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 XI Ch-13 | Limits and derivatives

Math Assignment  Class XI | Chapter 13 | Limits and derivatives
Math Assignment  Class XI  Chapter 13  Limits and derivatives, Extra questions on Limits and Derivatives, Important questions on limits and derivatives

 IMPORTANT QUESTIONS ON LIMITS

Question 1 :    Evaluate the  limits \[\lim_{x\rightarrow 0}\frac{cot2x-cosec2x}{x}\]

Question 2 :    Evaluate the  limits \[\lim_{x\rightarrow 0}\frac{sinx-2sin3x+sin5x}{x}\]

Question 3:    Evaluate the  limits \[\lim_{x\rightarrow 0}\; \frac{sin2x+sin6x}{sin5x-sin3x}\; \; \; \;\; \; [Ans:\; 4]\]

Question 4 :    Evaluate the  limits \[\lim_{x\rightarrow 0}\;\; \frac{sin^{2}3x}{x^{2}}\]

Question 5 :    Evaluate the  limits \[\lim_{x\rightarrow \infty }\;\; \frac{n!}{(n+1)!-n!}\]

Question 6:    Evaluate the  limits \[\lim_{x\rightarrow \infty }\;\; \frac{n!}{(n+1)!-n!}\; \; \; \; \; \; [Ans: 0]\]

Question 7 :    Evaluate the  limits \[\lim_{x\rightarrow \infty }\;\; \frac{1+2+3+........+n}{n^{2}}\; \; \; \; \; \; [Ans: 0]\]

Question 8 :    Evaluate the  limits \[\lim_{x\rightarrow 9 }\;\; \frac{x^{3/2}-27}{x-9}\; \; \; \; \; \; [Ans: \frac{9}{2}]\]

Question 9 :    Evaluate the  limits \[\lim_{x\rightarrow 4 }\;\; \frac{x^{2}-16}{\sqrt{x^{2}+9}-5}\; \; \; \; \; \; \; [Ans: 10]\]

Question 10 :    Evaluate the  limits \[\lim_{x\rightarrow 2 }\;\; \frac{x^{2}-4}{\sqrt{3x-2}-\sqrt{x+2}}\; \; \; \; \; \; \; [Ans: 8]\]

Question 11 :    Evaluate the  limits \[\lim_{x\rightarrow 4 }\;\; \frac{(x^{2}-x-12)^{18}}{(x^{3}-8x^{2}+16x)^{9}}\; \; \; \; \; \; \; [Ans:\left ( \frac{7}{2} \right )^{18}]\]

Question 12 :    Evaluate the  limits \[\lim_{x\rightarrow 1 }\;\; \left [ \frac{2}{1-x^{2}}+\frac{1}{x-1} \right ]\; \; \; \; \; \; \; [Ans: 1/2]\]

Question 13 :    Evaluate the  limits \[\lim_{x\rightarrow 2 }\;\; \frac{x^{3}-6x^{2}+11x-6}{x^{2}-6x+8}\; \; \; \; \; \; \; [Ans: 1/2]\]

Question 14 :    Evaluate the  limits \[\lim_{x\rightarrow 2 }\;\; \frac{x^{3}-3x^{2}+4}{x^{4}-8x^{2}+16}\; \; \; \; \; \; \; [Ans: 3/16]\]

Question 15 :    Evaluate the  limits \[\lim_{x\rightarrow 1/2 }\;\; \frac{8x^{3}-1}{16x^{4}-1}\; \; \; \; \; \; \; [Ans: 3/4]\]

Question 16 : \[\lim_{x\rightarrow 0}\left [ \frac{\sqrt{1+tanx}-\sqrt{1-tanx}}{sin2x} \right ]\]

Question 17 \[\lim_{x\rightarrow \frac{\pi }{3}}\frac{\sqrt{3}-tanx}{\pi -3x}\; \; \; \; \; \; \; \; \; Ans:\frac{4}{3}\]

Question 18 Evaluate \[\lim_{x\rightarrow \frac{\pi }{2}}\frac{1-sinx}{cos^{2}x}\; \; \; \; \; \; \; \; \; Ans:\frac{1}{2}\]

Question 19 Evaluate: \[\lim_{x\rightarrow \pi }\frac{sin3x-3sinx}{(\pi -x)^{3}}\]

.


DERIVATIVES

Question 1:  Differentiate the following  by first principal

(i)  sin 2x    (ii) sin2x     (iii)  sin x2     (iv)      (v)   x ex      (vi)  x2cosx       (vii) Cos2x      (viii)  x2ex

Question 2 : \[Differentiate:\; \; y=\frac{(x^{3}+1)(x-2)}{x^{2}}\]

Question 3 : \[Differentiate:\; \; y=e^{xloga}+e^{alogx}+e^{aloga}\]

Question 4 : \[Differentiate:\; \; y=\left ( sin\frac{x}{2}+cos\frac{x}{2} \right )^{2}\]

Question 5 : \[Differentiate:\; \; y=\frac{x^{3}sinx}{cosx}\]

Question 6 :\[Differentiate:\; \; y=(x+secx)(x-tanx)\]

Question 7 : \[Differentiate:\; \; y=(1-2tanx)(5+4sinx)\]

Question 8 : \[Differentiate:\; \; y=x^{2}\; sinx \; logx\]

Question 9 : \[Differentiate:\; \; y=x^{5}\; e^{x} +x^{6}\; logx\]

Question 10 : \[Differentiate:\; \; y=\frac{1+tanx}{1-tanx}\]

Question 11 : \[Differentiate:\; \; y=\frac{x+e^{x}}{1+logx}\]

Question 12 : \[Differentiate:\; \; y=\frac{e^{x}-tanx}{cotx-x^{n}}\]

Question 13 : Find the derivative of the following by first principal\[(i)\; \; f(x)=\sqrt{cosx} \;\;\;\; (ii)\; \;f(x)= \sqrt{tanx}\]

Question 14 : \[Differentiate:\; \; y=\frac{e^{x}-tanx}{cotx-x^{n}}\]




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