Given : $\mathrm{P}\left({ }^{\bar{A}}\right)=0.4, \mathrm{P}(\mathrm{A}$ or $\mathrm{B})=0.7$ and $\mathrm{P}(\mathrm{A}$ and $\mathrm{B})=0.3$ To find : P(B) Formula used : $\mathrm{P}(\mathrm{A})=1-\mathrm{P}(\bar{A})$ P(A or B) = P(A) + P(B) - P(A and B) We have $\mathrm{P}(\bar{A})=0.4$ $P(A)=1-0.4=0.6$ We get $P(A)=0.6$ Substituting in the above f...
Read More →A Zener of power rating 1 W is to be used
Question: A Zener of power rating 1 W is to be used as a voltage regulator. If Zener has a breakdown of 5V and it has to regulate voltage which fluctuated between 3V and 7V, what should be the value of Rs for safe operation in the figure? Solution: Power = 1W Zener breakdown voltage = 5V Minimum voltage = 3V Maximum voltage = 7V P = VI = 0.2A Rs = 10 Ohms....
Read More →