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 IX Ch-2 | Polynomials

 Maths Assignment Class 9th Chapter 2

Polynomials

Important maths assignment questions based on chapter 2 class 9. Extra questions based on the topic Polynomials. Extra questions along with questions of NCERT book complete the topic.

Students first revise all the topics from NCERT book and then Solve the examples and then solve the sums of this worksheet.

Maths Assignment on Polynomials 

Class IX chapter 2

1. Find the value of p(x) = 3x- 2x + 8 at

a)  x = 0     
b)  x = -2                      
c)  x = 3                
d)  x = -5

2. Find the remainder when x3-3x2+3x-1 is  divided by

a)     x - 1         Ans 0
b)   x + 1         Ans -8                                





f)    3-x           Ans 8

3. a)Show that 2x - 3 is a factor of 2x- 9x+ x + 12.

   b)Show that x+2 is a factor of x- x- 12.

Hint: Find the remainder. If remainder = 0 then given function the the factor of the given polynomial otherwise not.


4. Find the value of k if x+1 is a factor of
a) 3x – kx + √3         Ans   -3 - √3
b) √2x – kx + k + 2  Ans  
c) k – kx + Kx         Ans 0
d) x - 3x + kx          Ans - 4
5) Find “a” if x+1 is a factor of  ax3 - 9x2 + x + 6a        Ans:- 2
6) If (x -2)and(x + 3) are factors of p(x) = ax+ 3x- bx - 12.  Find a and b.     
Ans: a = 1, b = 4

7. If x - 5 is a factor of x+ ax+ bx - 20  and leaves a remainder -2 when divided by x - 3. Find a and b.
Ans (-9, 24)

8. Factorize:

a) x+ 11x + 30      : Ans  (x + 5)(x + 6)

b) a- 16a + 63       : Ans  (a - 7)(a - 9)

c)15 - 2x - x2           : Ans    (3 - x)(5 + x)

d) 3 + 5x - 2x2       : Ans   (1+ 2x)(3 - x)                                                        

e) 3m- 20m - 7   : Ans  (3m+1)(m - 7)                            

f) 24m+ m - 23      : Ans (m + 1)(24m - 23)

g) 2x+ 11xy - 21y    : Ans    (x + 7y)(2x - 3y)                            

h) 7(x + y)2 + 48(x + y) - 7       : Ans  (x + y + 7)(7x + 7y - 1)

I) 2m4n - 6m2n + 4n                 : Ans  2n(m+1)(m-1)(m2-2)                        

 j) 36(a+3b)- 36(2a-3b)2   : Ans  (16a+3b)(33b-4a)

k) x+ 3x- 4x + 12                   : Ans (x - 2)(x + 2)(x + 3)                          

l) 2x- 9x +x + 12                   : Ans  (x + 1)(x - 4)(2x - 3)

m) x-3x-10x+24              : Ans   (x + 3)(x - 4)(3x - 2)                            

n) 2x-7x- 3x + 18               : Ans  (x - 2)(x - 3)(2x + 3)

o) 3x+ x - 38x + 24               : Ans   (x - 3)(x + 4)(3x - 2)                          

p)(x3 - (y - z)3)              : Ans  (x – y + z)(x2 + y2 + z2 - 2yz – xy - xz)

  


9.  Evaluate by using identity:

a)   92×108        Ans:- 9936

b)  6.7×5.3        Ans:- 35.51

c)104×107        Ans:- 11128

10.Factorize:

a)  8x- 125y- z- 30xyz                            

b)  125x- 8 + 27y+ 90xy      

c)  3√3a3 - 5√5b3 - 8c3 - 6√15abc           

d)  (5a - 4b)3 + (4b - 6c)+ (6c - 5a)3

e)  a+ (a - 1)+ (1 - 2a)3                                                     

f)  (3x + 3y - 5z)+ (2y + 3z - 5x)+ (2z + 2x - 5y)3

g)  (2x + y)3 - (x + y)3                      

h)  64m6-n6  : Ans:  (2mn + n)(4m - 2mn + n)(2m - n)(4m + 2mn + n)

11.Evaluate by using identity:

a)  (-15)3 + (-13)3 + (28)3     Ans: 16380
b)  (75)3 + (-50)3 + (-25)3          Ans: 281250

12.Simplify:  
       

13.If   a = 1 - √2, find  the value of    Ans: 8

14.If a+ b+ c= 3abc  and a + b + c = 0 then show that



15. If              
16.  Evaluate:  
17.  If     =  83, then find          Ans:  756
18.  If   , then find the value of        Ans: 52
19).  If    ,  then find the value of       Ans: 36
20.  If  , then find the value of      Ans :  
21.  Find the value of                Ans : 
22.  If  , then find the value of         Ans:  
23.  If   , then find          
24)  If    , then find            [Ans 6 ]
25.  Find the remainder when x4 + 3x2 + 3x + 1 is divided by x+1   [Ans : 2]

26.  If x3 + ax2+ bx + 6 has (x - 2) as a factor and leaves remainder 3, when divided by (x – 3), find a and b      Ans[a = -3,b = -1]

27.  For what value of a is 2x3 + ax2 + 11x + a + 3 divided by 2x - 1     Ans[a = -7 ]


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  1. Very very nice assigament, thank ku so much.

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