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 X Ch-5 | Arithmetic Progression

MATHEMATICS ASSIGNMENT   [CHAPTER 5]

Extra questions of chapter 5 class 10 Arithmetic Progression with answer and  hints to the difficult questions. Important and useful math assignment for the students of class 10

For better results

  • Students should learn all the basic points of  Arithmetic Progression 
  • Student should revise N C E R T book thoroughly with examples.
  • Now revise this assignment. This assignment integrate the knowledge of the students.

CLASS  10TH Arithmetic Progression (AP)


Level 1

 1.  Which term of the AP:-  5,9,13,17..........is 81.                                

 Ans [20th term]

 2.  Which term of the following APs are equal    a) 13, 19, 25...........     b) 69, 68, 67 ..........

             Ans  [9th term]

 3.  How many terms of the AP: 3, 5, 7.......must be taken so that   Sn =   120.         

 Ans [10 terms]

 4. Find the 10th term from the end of the AP :-  4,9,14..........254                     

          Ans [209]

 5.  If 7th term  of an AP is  -4 and 13 term is -16 find the AP                                          

Ans  [8,6,4,2,0.........]

 6.  Find k for which 8k + 4, 6k - 2 and 2k + 7 are in AP.                                                     

  Ans [k = 15/2]

 7.  Find a So that  3a + 2,  3a - 1,  5a + 4  are in AP.                                                            

  Ans  [-4]

 8.  If a = 7, a60 = 125, find a32                                                                                              

   Ans  [69]

 9.  Which term of the AP: 5, 13, 21, .... is 181.                                                                   

  Ans [23rd ]

 10. Find AP whose 3rd term is 16 and difference of 5th term from 7th term is 12.  

Ans [4,10,16,22...]

 11. Which term of the AP: 3,15,27,39........will be 120 more than its 64th term      

 Ans [[74th]

 12. Which term of the AP: 3,15,27,39........will be 132 more than its 60th term       

Ans [ 71st term]

 13. Which term of the AP : 8,14,20,26........will be 72 more than its 41st term.        

Ans  [53rd ]

 14. The 3rd  term of an AP is 3 and its 11th term is -21. Find its first term and c.d.  

Ans [a = 9, d = - 3]

 15.    The 7th term of an AP is 32 and its 13th term is 62. Find the AP                         

Ans [2,7,12......]

 16.   The 6th term of an AP is -10 and 10th term is -26. Find the 15th term of the AP.

 17.   If Sn  = 5n2+3n. Find its nth term.                                                                               

 Ans [10n-2]

 18.    If Sn  = 4n2-3n.. Find its nth term.                                                                              

 Ans [8n-7]

 19.   Sn = 2n2 + 5n,   find  its nth term                                                                               

  Ans  [4n + 3]

 20.   In an AP, the sum of its first n terms is 3n2 + n. Find its 22nd term.                   

 Ans [130]

Level 2

21.   The sum of the first n terms of an AP. Is  3n2 + 6n. Find the nth term of this A.P.    

Ans [6n+3]

22.    If tn = 4n-5. Then find the sum of first 25 terms.                                               

 Ans [1175]

23.    If tn = 2-3n. Then find the sum of first 25 terms.                                               

Ans [-925]

24.    Find the sum of all two digit no. Which are divisible by 4. 

Ans [1188]

25.    Find the no. Of terms of an AP: 54,51,48....... so that their sum is  513.          

Ans [18 or 19]

26.    Find the sum of all natural no. Between 100 & 300 which are divisible by 6        

Ans [6534]

27.    Find the sum of all natural no. Between 200 & 300 which are divisible by 4        

Ans [6000]

28.   The 5th term of  an AP is zero. Show that its 33rd term is 4 times its 12th term.
29.    If 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
30.   If m times the mth term of an AP is equal to the n times of the nth term then show  that  its    (m + n)th is zero.
31.   If 7 time the 7th term of an Ap is equal to the 11 times  the 11th term. Show that the 18th term of the AP is zero.

32.    Find the sum of 11 terms of an AP whose middle term is 30.                              

Ans [330]

33.   Find the sum of all integers between 50 & 500 which are divisible by 7             

Ans [17696]

34.   The sum of first 15 terms of an AP is 105 and the sum of next 15 terms is 780. Find first   three terms of an AP.                                                                                                           

Ans [-14,-11,-8]

35.   Find the common difference of an AP whose 1st term is 100 and the sum of whose first 6 terms  is 5 times  the sum of next 6 terms                                                                                   

Ans [-10]

36.    Find the no. Of  natural no. Which lie between 101 and 304 and are divisible by  3 or  5. Also find their sum.                                                                                                      

 Ans [94 terms , sum= 19035]

37.   The ratio of the 7th to the 3rd term of an AP is 12 : 5 Find t13  :  t14                               

 Ans [90 : 97]

38.   Find the sum of all 3 digit no. Which leaves remainder 3 when divided by 5      

Ans [99090]

39.    The sum of 4 terms in an AP is 42. If product of extreme terms is 90. Find no.  

Ans [6,9,12,15]

40.    Sum of 3 terms of an AP is  21 and their product is 231. Find the numbers.        

Ans [3,7,11]

Level 3

41.   Find 4 numbers in AP whose sum is 20 and sum of whose square is  120.            

Ans [2,4,6,8]

42.   If angles of a quadrilateral are in AP whose c. d. Is 10. Find all the angles.    

Ans [75,85,95,105]

43.    The first and last term of an AP is a  & l show that sum of the nth term from the beginning and nth term from the last is a + l.

44.   Find the sum of first hundred even natural number which are divisible by 5.           

Ans [50500]

45.   Which term of the AP: 5,9,13,17.....is 81 also find their sum.                          

Ans [20th , 860]

46. If in an AP sum of first 10 terms is -80 and the sum of its next 10 terms is -280. Then find AP.                                                                                                                               

 Ans [1,-1,-3,-5]

47.   Find the sum of all multiple of 8 lying between  201 and 950.

48.   If 21, a,  b, -3 are in AP. Then find the value of  (a+b)                                    

Ans[18]

49.   Find the 9th term from the end of the AP:   5, 9, 13, …….185.                      

Ans [153]

50.   The angles of a triangle are in AP. The greatest angle is twice  the least. Find the angles of the triangle.                                                                                                             

Ans[40o, 60o and 80o]

51.   If the seventh term of an AP is 1/9 and its 9th term is 1/7, find its 63rd term.     

 Ans[1]


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