Bramha Dutta Pandey
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About
I have been teaching in one of the best Institutes in India (Institute of Engineering and Technology, Lucknow (U.P.) for over six years with diligence and a sense of purpose. Teaching Mathematics is a passion for me, as I always wanted to develop the cognitive skills to deal with Mathematical problems. I have been endowed with excellent communication and presentation skills. I worked as a guest lecturer of Mathematics at the Institute of Engineering and Technology, Lucknow for the past six years, but now I am working as a lecturer of Mathematics, department of I.T. in Salalah College of Technology, Ministry of Manpower at Salalah in Sultanate of Oman.
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Answered a Question in Math
`sqrt(3)sinxcosx=0` `sqrt(3)/2 sinx(1/2)cosx=0` `sin(pi/3) sinxcos(pi/3)cosx=0` `cos(x+pi/3)=cos(2n pi+pi/2)` `x+pi/3=2n pi+pi/2` `x=2n pi+(pi/2pi/3)` `x=2n pi+pi/6` Ans. ` ` 
Answered a Question in Math
`sqrt(343x^13)` =`sqrt(7^3 x^13)` `=(7^2 7.x^12 x)^(1/2)` (by law of... 
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Given `sin^3xsin3x=sum_(m=0)^n c_m cosmx` (1) We have to find the value of n. Now ... 
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In discuusing the arithmetic series we talk about common difference not the common ratio. Clearly the terms 2,6,10,.... are terms of an arithmetic series with first term 2 and common... 
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When a>0 and b>0 `a^(x+3)=b^1` `(x+3)loga=logb` `(x+3)=logb/loga` or, `x=3logb/loga` When a<0 the problem has no slution at all. when a=0 and b=0 , the problem has no slution.... 
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Actually when a<0 and x takes fractional values the fuction will not remain in R. So we can not take a<0 for all real values of x. 
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Given problem is `lim_(x>0)(1cos^2(2sinx))/(1cos(2x))` Now we know that `1cos^2x=sin^2x` and `cos2x=12sin^2x` . Substituting these values inthe... 
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given function is y=mod(x1)+2. We know that mod(x)=x if x>0... 
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Preface As it is clear from its name that it describes in brief "what about your project". It means, what is your goal in preparing the project. Because you are a student of mathematics, so... 
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In 1 2 ... 
Answered a Question in History
In December 1991 the Soviet Union partitioned into 15 countries. The largest country by area is the Russia which lies in eastern part of Europe.Other eastern European countries of Soviet Union are... 
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We know that probability of an event ranges between 0 and 1. Now by the rule ... 
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In my opinion Functions which you have studied previously is the definion of functions and some other elementary things related to functions. Now at Grade 11 you will study various types of... 
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Preface. In the preface section, you should write the topic's history in brief and why you have decided to create the project. For example: (This topic started in  and this mathematician... 
Answered a Question in Math
Given g(x)=x^2+2. But the expresion for f(x) is not given. Now g[f(x)]={(f(x))^2}+2. Now suppose that f(x)=(x+1). Then g[f(x)]={(x+1)^2}+2... 
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The "proportional Part" defines a relation that 'how two different variable in an equation are connected' . i.e. if x and y are two variables in an equation , then proportional means if we increase... 
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Given expression is `(2^1+2^3)(8^(1/3))` ........(1). Now `2^1=1/2` and `2^3=1/2^3=1/8` . So, ... 
Answered a Question in Math
Given the function `y=(15e^(5x))/x` . We know that equation of tangent to the curve y=f(x) at `(x_1,y_1)` is given by... 
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(b) Now linearization of `f(x)=6x^25x+6` near `x_0=3` . `L(x_0)=f(x_0)+(xx_0)f'(x_0)` . `f(3)=45` . `f'(3)=31.` So, `L(3)=45+(x3)31`... 
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Given function is f(x)=`6x^25x+6` . To linearize a function f(x) near a point `x=x_0` , we symply give the Taylor's expansion of the first order about `x=x_0.`... 
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Let the car is moving with velocity u ft/second. And final velocity of the car is v ft/second. After appllying the break the deceleration f of the car is given by f=40 ft/second^2. As when... 
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Given equation is `x/33/4=(5x)/6` or we can write `x/3(5x)/6=3/4`... 
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Given `int_0^3(x/21)dx` . We know that the area bounded by the curve `y=f(x)` and the xaxis is given by... 
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Let `h(x)=int{(1+x)/(1x)^3}dx` or, `h(x)=int{(1+x)(1x)^3}dx` (1). Expanding `(1x)^3` by binomial expansion we get... 
Answered a Question in Math
To factor a general quadratic expression `x^2+bx+c` we will proceed as under  Let `(xalpha)` and `(xbeta)` are the factors of the above expression.... 
Answered a Question in Science
(a) Given radius of the orbit (r)=4.6x10^7 m Gravitational force(F)=228 N. Let mass of the earth be M and mass of the... 
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(1) Mean=1.9 bars and Standard Deviation=0.15 bars. We have to find the probability that the pressure in the tyres should be between 1.82 bars and 1.92 bars. If we let X denote the tyre... 
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We want to find the area bounded by y=3/x, y=12x and y=(1/12)x. Clearly the desired region has its upper boundary y=12x and the lower boundary y=(1/12)x. Solving Y=3/x and y=12x we get x=1/2 ... 
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Given differential equation is `(d^2y)/(dx^2)+kdy/dx+9y=36sin3x` and the initial conditions are... 
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Given function is `z=w^(3/2)(w+ce^w)` . Differentiating with respect to w we get ... 
Answered a Question in Science
The five steps of the scientific method are as follows: Step 1. State the problem example: What gets hotter in the sun: water in a black cup or water in a white cup? Step 2. Gather existing... 
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Given g(t)=`(tsqrtt)/t^(1/3)` . we can rewrite `g(t)=t/t^(1/3)t^((1/2)(1/3))` =`t^(2/3)t^(1/6)` . `d/dtg(t)=d/dt{t^(2/3)t^(1/6)}` =`d/dtt^(2/3)d/dtt^(1/6)` (As `d/dtt^n=nt^(n1)` )... 
Answered a Question in Math
Given matrix is `A=[[2,0,0],[1,1,2],[1,1,0]]` . now `det(AkI_3)=(k2)^2(k+1)` (As per the previous part of the question). Now we want to find the non zero vector `v_k` in the null... 
Answered a Question in Math
True. If we take the matrix A to be n x n. Because the row space of A is R^n. Means the rows of the matrix A forms a basis of R^n. i.e. the row vectors are linearly independent. So by the... 
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True. Because elementary matrices are a result of identity matrices by applying elementary operations. Also an elementary matrix is invertible. And as determinant of an identity... 
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Let `u=(u_1,u_2,u_3), v=(v_1,v_2,v_3), w=(w_1,w_2,w_3)` then `u.(vxxw)=det[[u_1,u_2,u_3],[v_1,v_2,v_3],[w_1,w_2,w_3]]` . Now we have to find ... 
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Let `u=(u_1,u_2,u_3),v=(v_1,v_2,v_3),w=(w_1,w_2,w_3)` . Now `u.(vxxw)=det[[u_1,u_2,u_3],[v_1,v_2,v_3],[w_1,w_2,w_3]]` . By given problem, `u.(vxxw)=20` . We want to find... 
Answered a Question in Math
We know that `det (AB)=det(A)det(B)` wher A and B are given square matrices of order nxn. Given `det(A)=4, det(B)=3` So, `det(AB)=det(A)det(B)=(4)(3)=12.` Answer. 
Answered a Question in Math
The series `sum_(n=1)^ooa_n` where `a_n` is non zero is (i) convergent if the ratio `lim_(n>oo)mod(a_(n+1)/a_n)<1` (ii)divergent if the ratio... 
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Given `det [[a,b,c],[d,e,f],[g,h,i]]=1.` We want to find the determinant of the matrix `[[a,b,c],[8a,8b,8c],[g,h,i]]` . Now `det[[a,b,c],[8a,8b,8c],[g,h,i]]` `=8det[[a,b,c],[a,b,c],[g,h,i]]` by... 
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We know that the length of arc `L=rtheta` . where `r` is the radius of the circle and `theta` is the angle in radian subtended by this arc at the centre of the circle.... 
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Given matrix is `A=[[c,1,0],[1,c,1],[0,1,c]]` . Inverse of the matrix A will exist only when `det A!=0` . Now det A=`c^32c!=0` . i.e. `c!=0` and ... 
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9 True. If the matrix A of type nxn is invertible then there are exactly n non zero rows in the row reduced echelon form of the matrix A. And the row reduced Echelon form of A is... 
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Given matrix is `A=[[1,1,0,0],[2,3,0,0],[0,0,1,1],[0,0,2,3]]` . Now to find the inverse of the matrix A we write the matrix equation as `AI=A.` where I is the `4xx4` identity... 
Answered a Question in Math
The given matrix equation is `[[1,0,0],[0,1,0],[0,0,6]]X=[[8,7,10],[9,1,8],[1,10,9]]` . We know that if `AX=B` , then `X=A^1B` provided `A^1` exists. Here we see that the... 
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Given `A=[[1,2,0],[2,5,0],[k,2k+1,2k+4]]` We know that an `nxxn` matrix is invertible if and only if `det A!=0` . Now if we see the given matrix, we observe that the first... 
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Given logarithmic equation is `log_9(2x^29)log_9 8=1` . Now we know that `log_b mlog_b n=log_b (m/n)` . Also `1=log_b b` .... 
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Given logarithmic equation is `ln(x+30)+lnx=ln31` We know that... 
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given `ln3+ln(3x^2)=4` Because we are working with natural logarithm, it means always the base is e. Also we know that `lnm+ln n=ln(mn)`... 
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To factorize any expression we express it in terms of its simple factors preferably linear expressions if possible. Now given expression is `(x^4+216).` Now, `(x^4+216)=(x^(4/3))^3+6^3` We...
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