OUR SUCCESSFUL STUDENTS in IFOS-2014Heartiest Congratulations to

Our Candidates in IFoS-2014SUCCESSFUL

VARUN GUNTUPALLI

4

13

18

SIDHARTHA GUPTA

PARTH JAISWAL

AMIT CHAUHAN

KUMBHEJKAR YOGESH VIJAY

APOORVA KRISHNASRIVASTAVA

3

5

14

48 57SURYA KANT PAWAR BIPIN KUMAR

And many more..

H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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TOTAL278

1000

TOTAL359

1000

TOTAL296

1000

TOTAL319

1000

TOTAL306

1000

TOTAL289

1000

TOTAL272

1000

TOTAL305

1000

TOTAL256

1000

TOTAL257/500

TOTAL218/500

TOTAL251/500

TOTAL221/500

TOTAL242/500

TOTAL260/500

TOTAL215/500

TOTAL247/500

TOTAL214/500

Our Toppers Marks List(2)

Our Toppers Marks ListH.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987

Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

Our Toppers Marks List(3)

Our Toppers Marks ListH.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987

Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

Feedback Students with Testimonial(4)

H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

(5)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

KULRAJ SINGH (AIR-16) (IFoS-2013)

NITISH KUMAR (AIR-39) (IFoS-2013)

NAVIN P. SHAKYA (AIR-72) (IFoS-2013)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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RAMESH RANJAN (AIR-76) (IAS-2012)

ANKIT VERMA (AIR-247) (IAS-2012)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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PRADEEP MISHRA (AIR-633) (IAS-2012)

KETAN BANSAL (AIR-655) (IAS-2012)

SANJAY KR. JAIN (AIR-667) (IAS-2012)I want to thank Venkanna Sir for his continuous guidance and support all through my preparation of civil services. He is great mentor, and guided me not just in mathematics but in other areas as well. Without his efforts and unflinching faith in me, this would not have been possible. Sanjay Kumar Jain Rank – 667

SANTOSH KUMAR (AIR-849) (IAS-2012)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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ANUPAM SHUKLA (AIR-7) (IFoS-2012)

DILEEP KUMAR YADAV (AIR-48) (IFoS-2012)

SUSHEEL KUMAR (UP-PCS-2011)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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HIMANSHU GUPTA (AIR-7) (IAS-2011)

ARIJIT MUKHERJEE (AIR-25) (IAS-2011)Consolidated Reserve List

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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GULNEET SINGH KHURANA (AIR-220) (IAS-2011)

AJIT PRATAP SINGH (AIR-288) (IAS-2011)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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MEGHA AGARWAL (AIR-538) (IAS-2011)

BHAGWATI PRASAD KALAL (AIR-154) (IAS-2010)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

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ABHISHEK (AIR-223) (IAS-2010)

AWAKASH KUMAR (AIR-276) (IAS-2010)

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

SYLLABUS for IAS (Main) Examination

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PAPER-I(1) Linear AlgebraVector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence's and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues. (2) CalculusReal numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian. Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes. (3) Analytic GeometryCartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties. (4) Ordinary Differential EquationsFormulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution. Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters. Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients. (5) Dynamics & StaticsRectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces. Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions. (6) Vector AnalysisScalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet's formulae. Gauss and Stokes' theorems, Green's identities.

PAPER-II(1) Algebra:Groups, subgroups, cyclic groups, cosets, Lagrange's Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley's theorem. Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields. (2) Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima. (3) Complex Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula, power series representation of an analytic function, Taylor's series; Singularities; Laurent's series; Cauchy's residue theorem; Contour integration. (4) Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems. (5) Partial differential equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy's method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions. (6) Numerical Analysis and Computer programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton's (forward and backward) interpolation, Lagrange's interpolation. Numerical integration: Trapezoidal rule, Simpson's rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods. Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems. (7) Mechanics and Fluid Dynamics: Generalized coordinates; D' Alembert's principle and Lagrange's equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler's equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

PAPER - I(Section-A)

Linear Algebra:Vector, space, linear dependence and independence, subspaces, bases, dimensions. Finite dimensional vector spaces. Matrices, Cayley-Hamilition theorem, eigen-values and eigenvectors, matrix of linear transformation, row and column reduction, Echelon form, equivalences, congruences and similarity, reduction to cannonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skewhermitian forms- their eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite quardratic forms.Calculus:Real numbers, limits, continuity ,differentiability, mean-value theorems, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes. Functions of several variables: continuity, differentiability, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals, indefinite integrals, infinite and improper integrals, beta and gamma functions. Double and triple integrals (evaluation techniques only). Areas, surface and volumes, centre of gravity.Analytical Geometry:Cartesian and polar coordinates in two and three dimensions, second degree equations in two and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

(Section-B)Ordinary Differential Equations:Formulation of differential equations, order and degree, equations of first order and first degree, integrating factor, equations of first order but not of first degree, Clariaut’s equation, singular solution. Higher order linear equations with constant coefficients, complementary function and particular integral, general solution, Euler-Cauchy equation. Second order linear equations with variable coefficients, determination of complete solution when one solution is known, method of variation of parameters. Dynamics, Statics and Hydrostatics: Degree of freedom and constraints, rectilinear motion, simple harmonic motion, motion in a plane, projectiles, constrained motion, work and energy, conservation of energy, motion under impulsive forces, Kepler’s laws, orbits under central forces, motion of varying mass, motion under resistance. Equilibrium of a system of particles, work and potential energy, friction, common catenary, principle of virtual work, stability of equilibrium, equilibrium of forces in three dimensions. Pressure of heavy fluids, equilibrium of fluids under given system of forces, Bernoulli’s equation, centre of pressure, thrust on curved surfaces, equilibrium of floating bodies, stability of equilibrium, meta-centre, pressure of gases.Vector Analysis: Scalar and vector fields, triple products, differentiation of vector function of a scalar variable, gradient, divergence and curl in Cartesian, cylindrical and spherical coordinates and their physical interpretations. Higher order derivatives, vector identities and vector equations.Application to Geometry:Curves in space curvature and torision. Serret-Frenet’s formulae, Gauss and Stokes’ theorems, Green’s identities.

SYLLABUS for IFoS (Main) Examination

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PAPER - II(Section-A)

Algebra:Groups, sub-groups, normal subgroups, homomorphism of groups, quotient groups, basic isomorphism theorems, Sylow’s group, permutation groups, Cayley theorem, rings and ideals, principal ideal domains, unique factorization domains and Euclidean domains. Field extensions, finite fields.Real Analysis: Real number system, ordered sets, bounds, ordered field, real number system as an ordered field with least upper bound property, Cauchy sequence, completeness, Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals, absolute and conditional convergence of series of real and complex terms, rearrangement of series, Uniform convergence, continuity, differentiability and integrability for sequences and series of functions. Differentiation of functions of several variables, change in the order of partial derivatives, implicit function theorem, maxima and minima, Multiple integrals.Complex Analysis:Analytic function Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series, Taylor’s series, Laurent’s Series, Singularities, Cauchy’s residue theorem, contour integration, Conformal mapping, bilinear transformations.Linear Programming:Linear programming problems, basic solution, basic feasible solution and optimal solution, graphical method and Simplex method of solutions, Duality. Transportation and assignment problems, Travelling salesman problems.

Section-BPartial differential equations:Curves and surfaces in three dimensions, formulation of partial differentiation equations, solutions of equations of type dx/p=dy/q=dz/r; orthogonal trajectories, Pfaffian differential equations; partial differential equation of the first order, solution by Cauchy’s method of characteristics; Charpit’s method of solutions, linear partial differential equations of the second order with constant coefficients, equations of vibrating string, heat equation, Laplace equation.Numerical analysis and Computer programming:Numerical methods: solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods, solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct) methods, Gauss-Seidel (iterative) method. Newton’s (Forward and backward) and Lagrange’s method of interpolation.Numerical integration:Simpson’s onethird rule, tranpezodial rule, Gaussian quardrature formula. Numerical solution of ordinary differential equations:Euler and Runge Kuttamethods. Computer Programming: Storage of numbers in computers, bits, bytes and words, binary system, arithmetic and logical operations on numbers, Bitwise operations. AND, OR, SOR, NOT, and shift/rotate operators, Octal and Hexadecimal Systems. Conversion to and form decimal Systems. Representation of unsigned integers, signed integers and reals, double precision reals and long integrers.Algorithms and flow charts for solving numerical analysis problems. Developing simple programs in Basic for problems involving techniques covered in the numerical analysis.Mechanics and Fluid Dynamics:Generalised coordinates, constraints, holonomic and non-holonomic, systems, D’ Alembert’s principle and Lagrange’s equations, Hamilton equations, moment of inertia, motion of rigid bodies in two dimensions. Equation of continuity, Euler’s equation of motion for inviscid flow, stream-lines, path of a particle, potential flow,two-dimensional and axisymetric motion, sources and sinks, vortex motion, flow past a cylinder and a sphere, method of images. Navier- Stokes equation for a viscous fluid.

H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.

S.No. Name of the Topic Topic to be Topic to be Class timings No. of Remarks started ended Lectures1. ODE (Ordinary Differential Equations) 7AM / 5PM

2. PDE (Partial Differential Equations) -Do- - 3. LPP (Linear Programming Problem) -Do- -

4. Calculus & Real Analysis -Do- -

5. Complex Analysis -Do- -

6. Vector Analysis -Do- -

7. Numerical Analysis & CP -Do- -

8. 3-Dimensional Geometry -Do- -9. Modern Algebra -Do- -

10. Linear Algebra -Do- -

11. Dynamics & Statics -Do- -

12. Mechanics & Fluid Dynamics -Do- -

Schedule for IAS/IFoS Classroom Programme: 2014-15

IAS/IFoS OPTIONAL MATHEMATICS by K. Venkanna (14 yrs teach. exp.)

REGULAR CLASSROOM Time Table for Mukherjee Nagar & Rajinder Nagar Centre

Timings: (Mukherjee Nagar: 7:00am to 10:00am) & (Old Rajinder Nagar: 5:00pm to 8:00pm)

WEEKEND CLASSROOM Time Table for Mukherjee Nagar & Rajinder Nagar Centre

Timings: (Mukherjee Nagar: 7:00am to 12:00noon) & (Old Rajinder Nagar: 3:00pm to 8:00pm)

NOTE:Regular Classes from Monday to Friday at Both the centresWeekend classes: Saturday & SundayRegular class students must attend the weekend classes to complete the syllabus quickly

&

S.No. Name of the Topic Topic to be Topic to be Class timings No. of Remarks started ended Lectures1. Modern Algebra 7AM / 3PM

2. 3-Dimensional Geometry -Do- - 3. Numerical Analysis & CP -Do- -

4. Linear Algebra -Do- -

5. Vector Analysis -Do- -

6. ODE (Ordinary Differential Equations) -Do- -

7. PDE (Partial Differential Equations) -Do- -

8. Calculus & Real Analysis -Do- -9. Complex Analysis -Do- -

10. LPP (Linear Programming Problem) -Do- -

11. Dynamics & Statics -Do- -

12. Mechanics & Fluid Dynamics -Do- -

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H.O.: B.O.: 105-106, Top Floor, Mukherjee Tower, Mukherjee Nagar, Delhi-9. 25/8, Old Rajender Nagar Market, Delhi-60. Ph.:9999197625, 9999329111, 011-45629987Regional Office: H.No. 1-10-237, 2nd floor, Room No. 202 R.K’S-Kacham’s Blue Sapphire Ashok Nagar Hyderabad-20. Mobile Nos: 09652351152, 9652661152.