Sample Question Paper - CBSE Class 10 (Mathematics) (2017) Class 10 Notes | EduRev

Class 10 : Sample Question Paper - CBSE Class 10 (Mathematics) (2017) Class 10 Notes | EduRev

 Page 1


SAMPLE QUESTION PAPER 
Summative Assessment – II 
Class-X (2016 –17) 
Mathematics 
Time Allowed: 3 Hours        Max. Marks: 90 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of31 questions divided into four sections A, B, C and D 
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of2 
marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 
questions of 4 marks each.  
4. Use of calculators is not permitted. 
 
SECTION – A 
(Question numbers 1 to 4 carry 1 mark each) 
 
1. A letter is chosen at random from the l e t t er of t h e ? word PROBABILITY ?. Find 
the probability that it is a not a vowel. 
2. Find the 17th term from the end of the AP : 1, 6, 1 1 , 1 6 ….. 2 1 1 , 216 
3. A pole 6 m high casts a s h a d o w 2v 3 m lo n g o n t h e g ro u n d , t h en find t h e angle of 
elevation of the sun. 
4. In the given figure PA and PB are tangents to a circle with centre O. If  
?APB = (2x   3     an d ?AOB = (3x   7   , t h e n fi n d t h e va l u e o f x 
 
SECTION – B 
(Question numbers 5 to 10 carry 2 marks each) 
 
5. Find the sum of all natural numbers that are less than 100 and divisible by 4. 
6. Find the value of p for which the points ( -1 , 3 ) , ( 2 , p ) and ( 5 , - 1 ) are 
collinear. 
7. Find the value(s) of  , for which the equation   
 
         has equal 
roots. 
Page 2


SAMPLE QUESTION PAPER 
Summative Assessment – II 
Class-X (2016 –17) 
Mathematics 
Time Allowed: 3 Hours        Max. Marks: 90 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of31 questions divided into four sections A, B, C and D 
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of2 
marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 
questions of 4 marks each.  
4. Use of calculators is not permitted. 
 
SECTION – A 
(Question numbers 1 to 4 carry 1 mark each) 
 
1. A letter is chosen at random from the l e t t er of t h e ? word PROBABILITY ?. Find 
the probability that it is a not a vowel. 
2. Find the 17th term from the end of the AP : 1, 6, 1 1 , 1 6 ….. 2 1 1 , 216 
3. A pole 6 m high casts a s h a d o w 2v 3 m lo n g o n t h e g ro u n d , t h en find t h e angle of 
elevation of the sun. 
4. In the given figure PA and PB are tangents to a circle with centre O. If  
?APB = (2x   3     an d ?AOB = (3x   7   , t h e n fi n d t h e va l u e o f x 
 
SECTION – B 
(Question numbers 5 to 10 carry 2 marks each) 
 
5. Find the sum of all natural numbers that are less than 100 and divisible by 4. 
6. Find the value of p for which the points ( -1 , 3 ) , ( 2 , p ) and ( 5 , - 1 ) are 
collinear. 
7. Find the value(s) of  , for which the equation   
 
         has equal 
roots. 
8. Using the figure given below, prove that AR =  
 
 
   (perimeter of triangle ABC)  
 
 
 
9. P and Q are the points with co-ordinates (2, -1) and (-3, 4). Find the co-
ordinates of the point R such that PR is  
 
 
 of PQ. 
10. In the given figure, common tangents AB and CD to the two circles intersect at 
E. Prove that AB = CD. 
 
SECTION – C 
(Question numbers 11 to 20 carry 3 marks each) 
 
11. Solve the given equation by the method of completing the squares:  
                      x
2
 + 12x – 45 = 0 
12. The sum of first six terms of an A.P. is 42. The ratio of its 10
th
 term to its 30
th 
term 
is 1:3.  Find the first term of the A.P. 
13. From the top of a lighthouse 75 m high, the angles of depression of two ships are 
observed to be 30 ? and 45 ? respectively. If one ship is directly behind the other on 
the same side of the lighthouse then find the distance between the two ships. 
14. The vertices of a triangle are A (-1, 3), B (1, -1) and C (5, 1). Find the length of the 
median through the vertex C. 
Page 3


SAMPLE QUESTION PAPER 
Summative Assessment – II 
Class-X (2016 –17) 
Mathematics 
Time Allowed: 3 Hours        Max. Marks: 90 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of31 questions divided into four sections A, B, C and D 
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of2 
marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 
questions of 4 marks each.  
4. Use of calculators is not permitted. 
 
SECTION – A 
(Question numbers 1 to 4 carry 1 mark each) 
 
1. A letter is chosen at random from the l e t t er of t h e ? word PROBABILITY ?. Find 
the probability that it is a not a vowel. 
2. Find the 17th term from the end of the AP : 1, 6, 1 1 , 1 6 ….. 2 1 1 , 216 
3. A pole 6 m high casts a s h a d o w 2v 3 m lo n g o n t h e g ro u n d , t h en find t h e angle of 
elevation of the sun. 
4. In the given figure PA and PB are tangents to a circle with centre O. If  
?APB = (2x   3     an d ?AOB = (3x   7   , t h e n fi n d t h e va l u e o f x 
 
SECTION – B 
(Question numbers 5 to 10 carry 2 marks each) 
 
5. Find the sum of all natural numbers that are less than 100 and divisible by 4. 
6. Find the value of p for which the points ( -1 , 3 ) , ( 2 , p ) and ( 5 , - 1 ) are 
collinear. 
7. Find the value(s) of  , for which the equation   
 
         has equal 
roots. 
8. Using the figure given below, prove that AR =  
 
 
   (perimeter of triangle ABC)  
 
 
 
9. P and Q are the points with co-ordinates (2, -1) and (-3, 4). Find the co-
ordinates of the point R such that PR is  
 
 
 of PQ. 
10. In the given figure, common tangents AB and CD to the two circles intersect at 
E. Prove that AB = CD. 
 
SECTION – C 
(Question numbers 11 to 20 carry 3 marks each) 
 
11. Solve the given equation by the method of completing the squares:  
                      x
2
 + 12x – 45 = 0 
12. The sum of first six terms of an A.P. is 42. The ratio of its 10
th
 term to its 30
th 
term 
is 1:3.  Find the first term of the A.P. 
13. From the top of a lighthouse 75 m high, the angles of depression of two ships are 
observed to be 30 ? and 45 ? respectively. If one ship is directly behind the other on 
the same side of the lighthouse then find the distance between the two ships. 
14. The vertices of a triangle are A (-1, 3), B (1, -1) and C (5, 1). Find the length of the 
median through the vertex C. 
15. The king, queen and jack of diamond are removed from a deck of 52 playing cards 
and then well shuffled. Now one card is drawn at random from the remaining 
cards. Determine the probability that the card drawn is : 
i) A face card. 
ii) A red card. 
iii) A king. 
16. Find the area of the minor segment of a circle of radius 42cm, if the length of the 
corresponding arc is 44 cm. 
17. A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 
20 meter per minute. How long would it take to fill a conical tank of radius 40 cm 
and depth 72cm? 
18. In given figure, PS  is the diameter of a circle of radius 6 cm. The points Q and R 
trisects the diameter PS. Semi circles are drawn on PQ and QS as diameters.  Find 
the area of the shaded region. 
 
 
19.  Find the number of spherical lead shots , each of  diameter 6 cm that can be made 
from a solid cuboid of  lead  having dimensions 24 cm ? 22 cm ? 12 cm.  
20.  A wooden souvenir is made by scooping out a hemisphere from each end of a 
solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 
cm then find the total cost of polishing the souvenir at the rate of Rs. 10 per cm
2
. 
 
SECTION – D 
(Question numbers 21 to 31 carry 4 marks each) 
21. D raw a ? A BC w i t h s i d es BC = 5 cm , A B = 6 cm an d A C = 7 cm an d t h e n c o n s t ru c t a triangle similar to ?ABC whose sides are 
 
 
 of the corresponding sides of ?ABC.  
22. A train covers a distance of 90 kms at a uniform speed. It would have taken 30 
minutes less if the speed had been 15 km/hr more. Calculate the original duration of 
the journey 
Page 4


SAMPLE QUESTION PAPER 
Summative Assessment – II 
Class-X (2016 –17) 
Mathematics 
Time Allowed: 3 Hours        Max. Marks: 90 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of31 questions divided into four sections A, B, C and D 
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of2 
marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 
questions of 4 marks each.  
4. Use of calculators is not permitted. 
 
SECTION – A 
(Question numbers 1 to 4 carry 1 mark each) 
 
1. A letter is chosen at random from the l e t t er of t h e ? word PROBABILITY ?. Find 
the probability that it is a not a vowel. 
2. Find the 17th term from the end of the AP : 1, 6, 1 1 , 1 6 ….. 2 1 1 , 216 
3. A pole 6 m high casts a s h a d o w 2v 3 m lo n g o n t h e g ro u n d , t h en find t h e angle of 
elevation of the sun. 
4. In the given figure PA and PB are tangents to a circle with centre O. If  
?APB = (2x   3     an d ?AOB = (3x   7   , t h e n fi n d t h e va l u e o f x 
 
SECTION – B 
(Question numbers 5 to 10 carry 2 marks each) 
 
5. Find the sum of all natural numbers that are less than 100 and divisible by 4. 
6. Find the value of p for which the points ( -1 , 3 ) , ( 2 , p ) and ( 5 , - 1 ) are 
collinear. 
7. Find the value(s) of  , for which the equation   
 
         has equal 
roots. 
8. Using the figure given below, prove that AR =  
 
 
   (perimeter of triangle ABC)  
 
 
 
9. P and Q are the points with co-ordinates (2, -1) and (-3, 4). Find the co-
ordinates of the point R such that PR is  
 
 
 of PQ. 
10. In the given figure, common tangents AB and CD to the two circles intersect at 
E. Prove that AB = CD. 
 
SECTION – C 
(Question numbers 11 to 20 carry 3 marks each) 
 
11. Solve the given equation by the method of completing the squares:  
                      x
2
 + 12x – 45 = 0 
12. The sum of first six terms of an A.P. is 42. The ratio of its 10
th
 term to its 30
th 
term 
is 1:3.  Find the first term of the A.P. 
13. From the top of a lighthouse 75 m high, the angles of depression of two ships are 
observed to be 30 ? and 45 ? respectively. If one ship is directly behind the other on 
the same side of the lighthouse then find the distance between the two ships. 
14. The vertices of a triangle are A (-1, 3), B (1, -1) and C (5, 1). Find the length of the 
median through the vertex C. 
15. The king, queen and jack of diamond are removed from a deck of 52 playing cards 
and then well shuffled. Now one card is drawn at random from the remaining 
cards. Determine the probability that the card drawn is : 
i) A face card. 
ii) A red card. 
iii) A king. 
16. Find the area of the minor segment of a circle of radius 42cm, if the length of the 
corresponding arc is 44 cm. 
17. A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 
20 meter per minute. How long would it take to fill a conical tank of radius 40 cm 
and depth 72cm? 
18. In given figure, PS  is the diameter of a circle of radius 6 cm. The points Q and R 
trisects the diameter PS. Semi circles are drawn on PQ and QS as diameters.  Find 
the area of the shaded region. 
 
 
19.  Find the number of spherical lead shots , each of  diameter 6 cm that can be made 
from a solid cuboid of  lead  having dimensions 24 cm ? 22 cm ? 12 cm.  
20.  A wooden souvenir is made by scooping out a hemisphere from each end of a 
solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 
cm then find the total cost of polishing the souvenir at the rate of Rs. 10 per cm
2
. 
 
SECTION – D 
(Question numbers 21 to 31 carry 4 marks each) 
21. D raw a ? A BC w i t h s i d es BC = 5 cm , A B = 6 cm an d A C = 7 cm an d t h e n c o n s t ru c t a triangle similar to ?ABC whose sides are 
 
 
 of the corresponding sides of ?ABC.  
22. A train covers a distance of 90 kms at a uniform speed. It would have taken 30 
minutes less if the speed had been 15 km/hr more. Calculate the original duration of 
the journey 
23. Cards marked with numbers 1, 3 , 5 … 4 9 a re p l ace d i n a b o x an d m i x ed t h o r o u g h l y . One card is drawn from the box. Find the probability that the number on the card is  
(i) divisible by 3    
(ii) a composite number 
(iii) Not a perfect square 
(iv) Multiple of 3 and 5.  
24. In given figure, XY and PQ are two parallel tangents to a circle with centre O and 
another tangent AB with point of contact C intersecting XY at A and PQ at B. Prove 
that ?AOB = 90° 
 
25. Solve the following quadratic equation by applying the quadratic formula:  
 
 
 
 
 ( 
 
   
 
)    
 
   
26. The points A ( 1 , -2 ) , B ( 2 , 3 ), C ( k , 2 )and D ( - 4 , - 3 ) are the vertices of a 
parallelogram. Find the value of k and the altitude of the parallelogram 
corresponding to the base AB. 
27. From a point 100 m above a lake the angle of elevation of a stationary helicopter 
is30
?
 and the angle of depression of reflection of the helicopter in the lake is 60
?
. Find 
the height of the helicopter above the lake. 
28. A donor agency ensures   milk is supplied in containers, which are in the form of a 
frustum of a cone to be distributed to flood victims in a camp. The height of each 
frustum is 30 cm and the radii of whose lower and upper circular ends are 20 cm and 
40 cm respectively. . If this milk is available at the rate of Rs.35 per litre and 880 
litres of milk is needed daily for a camp.   
(a) Find how many milk containers are needed daily for the camp. 
(b) What daily cost will it put on the donor agency? 
(c)  What value of the donor agency is depicted in this situation? 
Page 5


SAMPLE QUESTION PAPER 
Summative Assessment – II 
Class-X (2016 –17) 
Mathematics 
Time Allowed: 3 Hours        Max. Marks: 90 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of31 questions divided into four sections A, B, C and D 
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of2 
marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 
questions of 4 marks each.  
4. Use of calculators is not permitted. 
 
SECTION – A 
(Question numbers 1 to 4 carry 1 mark each) 
 
1. A letter is chosen at random from the l e t t er of t h e ? word PROBABILITY ?. Find 
the probability that it is a not a vowel. 
2. Find the 17th term from the end of the AP : 1, 6, 1 1 , 1 6 ….. 2 1 1 , 216 
3. A pole 6 m high casts a s h a d o w 2v 3 m lo n g o n t h e g ro u n d , t h en find t h e angle of 
elevation of the sun. 
4. In the given figure PA and PB are tangents to a circle with centre O. If  
?APB = (2x   3     an d ?AOB = (3x   7   , t h e n fi n d t h e va l u e o f x 
 
SECTION – B 
(Question numbers 5 to 10 carry 2 marks each) 
 
5. Find the sum of all natural numbers that are less than 100 and divisible by 4. 
6. Find the value of p for which the points ( -1 , 3 ) , ( 2 , p ) and ( 5 , - 1 ) are 
collinear. 
7. Find the value(s) of  , for which the equation   
 
         has equal 
roots. 
8. Using the figure given below, prove that AR =  
 
 
   (perimeter of triangle ABC)  
 
 
 
9. P and Q are the points with co-ordinates (2, -1) and (-3, 4). Find the co-
ordinates of the point R such that PR is  
 
 
 of PQ. 
10. In the given figure, common tangents AB and CD to the two circles intersect at 
E. Prove that AB = CD. 
 
SECTION – C 
(Question numbers 11 to 20 carry 3 marks each) 
 
11. Solve the given equation by the method of completing the squares:  
                      x
2
 + 12x – 45 = 0 
12. The sum of first six terms of an A.P. is 42. The ratio of its 10
th
 term to its 30
th 
term 
is 1:3.  Find the first term of the A.P. 
13. From the top of a lighthouse 75 m high, the angles of depression of two ships are 
observed to be 30 ? and 45 ? respectively. If one ship is directly behind the other on 
the same side of the lighthouse then find the distance between the two ships. 
14. The vertices of a triangle are A (-1, 3), B (1, -1) and C (5, 1). Find the length of the 
median through the vertex C. 
15. The king, queen and jack of diamond are removed from a deck of 52 playing cards 
and then well shuffled. Now one card is drawn at random from the remaining 
cards. Determine the probability that the card drawn is : 
i) A face card. 
ii) A red card. 
iii) A king. 
16. Find the area of the minor segment of a circle of radius 42cm, if the length of the 
corresponding arc is 44 cm. 
17. A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 
20 meter per minute. How long would it take to fill a conical tank of radius 40 cm 
and depth 72cm? 
18. In given figure, PS  is the diameter of a circle of radius 6 cm. The points Q and R 
trisects the diameter PS. Semi circles are drawn on PQ and QS as diameters.  Find 
the area of the shaded region. 
 
 
19.  Find the number of spherical lead shots , each of  diameter 6 cm that can be made 
from a solid cuboid of  lead  having dimensions 24 cm ? 22 cm ? 12 cm.  
20.  A wooden souvenir is made by scooping out a hemisphere from each end of a 
solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 
cm then find the total cost of polishing the souvenir at the rate of Rs. 10 per cm
2
. 
 
SECTION – D 
(Question numbers 21 to 31 carry 4 marks each) 
21. D raw a ? A BC w i t h s i d es BC = 5 cm , A B = 6 cm an d A C = 7 cm an d t h e n c o n s t ru c t a triangle similar to ?ABC whose sides are 
 
 
 of the corresponding sides of ?ABC.  
22. A train covers a distance of 90 kms at a uniform speed. It would have taken 30 
minutes less if the speed had been 15 km/hr more. Calculate the original duration of 
the journey 
23. Cards marked with numbers 1, 3 , 5 … 4 9 a re p l ace d i n a b o x an d m i x ed t h o r o u g h l y . One card is drawn from the box. Find the probability that the number on the card is  
(i) divisible by 3    
(ii) a composite number 
(iii) Not a perfect square 
(iv) Multiple of 3 and 5.  
24. In given figure, XY and PQ are two parallel tangents to a circle with centre O and 
another tangent AB with point of contact C intersecting XY at A and PQ at B. Prove 
that ?AOB = 90° 
 
25. Solve the following quadratic equation by applying the quadratic formula:  
 
 
 
 
 ( 
 
   
 
)    
 
   
26. The points A ( 1 , -2 ) , B ( 2 , 3 ), C ( k , 2 )and D ( - 4 , - 3 ) are the vertices of a 
parallelogram. Find the value of k and the altitude of the parallelogram 
corresponding to the base AB. 
27. From a point 100 m above a lake the angle of elevation of a stationary helicopter 
is30
?
 and the angle of depression of reflection of the helicopter in the lake is 60
?
. Find 
the height of the helicopter above the lake. 
28. A donor agency ensures   milk is supplied in containers, which are in the form of a 
frustum of a cone to be distributed to flood victims in a camp. The height of each 
frustum is 30 cm and the radii of whose lower and upper circular ends are 20 cm and 
40 cm respectively. . If this milk is available at the rate of Rs.35 per litre and 880 
litres of milk is needed daily for a camp.   
(a) Find how many milk containers are needed daily for the camp. 
(b) What daily cost will it put on the donor agency? 
(c)  What value of the donor agency is depicted in this situation? 
29. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the 
bigger circle and BD is tangent to the smaller circle touching it at D and intersecting 
the larger circle at P, on producing. Find the length of AP. 
30. A manufacturer of TV sets produced 600 units in the 3rd year and 700 units in the 
7th year. Assuming that, production increases uniformly by a fixed number of units 
every year. Find 
(i) The production in 1
st 
year. 
(ii) The production in 10
th 
year. 
(iii) The total production in 7 years. 
31. 50 circular discs, each of radius 7cm and thickness 0.5cm are placed one above the 
other. Find the total surface area of the solid so formed. Find how much space will 
be left in a cubical box of side 25cm if the solid formed is placed inside it. 
--ooo — 
  
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

ppt

,

Viva Questions

,

Sample Paper

,

Exam

,

Sample Question Paper - CBSE Class 10 (Mathematics) (2017) Class 10 Notes | EduRev

,

Objective type Questions

,

mock tests for examination

,

MCQs

,

Sample Question Paper - CBSE Class 10 (Mathematics) (2017) Class 10 Notes | EduRev

,

Summary

,

shortcuts and tricks

,

Important questions

,

Sample Question Paper - CBSE Class 10 (Mathematics) (2017) Class 10 Notes | EduRev

,

Previous Year Questions with Solutions

,

video lectures

,

practice quizzes

,

Semester Notes

,

past year papers

,

Free

,

study material

,

pdf

,

Extra Questions

;