### 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-3 | Trigonometric Functions

Math Assignment / Class XI / Chapter 3 /  Trigonometric Functions

Extra questions of chapter 3 class 11 Trigonometric Functions with answer and  hints to the difficult questions. Important and useful math. assignment for the students of class 11

For better results

• Students should learn all the basic points of Trigonometry up to 11th standard
• Student should revise NCERT book thoroughly with examples.
• Now revise this assignment. This assignment integrate the knowledge of the students.

ASSIGNMENT FOR XI  STANDARD TRIGONOMETRY

 Question 1Find the degree measure for the following radian measure Question 2Find the radian measure for the following degree measure Question 3Find the magnitude, radian and degree, of the interior angles of a regular Question 4If sin θ =12/13 and θ lie in the second quadrant, then find the value ofsec θ + tan θ.   ………………    Ans. [- 5] Question 5Prove the followings  i)   cos24o + cos 55o + cos 125o + cos 204o + cos 300o = 1/2ii)  sin 600o tan(-690o) + sec 840o cot(-945o) = 3/2iii) Question 6:   Simplify   Solution Question 7Evaluate the following : Question 8Prove that : tan70o = tan20o + 2tan50oSolution Hint:Now cross-multiply and simplify the above fraction we get the required result. Question 9 Question 10 If tanA = ktanB, then show  that: Solution Hint: tanA = ktanB Now apply componendo and dividendo and using trigonometric formulas. Question 11If tan(A + B) = p, tan(A – B) = q, then show that :  Solution Hint: Start from RHS and then putting the value of p and q then simplify and get the result. Question 12An angle α is divided into two parts such that the ratio of the tangents of the two parts = k  and difference of two parts = x  then show that:  Solution hint:Let two parts of  α are  p and q, ThenATQ :  p + q = α,  p – q = x,  Now applying componendo and dividendo and simplify we get the required result. Question 13Prove that: Question 14  Prove that: Question 15Prove That : Solution Hint : Use tan θ = sin θ/cos θ, then using AB and CD formulas Question 16If cos(θ+2 α) = n cos θ , then prove that : Solution Hint: Applying componendo and dividendo  then applying CD formulas then simplify the fractions we get the required result. Question 17 Prove that :   sin20o sin40o sin60o sin80o = 3/16 Question 18 Prove that :   cos20o cos40o cos60o cos80o = 1/16 Question 19Find the value of sin18o  Solution:θ = 18o  ⇒ 5 θ = 90o  ⇒   2 θ + 3 θ = 90o ⇒   2 θ = 90o - 3 θNow taking sin on both side we getSin (2 θ) = Sin (90o - 3 θ)    Sin (2 θ) = Cos (3 θ)2Sin θ cos θ = 4Cos3 θ – 3cos θ     2Sin θ  = 4Cos2 θ – 32Sin θ  = 4(1-sin2 θ) – 34 sin2 θ + 2sin θ – 1 = 0Now using quadratic formula here and find the value of sin θ Question 20Prove that :  Solution Hint:

 Question 21i) Evaluate:  Solution Hint:  Using: ii)  Evaluate: Question 22Solve: Question 23 Solve: Question 24Solve: Solution  Hint: Question 25Solve: Solution Hint:   Dividing on both side by  i.e. by 2  Now proceed this question as previous one. Question 26Prove that :  Solution : Question 27Evaluate:  and  Solution: Note:  Each interior angle of a regular polygon is given by :  Where n is the number of sides.

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