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.


Question 1

Find the degree measure for the following radian measure

Question 2

Find the radian measure for the following degree measure

Question 3

Find the magnitude, radian and degree, of the interior angles of a regular

Question 4

If sin θ =12/13 and θ lie in the second quadrant, then find the value of

sec θ + tan θ.   ………………    Ans. [- 5]

Question 5

Prove the followings

  i)   cos24o + cos 55o + cos 125o + cos 204o + cos 300o = 1/2

ii)  sin 600o tan(-690o) + sec 840o cot(-945o) = 3/2


Question 6:   Simplify  


Question 7

Evaluate the following :

Question 8

Prove that : tan70o = tan20o + 2tan50o

Solution 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 11

If 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 12

An 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, Then

ATQ :  p + q = α,  p – q = x,  

Now applying componendo and dividendo and simplify we get the required result.

Question 13

Prove that:   

Question 14  

Prove that:  

Question 15

Prove That : 

Solution Hint : 

Use tan θ = sin θ/cos θ, then using AB and CD formulas

Question 16

If 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 19

Find the value of sin18o  


θ = 18o   5 θ = 90o     2 θ + 3 θ = 90o    2 θ = 90o - 3 θ

Now taking sin on both side we get

Sin (2 θ) = Sin (90o - 3 θ)    Sin (2 θ) = Cos (3 θ)

2Sin θ cos θ = 4Cos3 θ – 3cos θ     2Sin θ  = 4Cos2 θ – 3

2Sin θ  = 4(1-sin2 θ) – 3

4 sin2 θ + 2sin θ – 1 = 0

Now using quadratic formula here and find the value of sin θ

Question 20

Prove that :  

Solution Hint:


Question 21

i) Evaluate:  

Solution Hint:  Using: 

ii)  Evaluate:  

Question 22


Question 23


Question 24


Solution  Hint: 



Question 25


Solution Hint:  


Dividing on both side by 

 i.e. by 2 

 Now proceed this question as previous one.

Question 26

Prove that :  

Solution : 

Question 27

Evaluate:  and  



Note:  Each interior angle of a regular polygon is given by : 

 Where n is the number of sides.

PDF view of the assignment



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