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 Ch-6 Class X | Triangle

Maths. Assignment Class X Chapter 6 : Triangle
Extra questions of class x, chapter 6, extra questions of triangle chapter 6, class x

Important Result : 

Internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.    In Triangle ABC, if AD is the bisector of ∠A then \[\frac{AB}{AC}=\frac{BD}{DC}\]

For detailed study and basic concepts related to the similarity of triangles: Click Here

Solve the following questions

Question 1:

Q. 1. PA, QB and RC are each perpendicular to AC then

\[Prove\; that\; \; \frac{1}{x}+\frac{1}{z}=\frac{1}{y}\]


Question 2:

If the bisector of an angle of  triangle bisects the opposite side, then prove that the triangle is isosceles.

Question 3:

O is any point inside a triangle ABC. The bisectors of ∠AOB, ∠BOC and ∠COA meet the side AB, BC and CA in points D, E, F respectively. Show that AD X BE X CE = BD X EC X FA

Question 4:

In triangle ABC, AD is the internal bisector of ∠A which meets BC at point D. \[Prove\; that\; \frac{Ar(\Delta ABD)}{Ar(\Delta ACD)}=\frac{AB}{AC}\]

Question 5:

In the given figure express x in terms of a, b, c   


Question 6:

Q6 The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. Find the ratio of their corresponding heights? What is the ratio of their corresponding median.

Question 7:

In quadrilateral ABCD,  ∠B = 90o  If AD2 = AB2 + BC2 = CD2  Prove that ACD = 90o 

Question 8:

In the given figure PQR,   S and T trisects the side QR of a right triangle PQR. 
Prove that 8PT2 = 3PR2 + 5PS2   

Question 9:

Triangle ABC is right angled at B ,  D is the mid- point of BC. Prove that AC2 =  4AD2 - 3AB2

Question 10:

In triangle ABC, AD ⟂ BC and point D lies on BC such that 2BD = 3CD, Prove that 5AB2 = 5AC2 +BC2

Question 11:

△ABC is right angled at C. Let BC = a, CA = b, BC = c, and let p be the length of perpendicular from C on AB
Prove That :      

Question 12:

In △ABC, P and Q are the points on sides CA and CB respectively, which divides these sides in 2 : 1. Prove that 

(i) 9AQ2 = 9AC2 + 4BC2

(ii) 9BP2 = 9BC2 + 4AC2

(iii) 13AB2  = 9(AQ2 + BP2)

Question 13:

In △ABC, AC > AB,  D is the mid - point of BC and   AE⟂BC .
Prove that : 
 


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