**Ex-1:**

Do the following activities.

(i) Draw the graphs of the parabolas (π¦βπ)2=4π(π₯ββ) and (π₯ββ)2=4π(π¦βπ) for the given values of π,π,β and π. Determine the vertex, focus, axis, directrix, latus-rectum of each parabola and mark them on the graphs.

(ii) Draw the graphs of the ellipse (π₯ββ)2π2+(π¦βπ)2π2=1 for the given values of π,π ,β and π. Determine the eccentricity, centre, foci, vertices, major axis, minor axis, directrices, and latus-rectums and mark them on the graph.

**Ex-2:**

Do the following activities for the given image of a parabolic shaped satellite dish antenna.

(i) Draw a parabola which fits the given image of the dish antenna.

(ii) Write the equation of the parabola.

(iii) Find the vertex, focus, directrix and latus-rectum and mark them on the graph.

(iv) How far from the vertex should the receiver of the antenna be placed?

**Ex-3:**

Do the following activities.

i. Draw the graphs of sinπ₯,cosπ₯,tanπ₯,cosecπ₯,secπ₯ and cotπ₯ and write their domain and range. Find the maximum value, minimum value, amplitude and periodicity of sinπ₯,cosπ₯,tanπ₯,cosecπ₯,secπ₯ and cotπ₯.

ii. Draw the graphs of sinβ1π₯,cosβ1π₯,tanβ1π₯,cosecβ1π₯,secβ1π₯ and cotβ1π₯ and write their domain and range. Find the maximum value and minimum value of sinβ1π₯,cosβ1π₯,tanβ1π₯,cosecβ1π₯,secβ1π₯ and cotβ1π₯.

**Ex-4:**

The alternating current passing through a circuit is π(π‘)=πΌπsinππ‘, where πΌπ is the maximum value of current and π is the angular velocity. Let π
be the resistance and ππ be the maximum voltage.

i. Graph the sinusoidal waveform of π(π‘) for the given values of πΌπ and π.

ii. Calculate the maximum voltage ππ using the formula ππ=πΌππ
for the given value of π
.

iii. Graph the sinusoidal waveform of voltage using the formula π£(π‘)=ππsin(ππ‘+π2).

iv. Determine the value of root mean square (r.m.s) current.

v. Determine the frequency.

vi. Calculate the instantaneous value of the current at π‘ sec.

**Ex-5:**

Do the following activities.

i. Mark the given complex number π§ on the Argand plane. Find the real and imaginary parts of π§. Find the distance of π§ from π₯-axis and relate it to the real part of π§. Find the distance of π§ from π¦-axis and relate it to the imaginary part of π§.

ii. Find the conjugate of π§. Mark π§Μ
on the Argand plane. Find the reflection of π§ on π₯-axis and relate it to π§Μ
.

iii. Find the modulus of π§. Find the distance between π§ and origin of the Argand plane and relate it to the modulus of π§. Find the modulus of π§Μ
and relate it to the modulus of π§.

iv. Find the argument of π§. Find the angle between the line segment ππ§ and π₯ axis and relate it to the argument of π§. Find the argument of π§Μ
and relate it to the argument of π§.

**Ex-6:**

Do the following activities.

i. The representation of apparent power as phasor sum of active power and reactive power is given by π=550+952.63π. Draw the phasor diagram of the system. Find the numerical value of the apparent power. Also calculate the phase angle and power factor of the system.

ii. A machine takes 10KW (real power, P) at a power factor of 0.6 from 400V supply. Calculate the total load in KVA and KVAR. Represent the apparent power as a phasor sum of active power and reactive power.

**Ex-7:**

Do the following activities.

(i) Graph the polynomial function π(π₯)=πππ₯π+ππβ1π₯πβ1+β―+π1π₯+π0, where ππ,ππβ1,β¦,π0 are real numbers and ππβ 0. Find the value of π(π₯) at π₯=π and the limit of π(π₯) at π₯=π.

(ii) Graph the rational function π
(π₯)=πππ₯π+ππβ1π₯πβ1+β―+π1π₯+π0πππ₯π+ππβ1π₯πβ1+β―+π1π₯+π0, where ππ,ππβ1,β¦,π0,ππ,ππβ1,β¦,π0 are real numbers and ππ,ππβ 0. Find the value of π(π₯) and the limit of π(π₯) at π₯=π.

(iii) Graph the functions sinππ₯ππ₯ and tanππ₯ππ₯ where π and π are real numbers and π,πβ 0. Evaluate limπ₯β0sinππ₯ππ₯ and limπ₯β0tanππ₯ππ₯.

(iv) Graph the functions π (ππππ π‘πππ‘), π₯π, sinπ₯, cosπ₯, tanπ₯, cosecπ₯, secπ₯, cotπ₯, ππ₯ and logπ₯. Find their first derivative and second derivative.

**Ex-8:**

The alternating current passing through a circuit is π(π‘)=πΌπsinππ‘ where, πΌπ is the maximum value of current and π is the angular velocity. Let πΏ be the inductance.

(i) Graph the sinusoidal wave form of π(π‘) for the given values of πΌπ and π.

(ii) Graph the voltage using the formula π£(π‘)=πΏππ(π‘)ππ‘ for the given value of πΏ.

(iii) Determine the values of π(π‘) and π£(π‘) for a fixed π‘ and different values of π.

(iv) Determine the values of π(π‘) and π£(π‘) for fixed value of π and different values of π‘.

(v) Determine the values of π‘ for which π(π‘) and π£(π‘) are equal.

**Ex-9:**

Do the following activities.

i. Graph the functions π (ππππ π‘πππ‘), π₯π,πββ, ππ₯, sinπ₯, cosπ₯, sec2π₯, cosec2π₯, secπ₯tanπ₯ and cosecπ₯cotπ₯. Find their indefinite integrals.

ii. Evaluate the definite integral β«π(π₯)ππππ₯ and relate it to the area under the curve π¦=π(π₯) between π₯-axis, π₯=π and π₯=π.

iii. Find the volume of the solid generated by the revolution of the area bounded by π¦=π(π₯),π₯-axis, π₯=π and π₯=π about π₯-axis.

**Ex-9:**

Do the following activities.

i. Graph the functions π (ππππ π‘πππ‘), π₯π,πββ, ππ₯, sinπ₯, cosπ₯, sec2π₯, cosec2π₯, secπ₯tanπ₯ and cosecπ₯cotπ₯. Find their indefinite integrals.

ii. Evaluate the definite integral β«π(π₯)ππππ₯ and relate it to the area under the curve π¦=π(π₯) between π₯-axis, π₯=π and π₯=π.

iii. Find the volume of the solid generated by the revolution of the area bounded by π¦=π(π₯),π₯-axis, π₯=π and π₯=π about π₯-axis.

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