Solve your IGNOU Doubts

Question:

(a) Find the intervals of $\mathbb{R}$ , where the function f , defined by $f(x)=x^{3}-27x+36,$ is increasing or decreasing.

(b) Prove that $I_{n}=\int_{\frac{\pi }{4}}^{\frac{\pi }{2}}cot ^{n} X dx=\frac{1}{n-1}-I_{n-2},$ and hence evaluate $I_{4}.$

See Answer →

Question:

(a) Find the maximum height of the curve $y= 4\sin ^{2}x-3\cos ^{2}x$ above the x -axis.

(b) Evaluate $\int \frac{(4-2x)dx}{(x^{2}+1)(x-1)^{2}}^{}$

See Answer →

Question:

(a) Evaluate $\int \frac{x+3}{\sqrt{x^{2}+4x+5}}$

b) Give an example of a function which is one-one when defined on a domain $D_{1}\subseteq \mathbb{R},$ but not when defined on a domain .Justify your choice of example.

See Answer →

Question:

a) Find the length of the curve given by $x=e^{t}\cos t,y=e^{t} \sin t$ lying in $0\leq t\leq \pi .$

b) Find the derivative of $\cos ^{-1}(1-2x^{2})$ with respect to $\cos ^{-1}\sqrt{1-x^{2}}.$

See Answer →

Question:

a) If $y= e^{m tan-1 }x,$ show that

$(1+x^{2})y_{n+1}+(2nx-m)y_{n}+n(n-1)y^{n-1}=0.$

Write down the Taylor’s series for cos4x around zero. Hence, find out for which

value(s) of k the function f , given by

$f(x) =$ $\left\{\begin{matrix} \frac{1-\cos 4x}{x^{2}} , When X\neq 0& \\ k+(2+\sin^{2}X ),When X = 0 & \end{matrix}\right.$

is continuous at x = 0,

See Answer →

Question:

Which of the following statements are true. Give a short proof or a counter example is support of your answer.

(a) The function f , given by

$f(x)=\frac{1}{6}(x^{3}-6x^{2}+9x+6)$ ,has a point of inflection.

$\frac{d}{dx}\left [ \int_{3}^{3x^{2}} tan t^{2}dt\right ] =$ $6X sec^{2}(3x^{2}).$

c) The function y = sin x is monotonic on $\left [ \frac{-\pi }{2} ,\frac{\pi }{2}\right ]$

d) The graph of the function y = x − | x | lies in the 3^rd quadrant only.

e) The tangent to the curve $x^{2}+y^{2}-2x=0$ at the point )0,2( is parallel to the x -axis.

See Answer →

Question:

Determine all the first and second order partial derivatives for the function:

$u\left ( x,t \right )= Ce\left ( ^{1-n^{2}\pi ^{2}} \right )^{t} sin (n\pi x)$

See Answer →

Question:

Classify the following partial differential equations

i) $\frac{\partial u}{\partial x^{2}}+\frac{\partial ^{2}u}{\partial y^{2}}=x^{2}+y^{2}$

ii) $\frac{\partial u}{\partial x}+ 2x \frac{\partial u}{\partial y^{2}}=2xt^{2}$

iii) $\left ( \frac{\partial u}{\partial x} \right )^{2}+2y\frac{\partial u}{\partial y}+xy=0$

iv) $\frac{\partial^{2}u }{\partial x^{2}}+ \left ( \frac{\partial u}{\partial x} \right )\left ( \frac{\partial u}{\partial y} \right )+\frac{\partial^{2}u }{\partial y^{2}}=x^{2}y^{2}$ $\frac{\partial^{2}u }{\partial x^{2}}+ \left ( \frac{\partial u}{\partial x} \right )\left ( \frac{\partial u}{\partial y} \right )+\frac{\partial^{2}u }{\partial y^{2}}=x^{2}y^{2}$

v) $\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2}u }{\partial y^{2}}=\frac{e^{-x}}{x^{2}+y^{2}}$

See Answer →

Question:

Using the Frobenius method, solve the following ODE:

$x^{2}y^{N}+4xy^{t}+\left ( x^{2} \right )y=0$

See Answer →

Question:

Consider an LCR circuit with L = 0.1 H, C = 0.01 F and R = 3.0. Determine the electric current in the circuit, given that at t = 0, the charge in the circuit is zero and the current is 2 A.

See Answer →

Question:

An object of mass 20 kg is pushed on a floor with a force of 40sin 2t N. Given that the frictional force is 20 times the velocity and the object starts from rest, determine the velocity of the object as a function of time.

See Answer →

Question:

Solve the following ordinary differential equations:

i) $\left ( 3xy^{2} +5\right ) dx + \left ( 3x^{2}y -4 \right )dy=0$

ii) $\frac{dy}{dx}+\frac{2y}{x}=\frac{sin X}{X^{2}}; for$ $y (\pi ) =1$

iii) $\frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=8e^{3x}$

See Answer →

Question:

Compare the WAP architecture with OSI model.

See Answer →

Question:

Explain the functions available on the tool bar of a typical web-browser.

See Answer →

Question:

Write down the instructions involved in adding three numbers X, Y, Z and storing the result in memory location D.

See Answer →

Question:

What is network security? Explain its types.

See Answer →

Question:

In an optical fibre the refractive index of core is 1.52 and that of cladding is 1.48. Calculate the critical angle and acceptance angle when the fibre is immersed in glycerin. Refractive index of glycerin is 1.47.

See Answer →

Question:

Explain the construction of a Schottky diode and state its advantages over normal p-n junction diode.

See Answer →

Question:

Explain the image frequency and double spotting phenomena in case of AM receivers. How can they be overcome?

See Answer →

Question:

Explain the use of synchronising pulses in a TV signal.

See Answer →