CBSE/NCERT 10 Maths Guess Questions Chapter Arithmetic Progressions

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1) For what value of p, are 2p-1, 7 and 3p three consecutive terms of an A.P? (P=3)

2) Find the value of k, so that 3k + 7, 2k +5, 2k + 7 are in A.P  (k= -4)

3) Find the 15th term from the end of the A.P:   3, 5, 7,………, 201(173)

4) Find the 11th term from the end of the A.P:    10, 7, 4,……, - 62 (-32)

5) If Sn, the sum of first n terms of an A.P is given by Sn = 3n2 – 4n, then find its nth term

(6n – 7)

6) The sum of n terms of an A.P. is 3n2 + 5n. Find the A.P. Hence, find its 16th term

(6n + 2, 98)

7)  In the following A.P. find the missing term   -, 38, -, -  , - , -,22

8)  Find the sum of all natural numbers less than 100 which are divisible by 6                        (816)

9) Find the sum of 3 digit numbers which are not divisible by 7                  (424214)

10)  Find the sum of all three digit numbers which leave the remainder 3 when divided by 5      (99090)

11) Find the sum of first seven multiples of 5                                        (140)

12) Find the sum of all natural numbers up to 100, which are not divisible by 5           (4000)

13) In an A.P , if the 6th and 13th terms are 35 and 70 respectively, find the sum of its first 20 terms.

14) If the 3rd and 9thterm of an A.P. are 4 and -8 respectively, which term is zero (n = 5)

15) The sum of 4th and 8th terms of an A.P is 24 and sum of 6th and 10th term is 44. Find A.P.

16) The 4th term of an A.P is equal to 3 times the first term and the 7th term exceeds twice the 3rd term by 1. Find the A.P  (3 ,5 ,7, …)

17) Which term of the A.P.?  3, 15, 27, 39, will be 120 more than its 21st term   ( n = 31)

18) In an A.P., the first term is 25, nth term is -17 and sum to first n terms is 60.Find n and d the common difference.                                                              1

19) Which term of the sequence 114, 109, 104,is the first negative term?                (n =24)

20) If the 4th term of an A.P is twice the 8th term, prove that the 10th term is twice the 11th term

21) If 2 + 5 + 8 + …………………………+ x = 155, find x    (n = 10, x = a10=29)

22) For A.P. a1, a2, a3, ………., if a4/a7 = 2/3 , find a6/a8                          (4/5)

23) Find the sum of the following A.P:           1 + 3 + 5 + …….. + 199.        (10000)                   24) Find the common difference of an AP whose first term is 100 and sum of first six terms is 5 times the The sum of the next 6 terms                  (d= - 10)

25) Show that progression 7, 2, -3, -8, … ……..Is an A.P . Find its nth term      (12 – 5n)

26) The angles of a triangle are in A.P, the last being half the greatest. Find the angles.     (40˚, 60˚, 80˚)

27)  Find the sum of n terms of an A.P whose nth term is given by tn = 5 – 6n (2n – 3n2)

28) Find the middle term of A.P:     1, 8, 15,  ……………, 505        (253)

29) Find the number of terms of the A.P, 63, 60, 57,  ……….. So that their sum is 693 (n = 22, 21)

30) The sum of 3 numbers in A.P is 3 and their product is -35. Find the numbers

(7, 1, and -5)

31) How many terms of the sequence 18, 16, 14,  …………, should be taken so that their sum is 0                                                      (n= 19)

32) A sum of Rs 1400 is to be used to give 7 cash prizes to students of a school for their overall academic Performance if each prize is Rs40 less than the preceding price, find the value of each of the prizes.    (320, 280, 240, 200, 160, 120, 80)

33) Verify that a + b, (a + 1) + b, (a + 1) + (b + 1) ……….. Is an A.P. and then write its next term                              (a+2) + (b+1)

34) Determine the A.P whose 3rd term is 16 and 7th term exceeds the 5th term by 12                                                    (4, 6, 10, 16 ,…………)

35) If the nth term of the A.P. 9, 7, 5, ………… is the same as the nth term of the A.P. 15, 12, 9, ………., find n                       (n = 7 )

36) Find the sum of first 22 terms of an A.P. in which d = 7 and 22nd term is 149        (1661)

37) Find the sum of the following A.P:      3, 9/2, 6, 15/2,  ………. To 25 terms              (525)

38) The ratio of the sum to p terms and q terms of an A.P. is p2 : q2. Prove that the common difference of the A.P.is twice The first term

39) In an A.P., if the sum of its 4th and 10th terms is 40, and the sum of its 8th and 16th terms is 70, then find the sum of its  First 20 terms

40) Three consecutive positive integers are taken such that the sum of the square of the first and the product of the other two Is 154. Find the integers                        (3, 5, 7……….).

Download Guess Paper:

1. Quadratic Equations

2. Arithmetic Progressions

3. Height and Distance

4.Co-ordinate Geometry

5. Circles

IX Circle Geometry Important questions Test paper

1.       In the figure 9.5 If O is the centre of the circle and < AOC =100. Find < ABC. Give reason.

2.       In the figure 9.6 O is the centre of the circle. Find ∠BAC?

3.       Two concentric circles with centre O have A, B, C, and D as the points of intersection with the line l as shown in the figure 9.7. If AD=12 cm, BC = 8 cm, find the lengths of AB, CD, AC and BD.

4. In the given9.8, figure two circles intersect at A and B and AC and AD respectively diameters of the circle. Prove that the points C, B and D are collinear.
5. In the given figure 9.9, find the value of x

6.       In the given figure 9.10, AB is a diameter of the circle and CD II AB. If <DAC=25⁰. Calculate (i) <ACD, (ii) <CAD

7.       In the given figure 9.11, POQ is a diameter and PQRS is a cyclic quadrilateral. If <PSR=150. Find <RPQ.

8.       If two sides of a cyclic quadrilateral are parallel, prove that its remaining two sides are equal and the diagonals are equal

9       In the figure 9.13, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If <DBC=53 and<BAC=45. Find <BCD

10   Find the length of a chord which is at a distance of 8 cm from the centre of the circle of radius 17cm.

11. Equal chords of a circle subtend equal angles at the centre

12. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

13. Two chords of a circle intersect in the interior of the circle and make equal angles with the diameter passing through their point of intersection. prove that the chords are equal.

14. Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic

15.Prove The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Or,   Chords AB and CD intersect at P when produced. Chord BD is equal to radius .Prove <P = 60°.

X Surface area and Volume Excel exercise

9th circle test paper and Assignments

IX Circle Geometry Important questions Test paper

10th Ch-10 Tangent of Circle

10th Ch-6 Trigonometry 

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10th Chapter 3 Pair of Linear Equations in Two Variables

10th Chapter 4 Quadratic Equations

9th circle test paper and Assignments

CLASS IX                                            CIRCLE   GEOMETRY Test paper-1

1.       Define the following and mark them in a circle: (I) Centre of a circle (ii) Chord (iii) Secant (iv) Sector

(v) Major and minor segment

2.       Complete the following statements.

(I) Equal chords of a circle subtend....

(ii) If the angles subtended by the chords of a circle at the centre are equal, then....

(iii) The perpendicular from the centre of the circle to a chord. .. .

(iv) The  line drawn through the centre of a circle to bisect a chord is....

3.       Find the length of a chord which is at a distance of 5cm from the centre of the circle whose radius is 10cm.

4.       AB and CD are two parallel chords of a circle (lying on opposite sides of the centre) such that AB=10 cm, CD=24 cm. If the distance between AB and CD is 17cm, determine the radius of the circle.

5.       PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm. If PQ=16 cm and RS=12 cm, Find the distance between PQ and RS, if they lie (i) on the same side of the centre O, and (ii) on opposite sides of the centre O.

6.       Given an arc of a circle, show how to complete the circle.

7.       In the figure 9.1, if a diameter of a circle bisects each of the two chords of the circle, prove that the chords are parallel.

8.       In the figure 9.2, if two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.

9 In the figure 9.3, PQ and RQ are two chords equidistant from the centre. Prove that the diameter passing through Q bisects <PQR and <PSR.


10. In fig 9.4, AB and AC are two equal chords of a circle whose centre is O. If OD║AB and OE ║AC. prove that triangle ADE is an isosceles triangle.

 CBSE NCERT BOARD   IX-MATHEMATICS -Term -II- 2 
Test Papers,CBSE chapter-wise M C Q Multiple Choice Questions, Test Paper, Sample paper

1. Linear equations in two variables
2. Quadrilaterals
3. Area Of Parallelogram
4. Circles
5. Constructions
6. Surface Areas and Volumes
7. Statistics
8. Probability

X Surface area and Volume Sample paper

Q1.If the radii of the circular ends of a conical bucket, which is 16 cm high, are 20 cm and 8 cm, Find the capacity and the total surface area of the bucket. (10459.43cu.cm, 1961.14 sq. cm) 

Q2. Find the volume of right circular cylinder which has a height of 21cm and base radius 5cm.Find also the curved surface area. (1650 cu cm, 660 sq cm.) 

Q3. The base radii of two right circular cones of same height are in the ratio 3:5.Find the ratio of their volumes. (9:25) 

Q4. The circumference of the base of a 16m high solid cone is 3m.Find the volume of cone.(3.818 m3)

Q5 A circus tent is cylindrical upto a height of 3m and conical above it. If the diameter of the base is 105 m and the slant height of the conical part is 53 m. Find the total canvas used in making the tent. (9735 sq m.)


 Q6. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10cm and its base is of radius 3.5 cm. Find the total surface area of the article. (374 sq. cm)


Q7. A solid consists of a cylinder with a cone on one end and a hemisphere on the other end. If the length of the entire solid is 12.8cm and the diameter and height of the cylinder are 7cm and 6.5cm respectively. Find the total surface area of the solid. (269.28sq cm) 

Q8. A cylindrical container is filled with ice cream, whose radius is 6cm and height 15cm. The whole ice cream is distributed among 10 children in equal cones having hemispherical top .If the height of the conical portion is four times the radius of its base .Find the radius of the base of the cone. (3cm) 

Q9. A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2cm and the diameter of the base is 4cm.If a right circular cylinder circumscribes the solid, find how much more space it will cover. (π = π) (8 π cm3) 
Q 10. Water in a canal, 6m wide and 1.5m deep is flowing with a speed of 10km/hr.How much area will it irrigate in 30 minutes, if 8cm of standing water is needed. (56.25 hectares).



10TH MATHS BY JSUNIL": X Surface area and Volume Excel exercise: 1. Find the edge of a cube of volume equal to the volume of a cuboid of dimensions 63 cm × 56 cm × 21 cm. 2. Find the number of 5 cm cubes ...
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10th Maths SA-2 Chapter wise Test Papers Links
Quadratic Equations	Circles	Co-ordinate Geometry
Arithmetic Progressions	Area Related to Circles	Probability
Height and Distance	Surface Areas and Volumes	Sample papers

9th 10th CBSE Sample paper for maths and science 2012

GENERAL INSTRUCTIONS :
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections, namely
Section A : 10 questions (1 mark each)
Section B : 8 questions (2 marks each)
Section C : 10 questions (3 marks each)
Section D : 6 questions (4 marks each)
3. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks and 2 questions of four marks each.
4. Use of calculators is not allowed.
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CBSE VIII Maths Time and work

1. A can do piece of work in 30 days while B alone can do it in 40 days. In how many days can A and B working together do it? Ans 17 1/7
2. A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same working in ans 84 days
3. A can do a piece of work in 7days of 9 horse each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 2/5 hours a day ? ans 3 days
4. A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and them leaves. A alone can finish the remaining in ans : 7 1/ 2 days
5. A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 days in how many days both A and B together can do the wrok ans 9 3/8
6. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finished the remaining work in 42 days. The two together could complete the work in : ans 30 days
7. A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days A alone can finish the work in ans : 60 days
8. A and B can do a piece of work in 45 days and 40 days respectively. They began to go the work together but A leaves after some days and than B completed the reaminnig work in 23 days. The number o days after which A left the work was ans: 9
9. A does half as much work as B in three fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?ans 30 days
10. A can do a certain job in 12 days. B is 60% more efficient than A . The number of days, it takes B to do the same piece of work is ans 7 ½
11. A can do a certain job in 25 days which B alone can do in 20 days. A stared the work and was joined by B after 10 days. The number days taken in completing the work was ans 16 2/3
12. A is twice as good a work man as B and together they finish a piece of work in 14 days The number of days taken by A alone to finish the work. Ans: 21 days
13. A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes.B alone can do the while work work in : ans 15 days
14. A can do a piece work in 14 days which B can do in 21 days. They being together but 3 days the completion of the work. A leaves of the total number of days to complete the work is ans 10 1/5
15. If Ramesh, suresh and harish can do a piece of work in 15 days, 10 days and 6 days resp. How long will they take to do it, if all the three work it together. ? ans 3 days
16. A and B can do a piece of working 72 days : B and C and do it in 120 days ; A and C can do it in 90 days. In what time can A alone do it ? ans 120 days
17. A and B and C together can finish a piece of work in 4 days: alone can do it in 12 days and B in 18 days, then C alone can do it in : ans 9 days
18. If A and B C together can finish a piece of work in 4 days”: 
19. A and B can do a piece of work in 18 days: B and C can do it in 24 days : A and C can do it in 36 days. In
20. If A and B C together can finish a piece of work in 18 days” B and C can do it in 24 days: A and C do it in 36 days after A has been working it for 5 days for days C finished in 13 days. In how many days C alone will do the work ans : 24
21. A is twice as good as workman as B and together they complete a work in 15 days . in how many days can the work be complete by B alone ans 45
22. 45 men can complete a wok in 16 days. Six days after they started working 30 more men joined them. How many days will they now take to complete the remaining work? Ans 6
23. 12 men can complete a work in 18 days six days after they started working men joined them. How many days will all of them together complete the remaining work? Ans 9
24. Twelve men can complete a work in 8 days. Three days after started the work 3 more men joined. In how many days will all of them together complete the remaining work ans 4
25. A,B and C are employed to do a piece of work for Rs.529. A and C are supposed to finish 19/23 of the work together. How much shall be paid to B? Ans 9

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IX Maths Surface Areas and Volumes Concepts Chapter 13

A cuboid is a solid bounded by six faces that arerectangular in shape.
A cuboid whose length, breadth and height are equal is called a cube.
Any two faces other than the opposite faces are called adjacent faces.
Any two adjacent faces meet in a line segment, which is called an edge of the cuboid.
The point of concurrency of any three edges of a cuboid is called a vertex of thecuboid.
A cuboid has 8 vertices and 12 edges. Any faceof a cuboid may be called the base of the cuboid.
In that case, the four adjacent faces of the base are called thelateral faces of the cuboid.

The lateral surface area of the cuboid = 2 (l + b) h.
It is equal to sum of areas of all its lateral faces.
Lateral surface area of the cube=4a2
Total surface area of the cuboid=2(lb+bh+lh)
Total surface area of the cube=6a2
Volume of a solid object is the measure of the space occupied by it
The volume of substance that can be stored by the object is called its capacity.
Volume of Cuboid = length x breadth x height=lbh
Volume of a Cube =(edge)3=(a)3
L.S.A of a cuboid =2 (l + b) h
T.S.A of a cuboid =2(lb+bh+lh)
Volume of the cuboid =lbh
T.S.A of a cube =6a2
Total surface area of a cube=sum areas of all the faces of a cube
volume of the cube=a3

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. 

The flat surfaces are made up of two congruent circles that are parallel to each other. 

These flat surfaces are called thebases of the cylinder. 

The radius of the circular bases is the radius of the cylinder. 

The perpendicular line that passes through the centers of the two circular bases is the height of the cylinder or axis of the cylinder. 

A cylinder is said to be right circular cylinder if axis is perpendicular to the radius of the cylinder.
The curved surface joining the two basses of a right circular cylinder is called its lateral surface area.
For a right circular cylinder of radius r and height h

Lateral surface area of the Cylinder =  2prh

Base surface area of the Cylinder =pr² 
Total surface area of the Cylinder =2prh+pr² +pr²=pr(r+h)
Volume of the Cylinder = pr²h
Cone is solid figure with a circular base that tapers to a point or vertex.
 A Cone is said to be a right circular cone if its height is perpendicular to the radius of the base.
Let "r" be the base radius, "h" be the height, "l" be the slant height of a right circular cone.
Then l = √(r² + h² )
Base area of the cone = p r² 
Curved surface area of the cone =  p r l
Total surface area of the cone= p r l  + = p r²   =pr (l+r)
Volume of Cone = 1/3 p r² h

A sphere is a three dimensional figure, made up of points that are equidistant from a given point.
It does not have an edge or a vertex.
The surface of a sphere is uniform and smooth.
The centre of a sphere is a point, which is equidistant from all the points on a sphere.
The distance between the centre and any point on the surface of the sphere is called the radius of a sphere.
Generally the radius is denoted by the letter r.
A line segment through the centre of the sphere, and with the end points on the sphere is called a diameter of the sphere.

IX Maths Surface Areas and Volumes Important Concepts

1. Every cube is a cuboid but every cuboid is not a cube.
2. In a cube, the lengths of all edges are the same. 

3. Area of the four walls of the hall is the lateral surface area of cube or cuboid4. The outer surface of a cuboid is made up of six rectangles or six rectangular regions, called the faces of the cuboid
5. In case of a room, lateral surface area means the area of the four walls of the room, whereas total surface area means the area of
four walls plus the area of the floor and the ceiling.
6. Face diagonal of a cube or cuboid will always be shorter than the body diagonal.
7. The total surface area of any object will be greater than its lateral surface area.
8. The unit of measurement of both volume and capacity is cubic unit such as cubic feet, cubic cm. cubic m etc.
9. When an object of certain volume is recast into a cylinder, the volume of the cylinder formed will always be equal to the volume of the original object.

10. The solids having the same curved surface do not necessarily occupy the same volume.

11. When an object is dropped into a liquid, the volume of the displaced liquid is equal to the volume of the object that is dipped.
12. Volume of a Cone is one third of the volume of a cylinder of same height and radius of base

13. Volume of a hemisphere be exactly half of the corresponding sphere.
14. All the solids having a given volume, the sphere is the one with the smallest surface area; of all solids having a given surface area, the sphere is the one having the greatest volume

10TH MATHS BY JSUNILSample Paper X Mathematics CBSE SA 2 2012

MATH ADDA "10TH MATHS BY JSUNIL": Sample Paper X Mathematics CBSE SA 2 2012: SAMPLE PAPER X SUBJECT MATHEMATICS CBSE SA – 2 March 2012 SECTION-A 1. The circumference of two circles are in the ratio 2: 3 then the r...
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