10th Surface area and volume practice paper for CBSE Exam 2013

1. A solid iron rectangular block of dimensions 4.4 m, 2.6m, and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness 5cm. Find the length of the pipe. (Use Π = 22/7)   (Ans = 112m)

2. A well with inside diameter 7m, has been dug 22.5m deep and the earth dug our is used to form an embankment around it. If the height of the embankment is 1.5m, find the width of the embankment.  (Ans = 10.5m)

3. Water is flowing at the rate of 7m/ sec through a circular pipe whose internal diameter is 2cm, into a cylindrical tank of radius 40cm. Find the increase in water level in ½ hour.     (Ans = 7.875m)

4. Water is flowing at 5km/hr through a pipe of diameter 14cm into a rectangular tank which is 50m long and 44m wide. Find the time in which the water level in the tank rises by 7cm.   (Ans = 2 hours)

5. Water flows @ 10 m/ min through a cylindrical pipe having its diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth 24cm?    (Ans = 51min 12sec)

6. The radii of the internal and external surfaces of a metallic spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid right circular cylinder of height 32/3 cm. Find the diameter of the base of the cylinder.                                                (Ans = 7cm)

7. The radius of a solid iron sphere is 8cm. 8 rings of iron plate of external radius 20/3 cm and

the thickness 3cm are made by melting this sphere. Find the internal diameter of each ring.   (Ans = 8cm)

8. A tent of height 77dm is in the form of a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs 3.50/m2  (Ans = Rs. 5365.80)

9. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of hemisphere is 4.2cm and the total height of the toy is 10.2cm, find the volume of the wooden toy. (Ans = 266.11cm3)

10. A cylindrical container of radius 6cm & height 15cm is filled with ice-cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the cone.       (Ans = 3cm)

11. A solid is composed of a cylinder with hemispherical ends. If whole length of the solid is  98cm and diameter of cylinder is 8cm, find the total surface area & volume of the given solid .         

(Ans = 8624cm2 , 54618.67cm3)

12. A right triangle whose sides are 15cm and 20cm, is made to revolve about its hypotenuse. Find the volume and total surface area of the double cone so formed. (Use   Π = 3.14).  

(Ans 3768cm3, 318.8cm2)

13. A cylindrical road roller made of iron is 1m long. Its internal diameter is 54cm and the thickness of iron sheet used in making the roller is 9cm. find the mass of the roller, if 1cm3 of iron has 8gm mass.         (Ans = 1425.6kg) 

14. The difference between outside and inside surface areas of a metallic cylindrical pipe 14cm long is 44cm2  if the pipe is made of 99cm3 of metal, find the outer and inner radii of the pipe.   (Ans = 2.5cm, 2cm)

15. A bucket is in the form of a frustum of a cone and holds 28.49 litres of water. The radii of the top and bottom are 28cm, 21cm respectively. Find the height of the bucket.     (Ans = 15cm)

16. The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its

volume.                    (Ans = 1554cm3)

17. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base.If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?  (Ans = 20cm)

18. A tent is made in form of a conic frustum surmounted by a cone. The diameters of base and top of frustum are 20m & 6m respectively and height is 24m. If height of the tent is 28m, find the area of the canvas cloth required. (Ans = 340Πm2)

19. A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the cone’s altitude is divided by the plane (Ans = 1:2)

20.A cylinder and a cone have equal bases and equal heights. If their curved surfaces are in the ratio 8:5, determine the ratio of the radius of the base to the height of either of them  (Ans = 3:4)

21.Lead spheres of diameter 6cm are dropped into a cylindrical beaker containing some water and are completely submerged. If the diameter is 18cm and the water rises by 40cm, find the number of lead spheres dropped in the  water (Ans = 90) 

22. A circus tent is cylindrical to a height of 3m and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas cloth 5m wide required to make the tent.(Ans = 1947m)

23.  A cone, a hemi-sphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes as well the ratio of their total surface areas  (Ans = 1:2:3, (√2 + 1):3:4)

24.  A cone of radius 10cm is divided into two parts by drawing a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts of the cone (Ans = 1:7)

25. A building is in the shape of a cylinder surmounted by a hemi-spherical vaulted dome. The internal diameter of the building is equal to the total height of the building. If the volume of air space inside the building is 880/21 m3, find the height of the crown of the vault above the floor.             (Ans = 4m)

26. An inverted cone of vertical height 12cm and radius of the base 9cm has water to a depth of 4cm. Find the area of the internal surface of the cone not in contact with water.    (Ans = 376.8cm2)

27. The mass of a spherical iron shot-put 12cm in diameter is 5kg. Find the mass of a hollow cylindrical pipe 12cm long (made of the same metal), if it’s internal and external diameters are 20cm and 22cm, respectively.                                                                (Ans = 4.375kg)

X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank

X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank for CBSE EXAMS

( 1 Mark Questions ) 

1. If radii of the two concentric circles are 15cm and 17cm , then find the length of each chord of one circle which is tangent to one other. Ans. 16cm

2. If two tangents making an angle of 120⁰  with each other , are drawn to a circle of radius 6cm, then find the angle between the two radii, which are drawn to the tangents.           Ans. 600

3. PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that 

< QPT = 60 then find <PRQ.                                 Ans. 1200 

4. If a tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q such that OQ = 12 cm then find the length of PQ.                           Ans. √119cm 

5. From a point P, two tangents PA and PB are drawn to a circle C(O,r) . If OP =2r ,then what is the type of APB.                                                   Ans. Equilateral triangle

6. If the angle between two radii of a circle is 130,then find the angle between the tangents at the end of the radii. Ans. 500. 

7. ABCD is a quadrilateral. A circle centred at O is inscribed in the quadrilateral. If AB = 7cm , BC = 4cm , CD = 5cm then find DA.   '                        Ans. 8 cm

8. In a triangle  ABC , AB = 8cm , <ABC = 90. Then find the radius of the circle inscribed in the triangle.            Ans. 2cm

( 2 Mark Questions ) 

9. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that OAPB is a cyclic quadrilateral. 

10. If PA and PB are two tangents drawn to a circle with centre O , from an external point P such that PA=5cm and < APB = 60, then find the length of the chord AB. Ans. 5cm

11.   CP and CQ are tangents from an external point C to a circle with centre O .AB is another tangent which touches the circle at R and intersects PC and QC at A and B respectively . If CP = 11cm and BR = 4cm, then find the length of BC.              Ans. 7cm

12. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

13. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

( Three Marks Questions) 

14. If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB+CD=AD+BC.

15. Prove that the angle between the two tangents to a circle drawn from an external point, is supplementary to the angle subtended by the line segment joining the points of contact to the centre.

16. AB is a chord of length 9.6cm of a circle with centre O and radius 6cm. If the tangents at A and B intersect at point P then find the length PA. Ans. 8cm

17. The incircle of a ∆ABC touches the sides BC, CA &AB at D,E and F respectively. If AB=AC, prove that BD=CD.

18. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle

19. PQ and PR are two tangents drawn to a circle with centre O from an external point P. Prove that < QPR = 2< OQR.

( Four Marks Questions) 

20. Prove that the length of tangents drawn from an external point to a circle is equal. Hence, find BC, if a circle is inscribed in a ABC touching AB,BC &CA at P,Q &R respectively, having AB=10cm, AR=7cm &RC=5cm. Ans. 8cm

21. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following: If O is the centre of two concentric circles, AB is a chord of the larger circle touching the smaller circle at C, then prove that AC=BC.

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X Chapter : Circle Questions Bank for CBSE EXAMS
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10th Chapter : Tangent of Circle Solved CBSE Test Paper
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Guess paper 10th Chapter_Arithmetic Progression

10th Math : Arithmetic Progression : Guess paper part-II

1.        Find the sum of 20 terms of the A.P. 1,4,7,10………

2.        If the nth terms of an A.P is (2n + 1), find the sum of first n terms of the A.P.

3.        Find the sum of first 30 terms of an A.P.whose second term is 2 and seventh term is 22.

4.        Find the sum of first 10 terms of an A.P., in which 3^rd term is 7 and 7^th term is two more than thrice of its 3^rd term.

5.        Find the sum of all even integers between 2 to 100 divisible by 2.

6.        Find the number of terms in the series 20, 19 1/3 + 18 2/3 +………of which the sum is 300,explain the double answer.

7.        If the mth term of an A.P. is 1/n and the nth terms is 1/m, show that the sum of mn terms is ½(nm + 1).

8.        If the sum of n terms of an A.P.is same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

9.        Find the sum of first n odd natural numbers.

10.     If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms find the sum of first 20 terms.

11.     How many terms of A.P.: 24,21,18,…….. Must be taken so that their sum is 78?

12.     The angles of a triangle are in AP.If the greatest angle equals the sum of the other two, find the angles.

13.     Find the sum of two digits numbers, which are divisible by 7?

14.     Find the sum of number b/t 49 to 500 which are divisible by 7?

15.     If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n) and find the sum of first (p+q)^th term .

16.      How many terms of the sequence 18,16,14…… should be taken so that their sum is zero.

17.     Write the first 5 terms of an AP whose nth term is given by (2n+1)/3.

18.     How many terms in the sequence -6  , -11/2 , -5 , -9/2 , …are needed to give the sum 0 ?

19.     Find the sum of all the natural numbers less than 100 which are divisible by 6.

20.     The sum of n terms of an A.P.; be 3n2 – n and its common difference is 6,find its first and 27^th term.

21.     The sum of nth terms of an A.P. is 3n²+ 5n, then find its nth term.

22.     Find the sum of first 21 terms Ö2 + Ö8 + Ö18 + Ö32………….

ARITHMETIC PROGRESSIONS MATHEMATICS CASS X- Guess paper part-II

                                                                                                 

1. How many two-digit numbers are divisible by 3?
2. Which term of A.P :3,8,13,18,…………………,is  78?
3. Check whether –150 is a term of the A.P 11,8,5,2………
4. If 3^rd and 9^th terms of an A.P are 4 and – 8 respectively, which term is 106.find the 29^th term?
5. The 8^th term of an AP is zero. Find the ratio of its 38^th term and 18th term.
6. Which term of A.P is 3,15,27,39……. will be 132 more then its 54^th terms?
7. Find the 20^th terms from the last terms of the A.P: 3,8,13,…………..253.
8. Determine the 15^th and 5^th term from the end of the A.P.: 4,9,14,…….,254.
9. Which term of A.P. :9,13,17,21,25……………………is 109.
10. If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms.
11. If 10^th term of an A.P is 52 and 17^th terms is 20 more than the 13^th terms find the A.P.
12. Determine the general terms of A.P. whose 7^th terms is – 1 and 16^th term 17.also find it’s 25^th term.
13. How many numbers of two digits are divisible by 7 ?
14. Find the number of integers b/t 49 to 500 which are divisible by 7?
15. If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n ) and (p+q)^th term is zero.
16. If m times the m^th term of an A.P. is equal to n times the n^th term, show that the (m+n)^th terms of an A.P is zero.
17. The 4^th term of an A.P. is three times the first and 7^th term exceeds twice the third term by 1.find the A.P.
18. The sum of three numbers in A.P. is – 3 ,and their product is 8. Find the numbers.
19. If 2x,x + 10, 3x + 2 are in A.P., Find the value of x.
20. For what value of n ,the n^th terms of the arithmetic progressions 63,65,67……..and 3,10,17,…………are equal?

IX-Science-Sample-Paper-Term-2 CBSE Board

SCIENCE X : Sample Papers New (March 2014) - JS- Series

9th Solved Science SA-2 Sample paper-1
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9th Solved Science SA-2 Sample paper-2
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9th Solved Science SA-2 Sample paper-3
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9th Science SA-2 Sample paper [90 marks]-5
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X Statics mean median mode and Ogive MCQ

X Statics mean median mode and Ogive

MULTIPLE CHOICE QUESTIONS

1. If 35 is the upper limit of the class-interval of class-size 10, then the lower limit of the class-interval is :

(a) 20                                                               (b) 25

(c) 30                                                               (d) none of these

2. In the assumed mean method, if A is the assumed mean, than deviation di is :

(a) xi + A                                                        (b) xi – A

(c) A – xi                                                        (d) none of these]

3. Mode is:

(a) Middle most value (b) least frequent value (c) most frequent value (d) none of these

4. While computing mean of grouped data, we assume that the frequencies are :

(a) evenly distributed over all the classes       (b) centred at the class-marks of the classes

(c) centred at the upper limits of the classes   (d) centred at the lower limits of the classes

5. The curve drawn by taking upper limits along x-axis and cumulative frequency along y-axis is :

(a) frequency polygon                                      (b) more than ogive

(c) less than ogive                                           (d) none of these

6. For ‘more than ogive’ the x-axis represents :

(a) upper limits of class-intervals                    (b) mid-values of class-intervals

(c) lower limits of class-intervals                    (d) frequency

7. Ogive is the graph of :

(a) lower limits and frequency                        (b) upper limits and frequency

(c)lower/upper limits and cumulative frequency (d) none of these

8. The curve ‘less than ogive’ is always :

(a)ascending                                                    (b) descending

(c) sometimes ascending and sometimes descending (d) none of these

9. If mode = 80 and mean = 110, then the median is

(a)110                                                              (b)120

(c)100                                                              (d)90

10. The mean of the following data is : 45, 35, 20, 30, 15, 25, 40 :

(a) 15                                                               (b) 25

(c) 35                                                               (d) 30

11 . The mean and median of a data are 14 and 15 respectively. The value of mode is  (a) 16                                                                           (b) 17

(c) 13                                                               (d) 18

12 . For a given data with 50 observations the ‘less than ogive’ and the ‘more then ogive’ intersect at (15.5, 20). The median of the data is :

(a) 4.5                                                              (b) 20

(c) 50                                                               (d) 15.5

13. Which of the following is not a measure of central tendency ?

(a) Mean                                                          (b) Median

(c) Range                                                         (d) Mode

14. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its :

(a)mean                                                           (b) median

(c) mode                                                         (d) all the three above

15. The measures of central tendency which can’t be found graphically is

(a) mean                                                          (b) median

(c) mode                                                          (d) none of these

IX Maths Comprehensive Test Series Geometry Triangle SA-1

Ch: Triangle CBSE Exam Questions
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Comprehensive Test Series Geometry SA-1
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Download X SAMPLE PAPERS Maths SA 1 (with Solution) 2012-2014

CLASS X  SAMPLE PAPERS  SCIENCE  SA 1 (with Solution) 2012-2014
1. X SCIENCE SAMPLE PAER- 1	2. X SCIENCE SAMPLE PAER-2
3. X SCIENCE SAMPLE PAER-3	4. X SCIENCE SAMPLE PAER- 4
5. X SCIENCESAMPLE PAER- 5	Source: kv1madurailibrary
CLASS X SAMPLE PAPERS Maths SA 1 (with Solution) 2012-2014
1. X MATHSSAMPLE PAER- 1	2. X MATHS SAMPLE PAER-2
3. X MATHS SAMPLE PAER 3	4. X Maths SAMPLE PAER- 4
5. X MATHS SAMPLE PAER-5	Source: kv1madurailibrary

NCERT Solutions for Class 10th Maths by schools.aglasem

Chapter 1 – Real Numbers

Chapter 2 – Polynomials

Chapter 3 – Pair of Linear Equations in Two Variables

Chapter 4 – Quadratic Equations

Chapter 5 – Arithematic Progressions

Chapter 6 – Triangles

Chapter 7 – Coordinate Geometry

Chapter 8 – Introduction to Trigonometry

Chapter 9 – Some Applications of Trigonometry

Chapter 10 – Circles

Chapter 11 – Constructions

Chapter 12 – Areas related to Circles

Chapter 13 – Surface Areas and Volumes

Chapter 14 – Statistics

Chapter 15 – Probability