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CBSE SCIENCE CLASS X Assignments
CBSE Class X Science term - I
| 10th_chem_reac_and_equation_solvd_quess |
| 10th_chemical_reactions_and_equ_imp_qus. |
| X chemical_reactions - equations_solved_questions |
| 10th_acid_base_and_salt_notes |
| 10th_acid_base_and_salt_ solved questions |
| 10th_acid_base_and_salt_test_apaper-1.pdf |
| 10th_acid_base_and_salt_test_apaper-2.pdf |
| 10th_acid_base_and_salt_test_apaper-3.pdf |
| 10th_acid_base_and_salt_test_apaper-4.pdf |
| 10th_acid_base_and_salt_test_apaper-5.pdf |
| 10th_acid_base_and_salt_test_apaper-6.pdf |
| 10th_acid_and_base_cbse_guess_questions.pdf |
| 10th_acids_bases_and_salts_impq_1.pdf |
| Metals_and_non-metals_test_paper_solved-1. |
| 10th_metals_and_non_metals_impq_1.pdf |
ntse sample paper
NCERT Solutions For Class 10 Science
Chemical Reactions and Equations Download
Acids, Bases and Salts
Download
Metals and Non-metals
Download
Magnetic Effects of Electric Current
Download
Carbon and its Compounds
Download
Periodic Classification of Elements
Download
Light - Reflection and Refraction
Download
Human Eye and Colorful World
Download
How do Organisms Reproduce Download
Our Environment Download
Management of Natural Resources
Download
Heredity and Evolution
Download
CBSE CLASS 9TH: Heron Formula Proof
Drop an altitude (of length h) to the side of length c.
Then A = (1/2)c h,
So,
A2 = c2 h2 / 4.
Use the Pythagorean Theorem to obtain the following system:
(1) x2 + h2 = a2
(2) y2 + h2 = b2
(3) x + y = c
Substitute y = c - x into (2) and simplify.Then subtract
the result from (1).
You will find that
2cx = a2 - b2 + c2.
From (1),
4c2 h2 = 4a2 c2 - 4c2 x2
= (2ac + 2cx) (2ac - 2cx)
= (2ac + a2 - b2 + c2)(2ac - a2 + b2 -c2)
From (1),
4c2 h2 = 4a2 c2 - 4c2 x2
= (2ac + 2cx) (2ac - 2cx)
= (2ac + a2 - b2 + c2)(2ac - a2 + b2 -c2)
= ((a+c)2 - b2) (b2 - (a-c)2)
= (a+c+b)(a+c-b)(b+a-c)(b-a+c)
= (2s)(2s-2b)(2s-2c)(2s-2a)
= 16s(s-a)(s-b)(s-c)
Then A = (1/2)c h,
So,
A2 = c2 h2 / 4.
Use the Pythagorean Theorem to obtain the following system:
(1) x2 + h2 = a2
(2) y2 + h2 = b2
(3) x + y = c
Substitute y = c - x into (2) and simplify.Then subtract
the result from (1).
You will find that
2cx = a2 - b2 + c2.
From (1),
4c2 h2 = 4a2 c2 - 4c2 x2
= (2ac + 2cx) (2ac - 2cx)
= (2ac + a2 - b2 + c2)(2ac - a2 + b2 -c2)
From (1),
4c2 h2 = 4a2 c2 - 4c2 x2
= (2ac + 2cx) (2ac - 2cx)
= (2ac + a2 - b2 + c2)(2ac - a2 + b2 -c2)
= ((a+c)2 - b2) (b2 - (a-c)2)
= (a+c+b)(a+c-b)(b+a-c)(b-a+c)
= (2s)(2s-2b)(2s-2c)(2s-2a)
= 16s(s-a)(s-b)(s-c)
bcece result 2012
Bihar Combined Entrance Competitive Examination Board. Download BCECE-
Latest Entrance Exam Notifications
welcome to updates page. here you find latest entrance exams notifications about every type of exam so that you can stay updated to the latest notifications and that exponentially increases your chances of getting through.
Top Engineering Colleges in india
- Indian Institute of Technology IIT Kanpur
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Sarkari Naukri Latest Government Jobs in India 2012
Welcome to Sarkari Naukri 2012 Section. Sarkari Naukri ( Government Jobs ) are very popular these days due to the security and satisfaction they offer. Recently, Banks, Armed forces and other Public Sector Units (PSUs) in India have been hiring talented and qualified professionals and freshers at a very good rate due to many people retiring and firms opening new branches to serve wide range of People. .. so stay Updated!
Latest Category-Wise Sarkari Naukri In India 2012
 | UPSC Exams (Exams conducted by Union Public Service Commision). |
| | Latest Bank Jobs in India 2012 |
| | Latest Railway Jobs in India 2012 |
| | Latest Government Jobs 2012 for Engineers' in India |
| | Latest Government Teaching Jobs in India 2012 |
| | Latest Armed Forces (Defense) Jobs in India 2012 |
| | Latest State Police Jobs in India 2012 |
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| | Latest State PSC/SSC Jobs News 2012 |
Interview Call - Bank of Maharashtra Shortlists 2205 for 543 Clerks Posts
Bank of Maharashtra has Shortlisted Candidates and announced Interview schedule for its 543 Clerical Posts advertisement issued recently in Apr - May 2012.
As per the notice, Bank of Maharashtra will conduct Interviews for shortlisted candidates from July 9 - 12, 2012. The list of shortlisted candidates with name, Interview date and venue has been released and can be seen here.
Call letters for Interviews can also be downloaded from here. If required, Reprint Online Application form to be carried in the Interview.
Note that Bank of Maharashtra has not released Cut-off marks set by it to filter the candidates. we expect any similar announcement in the coming days.
About Interviews :-
As per the notice, Interview will be of 50 marks total and Min 40% in General Category and 35% for other categories will be required to pass it and to be considered for final selection (To be decided on the basis of overall performance in IBPS CWE + Interviews ).
Helpful Tips for getting Success in Bank Interviews.
We at Linkingsky.com wish All The Best to all those looking forward to this Interview process.
As per the notice, Bank of Maharashtra will conduct Interviews for shortlisted candidates from July 9 - 12, 2012. The list of shortlisted candidates with name, Interview date and venue has been released and can be seen here.
Call letters for Interviews can also be downloaded from here. If required, Reprint Online Application form to be carried in the Interview.
Note that Bank of Maharashtra has not released Cut-off marks set by it to filter the candidates. we expect any similar announcement in the coming days.
About Interviews :-
As per the notice, Interview will be of 50 marks total and Min 40% in General Category and 35% for other categories will be required to pass it and to be considered for final selection (To be decided on the basis of overall performance in IBPS CWE + Interviews ).
Helpful Tips for getting Success in Bank Interviews.
We at Linkingsky.com wish All The Best to all those looking forward to this Interview process.
Update June 8,2012:_Other Posts in "Bank of Maharashtra 543 Clerks Recruitment 2012 "
Bank of Maharashtra 543 Clerks Recruitment 2012 (Advertisement)
Second List Issued- United Bank of India 450 PO Recruitment Final Results
United Bank of India has become the first bank to issue a second list of selected candidates after appointing several candidates in the first phase.
United bank announced finally selected candidates for recruitment of 450 PO posts for which applications were Invited from IBPS PO CWE Qualified Candidates in Feb-Mar 2012.
About 450 finally selected candidates were asked to join the bank on June 20. But now the issuing of this second list of 358 candidates states that many of them wouldn't have joined the bank owing to multiple selections of a single candidate in many banks.
The trend is not new, some candidates reported that earlier, banks like Corporation Bank, Indian Bank, Union Bank of India also recalled some candidates from waiting list for Interviews without any formal announcement.
The obvious reason could be multiple selections of a single candidate in various banks. In the recent meeting between IBPS and Banks, several measures were decided upon to counter this from happening again during the course of next CWEs.
However, for now this announcement may bring some respite to many candidates asking if there are any chances of issuance of second select lists by banks for PO/Clerks Posts.
The newly selected candidates are expected to join the bank in Third Week of July and they will soon receive formal letter of appointment from the bank about the same.
We at Linkingsky.com congratulate all the newly selected United Bank of India Probationary Officers.
United bank announced finally selected candidates for recruitment of 450 PO posts for which applications were Invited from IBPS PO CWE Qualified Candidates in Feb-Mar 2012.
About 450 finally selected candidates were asked to join the bank on June 20. But now the issuing of this second list of 358 candidates states that many of them wouldn't have joined the bank owing to multiple selections of a single candidate in many banks.
The trend is not new, some candidates reported that earlier, banks like Corporation Bank, Indian Bank, Union Bank of India also recalled some candidates from waiting list for Interviews without any formal announcement.
The obvious reason could be multiple selections of a single candidate in various banks. In the recent meeting between IBPS and Banks, several measures were decided upon to counter this from happening again during the course of next CWEs.
However, for now this announcement may bring some respite to many candidates asking if there are any chances of issuance of second select lists by banks for PO/Clerks Posts.
The newly selected candidates are expected to join the bank in Third Week of July and they will soon receive formal letter of appointment from the bank about the same.
We at Linkingsky.com congratulate all the newly selected United Bank of India Probationary Officers.
Other Posts in "United Bank of India 450 PO Recruitment 2012 "
Indian Bank 1201 Clerks Recruitment 2012
Indian Bank is among the major nationalized public sector banks in India headquartered in Chennai. Indian Bank was Founded in 1907 and now has over 1950 CBS Enabled branches and a huge workforce of over 22000 employees.
Indian Bank has invited applications for 1200 Clerks posts from IBPS Common Clerical CWE passed candidates.
Apply Online for IOB Clerical Recruitment 2012.
You may also see helpful tips for bank Interviews.
Indian Bank has invited applications for 1200 Clerks posts from IBPS Common Clerical CWE passed candidates.
Vacancies and Payscale
1200 Clerical Vacancies across various States (Pay Scale - 7200 - 19300 / Month)Important Dates
Payment of fees and Online Registration : Till July 13, 2012.Eligibility Criteria
OR,
Pass in Diploma in Banking.- State-wise Vacancies and required TWS Score-
Selection Procedure
- Final selection list will then be issued later on the basis of overall performance in IBPS CWE and Interview.
- The probation period is Min 6 Months.
Application Procedure
- Interview schedule and shortlisted candidates will be announced later.
Apply Online for IOB Clerical Recruitment 2012.
You may also see helpful tips for bank Interviews.
Bihar Secondary, Higher Secondary Teacher Eligibility Test
Age: For Secondary School Teacher (21 to 37 years) and for Higher Secondary School Teacher (24 to 37 years). There is relaxation in upper age limit in case of OBC/ BC/ SC/ ST/ BC Female candidates of the state of Bihar.
Eligibility Requirements:
1. Secondary School Teacher
Candidates must be Graduate with minimum 50 percent marks and BEd. However, those candidates who are domiciled citizen of Bihar are eligible to apply on the basis of graduation degree (50 percent marks) . Such candidates of Bihar, who are applying on the basis of graduation degree would be required to complete one year course of BEd. in 1 year.
2. Physical Education Teacher (B PEd.)
Candidates must be graduate and Bachelor of Physical Education or equivalent.
3. Oriental Teacher
Candidates must be graduate of equivalent in Sanskrit / Farsi / Arabi with minimum 50 percent marks.
4. Music Teacher and Arts Teacher
Degree in Music or Arts from a recognized university or institute. One year BEd.
Higher Secondary School Teacher Candidates must be Post Graduate and BEd.
Candidates can apply for Secondary School Teacher TET in only one subject category:
1. Mathematics- Candidates must have studied Mathematics and at least two subjects out of the following:
Physics/ Chemistry/ Electronics/ Computer science/ Statistics.
2. Science: Candidates must have studied chemistry and Biology (Botany + Zoology) in graduation
3. Social Science: Candidates must have studied two subjects out of the following at graduation level:
History/ Geography / Political Science / Economics
Eligibility Codes:
Secondary Teacher- Graduate -1 , Graduate with B Ed -2
Higher Secondary Teacher- Post Graduate-1 , Post Graduate with B Ed- 2
Examination Fees: Rs. 150 and in case of SC/ ST (Rs 75)
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SAMPLE PAPER/MODEL TEST PAPER SUBJECT – MATH
CBSE 10th BOARD SA –II- 2012
Section – A ( 1 mark each )
1. A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is:
(a) 30 degree (b) 45 degree (c) 60 degree (d) 90 degrees
2. Which of the following cannot be the probability of an event?
(a) 4% (b) 0. 3 (c) 1 / 5 (d) 5/4
3. If the circumference of a circle is equal to the perimeter of a square then the ratio of their areas is:
(a) 7: 11 (b) 14: 11 (c) 7 : 22 (d) 22 : 7
4. Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to:
(a) 6 √ 3 cm (b) √ 2 cm (c) 2 √ 3 cm (d) √ 3 cm
5. The height of a cone is 60 cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1 / 64th the volume of original cone. The height from the base at which the section is made is:
(a) 15 cm (b) 30 cm (c) 45 cm (d) 20 cm
6. To draw a pair of tangents to a circle which is inclined to each other at an angle of 100 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be:
(a) 100 degree (b) 80 degree (c) 50 degree (d) 20 degrees
7. The sum of first five multiples of 3 is:
(a) 65 (b) 75 (c) 90 (d) 45
8. Which of the following equations has he sum of its roots as 3 ?
(a) – x2 +3x + 3 = 0 (b) 3x2 – 3x – 3 = 0 (c) √2x2 – 3/√2 x – 1 (d) x2 + 3 x – 5 = 0
9. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to others is:
(a) 16 cm (b) 30 cm (c) 17 cm (d) 8 cm
10. If the digit is chosen at random from the digits. 1,2,3,4,5,6,7,8,9, then the probability that it is odd, is:
(a) 5/9 (b) 1/9 (c) 2/3 (d) 4/9
Section – B ( 2 marks each )
11. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm 11 cm 12 cm ?
12. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
13. Find the roots of the following quadratic equation:
2/5 x2 – x – 3/5 = 0
14. If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.
15. A coin is tossed two times. Find the probability of getting atmost one head.
16. Two dice are thrown at the sametime. Find the probability of getting different numbers on both dice.
17. Show that the point P (-4, 2) lies on the line segment joining the points A ( -4, 6).
18. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Section – C ( 3 marks each )
19. Find the sum of the integers between 100 and 200 that are divisible by 9.
20. A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
21. A cooper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.
22. Prove that the parallelogram circumscribing a circle is a rhombus.
23. A hemispherical depression is cut out from one of a cubical wooden block such that the aiam eter t’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining soild.
24. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC = 60 degree. Then construct a triangle whose sides are ¾ time the corresponding sides of triangle ABC.
25. Cards with numbers 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.
26. The points A (2, 9), B (a, 5), C (5, 5) are the vertices of a triangle ABC right angled at B. Find the value of ‘a’ and hence the area of triangle ABC.
27. A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot or the tower, the angle of elevation of the top of the tower is found to be 60 degree. Find the height of the tower.
28. Prove that the points A (4, 3), B (6, 4), C (5, -6) and D (3, -7) in the order are the vertices of a parallelogram.
Section – D( 4 marks each )
29. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60n degree respectively. Find height of the tower.
30. The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
31. 21 glass sphere each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm , 8 cm , 8 cm and then the box is filled with water. Find the volume of water filled in the box.
OR, A well of diameter 3 m and 14 cm deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
OR ,Find two consecutive odd positive integers, sum of whose squares is 290.
34. A sum of Rs.1400 is to be used to give seven cash prize to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.
SAMPLE PAPER/MODEL TEST PAPER SUBJECT – MATH
CBSE 10th BOARD SA –II- 2012
Section – A ( 1 mark each )
1. A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is:
(a) 30 degree (b) 45 degree (c) 60 degree (d) 90 degrees
2. Which of the following cannot be the probability of an event?
(a) 4% (b) 0. 3 (c) 1 / 5 (d) 5/4
3. If the circumference of a circle is equal to the perimeter of a square then the ratio of their areas is:
(a) 7: 11 (b) 14: 11 (c) 7 : 22 (d) 22 : 7
4. Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to:
(a) 6 √ 3 cm (b) √ 2 cm (c) 2 √ 3 cm (d) √ 3 cm
5. The height of a cone is 60 cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1 / 64th the volume of original cone. The height from the base at which the section is made is:
(a) 15 cm (b) 30 cm (c) 45 cm (d) 20 cm
6. To draw a pair of tangents to a circle which is inclined to each other at an angle of 100 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be:
(a) 100 degree (b) 80 degree (c) 50 degree (d) 20 degrees
7. The sum of first five multiples of 3 is:
(a) 65 (b) 75 (c) 90 (d) 45
8. Which of the following equations has he sum of its roots as 3 ?
(a) – x2 +3x + 3 = 0 (b) 3x2 – 3x – 3 = 0 (c) √2x2 – 3/√2 x – 1 (d) x2 + 3 x – 5 = 0
9. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to others is:
(a) 16 cm (b) 30 cm (c) 17 cm (d) 8 cm
10. If the digit is chosen at random from the digits. 1,2,3,4,5,6,7,8,9, then the probability that it is odd, is:
(a) 5/9 (b) 1/9 (c) 2/3 (d) 4/9
Section – B ( 2 marks each )
11. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm 11 cm 12 cm ?
12. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
13. Find the roots of the following quadratic equation:
2/5 x2 – x – 3/5 = 0
14. If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.
15. A coin is tossed two times. Find the probability of getting atmost one head.
16. Two dice are thrown at the sametime. Find the probability of getting different numbers on both dice.
17. Show that the point P (-4, 2) lies on the line segment joining the points A ( -4, 6).
18. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Section – C ( 3 marks each )
19. Find the sum of the integers between 100 and 200 that are divisible by 9.
20. A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
21. A cooper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.
22. Prove that the parallelogram circumscribing a circle is a rhombus.
23. A hemispherical depression is cut out from one of a cubical wooden block such that the aiam eter t’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining soild.
24. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC = 60 degree. Then construct a triangle whose sides are ¾ time the corresponding sides of triangle ABC.
25. Cards with numbers 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.
26. The points A (2, 9), B (a, 5), C (5, 5) are the vertices of a triangle ABC right angled at B. Find the value of ‘a’ and hence the area of triangle ABC.
27. A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot or the tower, the angle of elevation of the top of the tower is found to be 60 degree. Find the height of the tower.
28. Prove that the points A (4, 3), B (6, 4), C (5, -6) and D (3, -7) in the order are the vertices of a parallelogram.
Section – D( 4 marks each )
29. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60n degree respectively. Find height of the tower.
30. The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
31. 21 glass sphere each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm , 8 cm , 8 cm and then the box is filled with water. Find the volume of water filled in the box.
OR, A well of diameter 3 m and 14 cm deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
OR ,Find two consecutive odd positive integers, sum of whose squares is 290.
34. A sum of Rs.1400 is to be used to give seven cash prize to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.
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SAMPLE PAPER/MODEL TEST PAPER SUBJECT – MATH
CBSE 10th BOARD SA –II- 2012
Section – A ( 1 mark each )
1. A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is:
(a) 30 degree (b) 45 degree (c) 60 degree (d) 90 degrees
2. Which of the following cannot be the probability of an event?
(a) 4% (b) 0. 3 (c) 1 / 5 (d) 5/4
3. If the circumference of a circle is equal to the perimeter of a square then the ratio of their areas is:
(a) 7: 11 (b) 14: 11 (c) 7 : 22 (d) 22 : 7
4. Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to:
(a) 6 √ 3 cm (b) √ 2 cm (c) 2 √ 3 cm (d) √ 3 cm
5. The height of a cone is 60 cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1 / 64th the volume of original cone. The height from the base at which the section is made is:
(a) 15 cm (b) 30 cm (c) 45 cm (d) 20 cm
6. To draw a pair of tangents to a circle which is inclined to each other at an angle of 100 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be:
(a) 100 degree (b) 80 degree (c) 50 degree (d) 20 degrees
7. The sum of first five multiples of 3 is:
(a) 65 (b) 75 (c) 90 (d) 45
8. Which of the following equations has he sum of its roots as 3 ?
(a) – x2 +3x + 3 = 0 (b) 3x2 – 3x – 3 = 0 (c) √2x2 – 3/√2 x – 1 (d) x2 + 3 x – 5 = 0
9. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to others is:
(a) 16 cm (b) 30 cm (c) 17 cm (d) 8 cm
10. If the digit is chosen at random from the digits. 1,2,3,4,5,6,7,8,9, then the probability that it is odd, is:
(a) 5/9 (b) 1/9 (c) 2/3 (d) 4/9
Section – B ( 2 marks each )
11. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm 11 cm 12 cm ?
12. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
13. Find the roots of the following quadratic equation:
2/5 x2 – x – 3/5 = 0
14. If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.
15. A coin is tossed two times. Find the probability of getting atmost one head.
16. Two dice are thrown at the sametime. Find the probability of getting different numbers on both dice.
17. Show that the point P (-4, 2) lies on the line segment joining the points A ( -4, 6).
18. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Section – C ( 3 marks each )
19. Find the sum of the integers between 100 and 200 that are divisible by 9.
20. A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
21. A cooper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.
22. Prove that the parallelogram circumscribing a circle is a rhombus.
23. A hemispherical depression is cut out from one of a cubical wooden block such that the aiam eter t’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining soild.
24. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC = 60 degree. Then construct a triangle whose sides are ¾ time the corresponding sides of triangle ABC.
25. Cards with numbers 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.
26. The points A (2, 9), B (a, 5), C (5, 5) are the vertices of a triangle ABC right angled at B. Find the value of ‘a’ and hence the area of triangle ABC.
27. A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot or the tower, the angle of elevation of the top of the tower is found to be 60 degree. Find the height of the tower.
28. Prove that the points A (4, 3), B (6, 4), C (5, -6) and D (3, -7) in the order are the vertices of a parallelogram.
Section – D( 4 marks each )
29. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60n degree respectively. Find height of the tower.
30. The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
31. 21 glass sphere each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm , 8 cm , 8 cm and then the box is filled with water. Find the volume of water filled in the box.
OR, A well of diameter 3 m and 14 cm deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
OR ,Find two consecutive odd positive integers, sum of whose squares is 290.
34. A sum of Rs.1400 is to be used to give seven cash prize to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.
SAMPLE PAPER/MODEL TEST PAPER SUBJECT – MATH
CBSE 10th BOARD SA –II- 2012
Section – A ( 1 mark each )
1. A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is:
(a) 30 degree (b) 45 degree (c) 60 degree (d) 90 degrees
2. Which of the following cannot be the probability of an event?
(a) 4% (b) 0. 3 (c) 1 / 5 (d) 5/4
3. If the circumference of a circle is equal to the perimeter of a square then the ratio of their areas is:
(a) 7: 11 (b) 14: 11 (c) 7 : 22 (d) 22 : 7
4. Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to:
(a) 6 √ 3 cm (b) √ 2 cm (c) 2 √ 3 cm (d) √ 3 cm
5. The height of a cone is 60 cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1 / 64th the volume of original cone. The height from the base at which the section is made is:
(a) 15 cm (b) 30 cm (c) 45 cm (d) 20 cm
6. To draw a pair of tangents to a circle which is inclined to each other at an angle of 100 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be:
(a) 100 degree (b) 80 degree (c) 50 degree (d) 20 degrees
7. The sum of first five multiples of 3 is:
(a) 65 (b) 75 (c) 90 (d) 45
8. Which of the following equations has he sum of its roots as 3 ?
(a) – x2 +3x + 3 = 0 (b) 3x2 – 3x – 3 = 0 (c) √2x2 – 3/√2 x – 1 (d) x2 + 3 x – 5 = 0
9. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to others is:
(a) 16 cm (b) 30 cm (c) 17 cm (d) 8 cm
10. If the digit is chosen at random from the digits. 1,2,3,4,5,6,7,8,9, then the probability that it is odd, is:
(a) 5/9 (b) 1/9 (c) 2/3 (d) 4/9
Section – B ( 2 marks each )
11. How many spherical lead shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm 11 cm 12 cm ?
12. Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.
13. Find the roots of the following quadratic equation:
2/5 x2 – x – 3/5 = 0
14. If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.
15. A coin is tossed two times. Find the probability of getting atmost one head.
16. Two dice are thrown at the sametime. Find the probability of getting different numbers on both dice.
17. Show that the point P (-4, 2) lies on the line segment joining the points A ( -4, 6).
18. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that AOBP is a cyclic quadrilateral.
Section – C ( 3 marks each )
19. Find the sum of the integers between 100 and 200 that are divisible by 9.
20. A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
21. A cooper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.
22. Prove that the parallelogram circumscribing a circle is a rhombus.
23. A hemispherical depression is cut out from one of a cubical wooden block such that the aiam eter t’ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining soild.
24. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC = 60 degree. Then construct a triangle whose sides are ¾ time the corresponding sides of triangle ABC.
25. Cards with numbers 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.
26. The points A (2, 9), B (a, 5), C (5, 5) are the vertices of a triangle ABC right angled at B. Find the value of ‘a’ and hence the area of triangle ABC.
27. A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot or the tower, the angle of elevation of the top of the tower is found to be 60 degree. Find the height of the tower.
28. Prove that the points A (4, 3), B (6, 4), C (5, -6) and D (3, -7) in the order are the vertices of a parallelogram.
Section – D( 4 marks each )
29. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 degree and 60n degree respectively. Find height of the tower.
30. The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
31. 21 glass sphere each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm , 8 cm , 8 cm and then the box is filled with water. Find the volume of water filled in the box.
OR, A well of diameter 3 m and 14 cm deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
32. Prove that the lengths of tangents drawn from an external point to a circle are equal.
33. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
OR ,Find two consecutive odd positive integers, sum of whose squares is 290.
34. A sum of Rs.1400 is to be used to give seven cash prize to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.
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