Trace the curve y²(x+1)=x²(3-x), clearly stating all the properties used for tracing it.

If the revenue function is given by dR /dx 15+2x-x², x being the input, find the maximum revenue. Also find the revenue function R, if the initial revenue is 0.

Find the area between the curve y²(4-x) = x³ and its asymptote parallel to y-axis.

Let f and g be two functions defined on R by:

f(x) = x³-x²-8x+12

and

i) Find the value of a for which f is continuous at x = -3.

ii) Find all the roots of f(x) = 0.

a) Find the least value of a² sec² x + b² cosec²x, where a>0,b>0.

b) Evaluate:

c) For any two sets S and T, show that:

Depict this situation in the Venn diagram.

Express     as a sum of partial fractions.

If z-1+2i|= 4, show that the point z+ i describes a circle. Also draw this circle.

The set R of real numbers with the usual addition (+) and usual multiplication (+) is given. Define (*) on R as:

Is (*) associative in R? Is (.) distributive (*) in R? Check.

Find the domain of the function f given by 

Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate.

a) The set {S∈ R: x²-3x+2=0} is an infinite set.

b) The greatest interger function is continuous on R.

c) 

d) Every integrable function is monotonic.

e) defines a binary operation on Q, the set of rational numbers.

Explain the organization of a typical microprocessor with the help of block diagram.

Explain with the help of circuit diagram working of 4-bit R-2R ladder network DAC using op-amp. 

Draw the circuit diagram of monostable multivibrator using an op-amp and explain its operation.

Explain the principle of switch mode power supply with the help of schematic diagram. State its advantages over linear power supply.

Explain with the help of circuit diagram the working of linear voltage regulator using bipolar junction transistor as series pass element. State its advantages over shunt regulator using zener diode.

Design a first order active band pass filter using op-amps to pass the signal in the frequency range of 1 kHz to 10 kHz with voltage gain of 10.

Design and draw the circuit of an inverting Schmitt trigger using op-amp with hysteresis of 40% of ±V_SAT-

What is slew rate of an op-amp? What is its effect on the performance of the op- amp? What is the minimum value of slew rate for reproducing a triangular wave of 100 kHz with ± 10 V amplitude at the output?

Design and draw the circuit using op amps to solve the following simultaneous equations:

2x + 3y = 13

-x + y = 1

Obtain the expressions for the individual gains of the 4 input channels shown in the following circuit, and thereby write down the expression for V_out.