X Standard
ARITHMETIC SEQUENCES
1. a) Write a sequence by adding 3 with the multiples of 7.
b) Write its algebraic form
c) Is 2000 a term of this sequence ?
2. . The common difference of two arithmetic sequence are equal. The difference between their first terms are 10. a) What is the difference between the second terms ? b) What is the difference between the nth terms?, c) What is the difference between the sums of first n terms ?3. The sum of first n terms of an arithmetic sequence is 3n2 + 4n
11. Fifth term of an arithmetic sequence is 18. Find the sum of scond
term and eight term ? If the common difference is 3 find the first
term ?
12. The algebraic expression of an arithmetic sequence is 6n+1
a) Write the sequence?. b) What is the remainder when the terms are
divided by 6? c) Write the algebraic expression of the sequence obtained
by the natural numbers which leaves a remainder 2 on division by 6?
13. The sum of first 15 terms of an arithmetic sequence is 300.
a) What is its 8th term?. b)If the first term is 6 find its common
difference? c) Write the algebraic expression of this sequence?
14. The algebraic expression of an arithmetic sequence is 5n-3.
a) Find the first term?. b) Find the sum of first 39 terms ?
15. The sum of first 5 terms of an arithmetic sequence is 60. Write the
sequence?
16.a). Write the arithmetic sequence with first term 1 and common difference
½? b) Find its 31st term?. c) Calculate the sum of its first 31 terms?
17. a), The 10th term of an Arithmetic sequence is 20 and 20th term is 10
b) What is its common difference?. c) Find its 30th term?
18. a).What is the common difference of the arithmetic sequence 80,76,72,.......
b). How many positive numbers are there in this sequence?. C). Which
is the first negative number in this sequence?, d. In which position
did the first negative number occur in this sequence?
19. a )What is the common difference of the arithmetic sequence
-100,-96,-92,...? b)Check whether Zero is a term in this sequence.
c) Which is the first positive number in this sequence?
20. a). Write the arithmetic sequence with first term 10 and common
difference 4? b) Write the difference of the terms in the same
position of the above sequence and the arithmetic sequence
11,17,23,....? c) Find the sum of first 20 terms of the sequence
thus obtained?
21. a) Write the sequence of perfect squares which are even.
b) Is it an arithmetic sequence?
22. a). The sum of first 9 terms of an arithmetic sequence is 360.
b )What is its 5th term? c) If the sum of first 5 terms is 100 , What is
its third term? d) What is the common difference of this sequence?
e) Write the sequence .
23. a ) Find the sum of first 30 natural numbers . b) Find the sum of first 30
multiples of 6? c) Write the algebraic form of the sequence obtained by
subtracting 2 from the multiples of 6? d) Find the sum of first 30 terms
of this sequence?
24 The algebraic expression of an arithmetic sequence is 8n+5. a ) What is
the common difference of this sequence? b) What is the difference
between the smallest four digit number and largest three digit number
in this sequence
25. Consider the arithmetic sequence 4,6,8 ...
a) What is the 5th term in the sequence? b) Write the ratio between the
first and third terms of this sequence? c) Write the ratio between the
fifth term and 15th term of this sequence?
26. a) Which is the first number above 200 which leaves a remainder 3 on
division by 7? b) How many such numbers are there between 200 and
400? c) Find the sum of these numbers?
27. a). Write the first three digit number which is a multiple of 9. b) Write the
sequence of all three digit numbers which are multiples of 9.
c) How many numbers are there in the above sequence ?
d) Find the sum of all these numbers.
28. X + 5 , 2X – 1 , 2X + 3 ... are three consecutive terms of an arithmetic
sequence . Find the value of X ? b ). Find the sequence ? c ). Find the
21st term of this sequence ?
29. 4
8 12
16 20 24
28 32 36 40
... ... ... ... ...
... ... ... ... ... ...
a) Write the next two rows in this pattern .
b) Write the first and last terms of the 11 th row.
30. 2
4 6 8
10 12 14 16 18
. . . . . . . . ..
a) Write the next line in this pattern.
b) How many numbers are there in the 10th row?
c) What are the last and first terms in the tenth row ?
Hint:
c) Identifies the last terms as 2x1², 2x2², 2x3²,...
Last term in the 10th row =2x10²=200
First term in the 10th row = 2x 9² + 2=164
31. Write an arithmetic sequence with common difference as 6 . Is the
difference between any two terms can be 500 ? .
32. Write an arithmetic sequence which leaves remainder 1 on dividing by 6 .
Is 2017 can be a term of this sequence ?
33. 7, a , b, c, d, 37 are first 6 terms of an arithmetic sequence , Find the
value of a, b, c, d ?
34. 15, a , 29 are three consecutive terms of an arithmetic sequence ,
Find the Value of a ? Can 345 be a term of this sequence?
35. Some chairs are arranged in a hall as an arithmetic sequence . 47 chairs
in the 6th row , 75 chairs in the 10th row. a). Find the number of chairs
in the first row ? b). Find the number of chairs in the 16th row ?
36. The sum of first n terms of an arithmetic sequence is 3n2 + 2n Find the
first term ? Common difference ? and algebric form of this sequence ?
37. Find the number of all three digit numbers which are divisible by 7 ?
38. How many numbers are there between 200 and 500 which leaves
remainder 3 on dividing by 9 ?
39. How many terms are there in the sequence 10, 17, 24.......................... .346.
40. The algebraic form of an arithmetic sequence is 3n−5. Write the sequence
What is its tenth term. Is 231 a term of this sequence
41. The 8th term of an arithmetic sequence is 40. Calculate the sum of first
15 Terms ?
42. Write the algebraic expression of the sequence 3, 6, 12, 24,..................
43. 20 is a term of an arithmetic sequence with common difference 3. Can
the sum of any 11 terms of this sequence be 517 ? why?
44. The tenth term of an arithmetic sequence is 65 and its 15th term is 80.
Is 200 a term of this sequence ?
45. How many 3 digit numbers are there which leaves remainder 5 on
dividing by 7
46. The angles of a pentagon are in an arithmetic sequence. Find the angles ?
47. There are 20 terms in an arithmetic sequence . Sum of first term and
last term is 88. Find the sum of 10th term and 11th term ? If 10th term
is 42 find 11th term ? Find the sequence ?
48. The difference between 12th term and 7th term is 50 and its 4th term
is 16. Find the common difference ? First term and the sum of
first n terms ?
49. 4, 9, 16,25, ........ write the nest two terms of this sequence and Find the
algebraic form
50. 1
2 3 4
5 6 7 8 9.
....................................................
a). Write the next two line. b). Find the first number in the 11th row
c). Find the lst number in the 11th row
d). Find the sum of all numbers from first row to 11th row.
51. If the sum of three consecutive terms of an arithmetic sequence is 24
and their product is 224. Find the terms?
52. The second and third term of an arithmetic sequence is b, c Find the
first term and fourth term ?
53. The 12th term of an arithmetic sequence is 50 and sum of its first 12 term
is 336. a). Find the first term ? b). Find the common difference ?
c). Is 478 a term of this sequence ? Give reason ?
54. The sum of three consecutive terms of an arithmetic sequence is 30 and
their product is 840 . Find the numbers ?
55. Three times of the third term of an arithmetic sequence is equal to five
times of the fifth term . Find the 8th term?
56. nth term of an arithmetic sequence is 3 + 4n
a. Find the 10th term ? b ). Which term will we get if we add 132 to
10th term ?
57. The difference between 7th and 2nd term of an arithmetic sequence is 20.
a. Find the common difference ?
b. Its 3rd term is 9 How many terms gives the sum as 153 ? (Form a
second degree equation )
58. The product of first two consecutive terms with common difference 5 is
266. Find the sequence ?
59. Sum of first five terms of an arithmetic sequence is 85 and sum of first
10 term is 320 . Find the sequence .
60. Sum of first 7 terms of an arithmetic sequence is 112 and the sum of next
seven terms are 259. Find the sequence ?
61. The expense for digging a well for the first one metre is 500 rupees, 50
rupees more for the next metre and so on. The total length of the well is
15 metre. How much is needed for digging the last metres of the well.
What is total expense for digging the well?
62. Write the sequence formed by the integer terms of the arithmetic
sequence 19/8, 11/4, 25/8,...... is 47 can be a term of this sequence ?
63. Prove that the squares of all the terms of the arithmetic sequence
4, 7, 10, .... belong to the sequence?
64. The difference between 7th and 2nd terms of an arithmetic sequence is 20.
Find the common difference ? Its 3rd term is 9 How many terms gives
the sum 153.
65. The difference between the 15th term and the 5th term of an A.S is 40.
Which number is to be added to its 12th term to get the 20th term?
Find the difference between its first term and 21st term?
66. When 60 is added to the first term of an A S we get its 11th term.
Which number should be added to its first term to get the 19th term ?
67. 52 X 54 X 56 X ....................... X 52n = (0.008)-30 Find the value of n
68 Write two A S with 100 as the sum of first four terms
69. If the sum of first 7 terms of an A S is 49 and the sum of first 17 terms
is 289. Find the sum of first n terms
70 If the nth term of an A S is 2n + 1 . Find the sum of first n terms
71 Find the 6th term from the end of the A S 17, 14, 11, .............. , -40.
is the ratio of the third term to the fifth term ?
73. The sum of the first 5 terms of an A S is 100 and the sum of First 10
terms is 350. Find the sum of First n terms
74 In an arithmetic sequence the ratio of 5th term to 7th term is 11 : 15
and its 10th term is 42, find the common difference and sequence?
75. The difference between the sum of first 20 terms and the sum of next
20 terms of an arithmetic sequence is 1600. Find the common difference
If the 7th term is 30 find the sequence.
76. Sum of first 6 terms of an A S is 162 and the sum of first 10 term is 430.
Find the common difference? First term?
1. A box contains 3 black balls and 7 white balls. Another box
contains one black and one white more. The probability of
getting a white ball from which box is more ?
(White ball from First = 7/10 , White ball from second = 8/12 = 2/3, 7/10. 2/3 →21, 20
First box is better choice )
2. One is asked tosay a two digit numbe. (10,11,12...... 99, n = 90)
a. What is the probability of it being a perfect square (Ans = 6/90 )
b. What is the probability of it being a multiple of 5 (Ans = 18/90 )
c. hat is the probability of bothdigits being the same (A = 9/90 )
3. In class X A has 25 boys and 15 girls, in X B, there are 10 boys
and 20 girls. One student is to be selected from each class.
a. What is theprobability of both being boys ( A = 250/1200)
b. What is theprobability of both being girls ( A = 300/1200)
c. What is theprobability of one boy and one girl (A= 650/1200 )
d. What is the probability of atleast one boy (A= 900/1200)
4. Arun tossed two coins simultaneously. Find the probability
of getting ( HH, HT, TH, TT )
a. One head (A = 2/4 = 1/2 )
b. Two head ( A = 1/4)
c. Atleast one head (A = 3/4)
d. Atmost one head ( Two heads are not needed A= 3/4)
5. A box contains some red balls and some green balls.
Probability of getting red ball is 3/7. What is the probability
of getting green balls? (Ans = 1-3/7 = 4/7)
6. A bag contains some black balls , some white balls and some
green balls. Probability of getting black ball is 2/5, probability
of gettinmg a white ball is 1/3, Find the probability of getting
a green ball?{Ans = 1-(2/5+1/3) = 4/15}
7. A bag contains some black balls and some white balls. No of white ball is 3 more than twice the black balls. Probability of
getting white ball is 5/7. Find the number of black balls and
white balls ? (Ans = No of black balls = x, No. of white ball = 2x+3,
Total ball = 3x+3, Black ball = 6, White ball = 15 ).
8. One box contains 8 black balls and 12 white balls. Another
box contains 9 black and 6 white balls. One ball is taken
from each box . (Ans. Hints Total pairs = 20x15= 300 )
a. What is the probability of getting both black (A = 6/25 )
b. What is the probability of getting both white (A = 6/25 )
c. What is the probability of getting one black and one white
(A = 39/75)
9. A box contains four slips numbered 1,2,3,4 and another box
contains three slips 1,2,3. If one slip is taken from each box
(1,1), (1,2), (1,3)
(2,1), (2,2), (2,3)
(3,1), (3,2), (3,3)
(4,1), (4,2), (4,3) Total = 12.
a. What is the probability of the product being odd ?
( (1,1) (1,3) (3,1) (3,3) ) (Ans = 1/3 )
b. What is the probability of the product being even ? (A=2/3)
c. What is the probability of getting sum as 5 ? (A = 3/12 =1/4)
d. Both digit are same (A = 1/4 )
10. Two dice with faces numbered from 1 to 6 are rolled together.
a. What are the possible sums? ( (1,1), (1,2), (1,3) .... (2,1), (2,2), (2,3 ...
.......(6,1), (6,2), (6,3), (6,4),(6,5), (6,6) ) Total 36
b. What is the probability of getting sum as 5 ? (A= 1/9)
c. What are the possible sums ? ( 2, 3,4,5,6,7,8,9,10,11,12 )
c. Which of these sums has the maximum probability (A=7)
SECOND DEGREE EQUATIONS
as equal to 18units, if possible find the length and breadth?
Ans. ( Hints. Find b² - 4ac ( yes it is possible ) by solving l = 6, b = 3 )
2. The square of a term in arithmetic sequence 2, 5, 8, ..... is 2500.
what is its position ? (Which term's square is 2500 )
Ans. (Hints. Find the algebric form and its square = 2500, by solving n = 17 )
3. The common difference of an arithmetic sequence is 4 and
its product of first and third term is 84 find the first term
and sequence
Ans. (Hins. Terms x, x+ 4 , x+8, x (x+8) =84 by solving x = 6, terms 6,10, 14 ........ )
4. How many terms of the arithmetic sequence 2, 6, 10,.......
must be added to get 288.
Ans. (Hints. n/2 ( x1 + xn ) = 280, find xn and by solving n = 12 )
5. Altitude of a triangle is 3cm more than its base and its area is
44 cm² Find the base and altitude ?
Ans. (Hints. base = x, altitude x+3, ½ x(x+3)= 44, Base = 8, Altitude = 11 )
6. Product of two consecutive multiples of 4 is 480 Find the
numbers Ans. (Hints First no. = x, second no. x+4, x(x+4) = 480, by solving nos = 20,24)
7. A 56 cm long wire is bent into a rectangle and the distance
from one corner to another corner is 20 cm . Find the length
and breadth of the rectangle ?
Ans. (Hints 2(l+b) =56, l+b = 28, l. = x, b= 28-x, hypotenuse= 20, l² + b² = h², l=16, b =12)
8. For completing a work Babu needs 5 days more than Abu
claimed. They together did the work in 6 days. Find the
number of days required by each person to complete the work
superately?
( Hints. Abu need x days, Babu need x+5 days, 1/x + 1/(x+5) =1/6 , x² -7x-30=0 , x= 13 )
9. If the sum of reciprocals of two consecutive even number is
9/40. Find the numbers
(Nos x, x+2 , 1/x = 1/(x+2) = 9/40, Nos. = 8, 10 )
10. 12x² + 4kx + 3 = 0 has only one solution find the value of K?
( a= 12, b= 4k, c=3 , b² -4ac = 0, K = +3, -3 )
11. In a two digit number the digit in the unit place is 1 more than
the twice of the digit in the tenth place. If theproduct of the
digis are 36, Find the number ( Ans. Hint Digit in the tenth place = x, Digit in
the unit place = 2x+1, No.= 10x+2x+1=12x+1, x(2x+1) = 36, x = 4, No 49 )
12. Sanu wrote a two digit number and he noticed that the product
of the digit is 14. When he added 45 to the number, the digits
are reversed. Find the original number (Ans. Hint Digit in the 10th place =x,
digit in the unit place = 14/x , Original No. 10x + 14/x, Reversed No. 140/x + x ,
10x + 14/x +45=140/x + x by multiplying by x , x² +5x-14 =0 , No. 27 )
13. If the total number of a diagonals of a polygon is 90, find the
number of sides of the polygon (Number of sides n , diagonal = n(n-3)/2 )
14. If x² + ax + b = 0 , has only one solution Prove that a² = 4b,
If x² + ax + 100 = 0 has only one solution find the value of a
If x² + 18x + b = 0 has only one solution find the value of b
(Ans. Hint. a = 1, b= a, c= b, b² - 4ac = 0 )
15. Can the sum of a number and its reciprocal be 3½, Why
(No. = x, Reciprocal 1/x, x +1/x = 7/2)
16. Find the discriminant of the following
a, x² + 4 = 0
b. x² + 4x = 0
c. x² - 4 = 0 (find Discriminant b² -4ac )
17. Raju solved a second degree equation as stated below can
you complete the problem by filling the blanks.
x² - 14x = 32
x² - 14x + ...... = 32 + ......
(x - ..... )² = .......
x - ..... = ,,,,,
x = ..... or .....
18. A bus travels a distance of 300km at a constant speed. If the
speed of the bus is increased by 5km/hr, the journey would
have taken 2 hours less. Find the original speed of the bus?
(Speed =x, Distance = 300, Time = 300/x , then s= x+5, S=300, T= 300/(x+5) ,
then 300/x- 300/(x+5) = 2 , by solvindg x = 25 )
19. The sum of the ages of a man and his son is 45, The product
of their ages before 5 years is 124. Find their present ages
(Present age of Man = x, Present age of son = 45-x, Age of man before 5 year = x-5,
Age of son before 5 year = 40-x, (x-5) (40-x) = 124, Age of man x= 36, Age of son = 9 )
20. Altitude of a right angled triangle is 7 cm more than its base
and the hypotenuse is 3 cm more than twice its base. Find
the sides of the triangle? (Base = x, Altitude = x+7, Hypotenuse = 2x+3,
Base² + Altitue² = Hypotenuse² , base = 5, Altitude =12 , Hypotenuse =13 )
TRIGONOMETRY
1. Sin A = 5/13 , Find CosA and Tan A ?
2. If Sin A = 0.6 Find the value of Cos A and Tan A ?
3. In Δ ABC ㄥC = 90 , BC = a, AC = b and AB = c , Show that
Sin² A + Cos² = 1, If SinA = 0.8 Find the value of Cos A?
4. In Δ ABC AB = 12 cm and AC = 10 cm and ㄥA = 60 ,
Find the area of the triangle ?
5. In Δ ABC AB = 8 cm and AC = 10 cm and ㄥA = 120 ,
Find the area of the triangle ?6. The area of a parallelogram is 30 sq.cm , one of its side is
5 cm and one of its angle is 60 degree
a. Find the height of the parallelogram ?
b. Find the length of the other side?
7. Two sides of a parallelogram are 12cm and 10 cm and angle
between them is 30 degree find the area of the parallelogram ?
8. The sides of an equilateral triangle are 6 cm long. Find the
radius of the circumcircle ?
9. The length of the chord of a circle is 10 cm long and the angle
between chord and a diameter is 30 degree find the radius of
the circle ?
10. One angle of a triangle is 110 degree and the side opposite to
it is 6 cm long . What is its circum radius ?
( Sin70 = 0.94, Cos70 = 0.34 and Tan 0 = 2.75 )
11. The sides of a parallelogram are 10 cm and 6 cm long and
angle between them is 30 degree Find the length of the
diagonals ?
12. A ladder leans against a wall and the ladder touched at the top
of the wall its foot is 2m away fromthe wall and it make 35
degree angle with the ground . Find the height of the wall and
length of the ladder? (Sin 35 = 0.57, Cos 35 =0.81, Tan35=0.7)
13. PA and PB are two tangents drawn from 8 cm away from the
centre of a circle and the angle between the tangents are 70
degree. Find the radius of the circle and length of the tangents ?
14. The anglebetween height and slant height of a cone is 60
degree and its slant height is 20 cm . Find the total surface
area volume of the cone ?
15. In ΔABC, AB = 8 cm , BC = 10 cm and ㄥB = 60 degree
Find AC
16. In ΔABC, AB = 12 cm and ㄥA = ㄥB = 30 degree
a. Find the perimeter of the triangle ?
b. Find the area of the triangle?
c. Find the ratio of the sides of the triangle?
17. In ΔABC, AB = 10 cm and ㄥA = 50, ㄥB = 65 degree
Find the area of the triangle ( Sin 50 = 0.77, Sin65 = 0.91)
18. A verticle tree is broken by the wind. The top of the tree
touches the ground and make an angle 30degree with it.
If the top of the tree touches the ground 30 maway from
its foot. Find the actual height of the tree ?
19. A 1.5 m tall boy sees the top a building at an elevition of
35 degree after walking 20 m towards the building he sees
the top of the building atan elevition of 55 degree
(Tan35 = 0. 7, Tan 55 = 1.4 )
a. Draw a rough figure
b. Find the height of the building
c. Find the distance between boy and building at present?
20. Standing 50 m away from a level road Anu sees her friend
Banu and Chippy at 48 degree and 57 degree angle of elevation
in the flat. If so what is the height difference in the position of
Banu and Chippy? (Tan 48 = 1.1, Tan 57 = 1.5 )
21. Two building in a plane ground are 30 m apart. From the top
of the smaller building one sees the base of the building at a
depression of 50 degree and its top at an elevation of 35degree.
( Tan 50 = 1.2 , tan 35 = 0. 7)
a. Draw a rough figure
b. Find the height of the smaller building
c. Find the height of the bigger building
22. Two verticle buildings are on a levelground, the smaller
one has height 20m, From the top of the larger building
a boy sees the top of thesmaller building at a depression
of 55 degree and bottom of the smaller building at a
depression of 70degree Find the height of the larger building?
23. A man 1.7 m tall, standing at the foot of a tower sees the top of a hill 40 m away at an elevation of 60 degree. On climbing
to the top of the tower he sees the top of the hill at an elevation
of 50 degree . Find the height of the hill and tower ?
( Sin 50 = 0.77, Cos 50 = 0.64, Tan50 = 1.19 )
24. A 1.6 m tall boy sees the top of a building under construction
at an elevation 30 degree. The building is completed 10 more
meters to its height, and t hen the boy sees the top of the
completed building at an elevation of 60 degree from the same
spot . Find the height of the building
25. A man 1.7 m tall looks down from the top of a light house
25m heigh and sees a boat at an angle of depression of 35
degree. How far is the boat from the foot of the light house ?
