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Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Math Assignment Class XII Ch-5 | Derivatives

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Math Assignment Class XII Chapter 5 Derivatives   Question 1 Use chain rule to find the derivative of \[y=\left ( \frac{2x-1}{2x+1} \right )^{2} \;\;\; Ans.1: \frac{8(2x-1)}{(2x+1)^{3}}\] Question 2 .  Differentiate the following w.r.t. x \[y=log_{10}x+ log_{x}10+log_{x}x+ log_{10}10 \] Answer 2 \[ \frac{dy}{dx}=\frac{1}{xlog10}-\frac{log10}{x(logx)^{2}} \] Hint for the solution: \[\frac{logx}{log10}+\frac{log10}{logx}+\frac{logx}{logx}+\frac{log10}{log10} \]\[=\frac{logx}{log10}+\frac{log10}{logx}+1+1\] Now differentiating w. r. t. x and taking log10 as constant. Question 3 . Differentiate the following w. r. t. x at x = 1\[y=e^{x(1+logx)}\; \; \; \; \; \; \; \;........\: \: Ans.[2e]\] Question 4 . \[ If\: \frac{x}{x-y}=log\frac{a}{x-y},\: then\: prove\: that\: \frac{dy}{dx}=\frac{2y-x}{y}\] Question 5 : Differentiate log(x  e x )  w. r. t.   xlogx.  Answer 5: \[ \frac{1+x}{x(1+logx)}\] Question 6 : Differentiate x 2 w. r. t. x 3 .        ...........    Ans:  2/3x. Question 7 : \[

Application of Integrals Chapter 8 Class 12

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Application of Integrals  Class 12 Chapter 8 Method of finding the area under the curve, explanation with different examples Introduction: In geometry, we have learnt formulas to calculate areas of various geometrical figures including triangles, rectangles, trapezium and circles. However they are inadequate for calculating the areas enclosed by curves. Now we shall study a specific application of integrals to find the area under simple curves, area between lines and arcs of circles, parabola and ellipses. Method of taking the limits: If limit is taken on the x-axis, then find the value of y in terms of x. If   limit is taken on the y- axis, then find the value of x in terms of y. Algorithm First of all find the limits on the x-axis or on the y-axis. If limit is on the x-axis, then find the value of y in terms of x. If limit is on the y-axis, then find the value of x in terms of y. Find the area under the curve by integrating the given function in the respective lim

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