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Question:

Find the Fourier sine transform of

$f(x)=\left\{\begin{matrix} x, & 0<x<1\\ 2-x,& 1<x<2\\ 0, & x>2 \end{matrix}\right.$

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Question:

Find the radius of convergence of the following series.

(i)

$\sum_{k=1}^{\infty }\frac{(-1)^{k+1}}{k!}(z-1-i)^{k}$

(ii)

$\sum_{k=1}^{\infty }\left ( \frac{6k+1}{2k+5} \right )^{k}(z-2i^{})^{k}$

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Question:

. Revolutionary Nationalists in Bengal

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Question:

Drain of Wealth

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Question:

. Reform Movements in nineteenth-century India

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Question:

Nehru Report (1928)

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Question:

Azad Hind Fauj

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Question:

Solve the following differential equation by power series method about $x=0:$

$(1-x^2)y'(x)-2xy'(x)+2y(x)=0$

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Question:

Discuss the non-Brahman movements in western and southern India.

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Question:

Describe the world of Indian Literature in the first half of twentieth century

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Question:

Write a note on the Non-Cooperation movement.

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Question:

Given

$\frac{dy}{dx}=-300y,y(0)=1$

Determine the value of h so that the second order Runge-Kutta method applied to be IVP produces stable results.

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Question:

Analyse the factors that led to the partition of India.

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Question:

Discuss the various phases of the Civil Disobedience Movement.

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Question:

Prove that

$\frac{d}{dx}(j_{n}^{2}(x))=\frac{x}{2n}[j_{n+1}^{2}(x)-j_{n+1}^{2}(x)]$

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Question:

Evaluate $\int_{c}^{}\frac{z^{3}+3}{z(z-i)^{2}}dz$ , where c is the eight like figure shown in Fig. 1

Image ignouassignments-ignouacademy-com--p-ignou-64982

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Question:

Find the solution of the initial boundary value problem , $\frac{\partial ^2u}{\partial ^2} = \frac{\partial ^2u}{\partial x^2},0 \leq x \leq1$

$u(x,0) = sin\pi x,0\leq x\leq 1 \frac{\partial u}{\partial t}(x,0)=0, u(0,t)=u(l,t)=0,t>0$

by using second order explicit method with . $h=\frac{1}{4},r=\frac{1}{3}$ Integrate for one time step.

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Question:

Find the maximum modulus of f (z) = 2z + 5i on the closed circular region defined by $\left | z \right |\leq 2.$

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Question:

What is Dincharya? Explain.

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Question:

What do you understand by the term consciousness? Briefly discuss the four states of consciousness

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