CBSE Mathematics Sample Paper Class 10 Notes | EduRev

Class 10 : CBSE Mathematics Sample Paper Class 10 Notes | EduRev

 Page 1


5 
 
SAMPLE PAPER 
CLASS-X 
 
General Instructions: 
 
1. All questions are compulsory. 
2. Section A consists of 10 questions of 1 mark each. 
     Section B consists of 5 questions of 2 marks each. 
     Section C consists of 10 questions of 3 marks each. 
     Section D consists of 5 questions of 6 marks each. 
3. There is no overall choice however internal choice has been provided. 
 
 
  SECTION-A
1. State fundam ental theorem of arithmatic.
2. O ne card is draw n at random from a well shuffled deck of 52 cards.
 Find the probability of getting a king of red suit.
3. If kx+y=7 and 3x-2y=11
o
 represent inte rsecting lines then find the 
value of K.
4.Find the 18th term of A.P. 2 , 3 2,5 2,........
5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A.
6.  If m ode of the following data is 15. Find K .
k
       10,15,17,15, 6,17, 20
2
7. In the given fig DE is parallel to BC.
AD 2
If  and AC =18 cm. Find AE.
BD 3
+
=
 
 
Page 2


5 
 
SAMPLE PAPER 
CLASS-X 
 
General Instructions: 
 
1. All questions are compulsory. 
2. Section A consists of 10 questions of 1 mark each. 
     Section B consists of 5 questions of 2 marks each. 
     Section C consists of 10 questions of 3 marks each. 
     Section D consists of 5 questions of 6 marks each. 
3. There is no overall choice however internal choice has been provided. 
 
 
  SECTION-A
1. State fundam ental theorem of arithmatic.
2. O ne card is draw n at random from a well shuffled deck of 52 cards.
 Find the probability of getting a king of red suit.
3. If kx+y=7 and 3x-2y=11
o
 represent inte rsecting lines then find the 
value of K.
4.Find the 18th term of A.P. 2 , 3 2,5 2,........
5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A.
6.  If m ode of the following data is 15. Find K .
k
       10,15,17,15, 6,17, 20
2
7. In the given fig DE is parallel to BC.
AD 2
If  and AC =18 cm. Find AE.
BD 3
+
=
 
 
6 
 
 
 
 
 
 
8. Find X in the give n fig. if PT is tangent to the circle. 
 
 
2
9. and are zeros of 2 5( 2), then find the product of  and .
22
10. Find the perimeter of a quadrant of circle of radius 7cm( = ).
2
                                     SECTION-B
11. Find 31 term 
If x x a ß a ß
p
+ - of an AP whose 11 term is 38 and 16 term is 73.
12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). 
Also find the point of intersection.
13. Evaluate without using trignometric table
tan 50 sec 50
cos 40 cos 50
cot 40 cos 50
ec
ec
+
+
+
 
 
 
 
 
                                   OR 
 
sec 4 cos ( 20 ), where 4A is an acute angle, 
find the value of A.
If A ec A = - 
 
  
14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm.
 Find the perimeter of APQ. ? 
 
Page 3


5 
 
SAMPLE PAPER 
CLASS-X 
 
General Instructions: 
 
1. All questions are compulsory. 
2. Section A consists of 10 questions of 1 mark each. 
     Section B consists of 5 questions of 2 marks each. 
     Section C consists of 10 questions of 3 marks each. 
     Section D consists of 5 questions of 6 marks each. 
3. There is no overall choice however internal choice has been provided. 
 
 
  SECTION-A
1. State fundam ental theorem of arithmatic.
2. O ne card is draw n at random from a well shuffled deck of 52 cards.
 Find the probability of getting a king of red suit.
3. If kx+y=7 and 3x-2y=11
o
 represent inte rsecting lines then find the 
value of K.
4.Find the 18th term of A.P. 2 , 3 2,5 2,........
5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A.
6.  If m ode of the following data is 15. Find K .
k
       10,15,17,15, 6,17, 20
2
7. In the given fig DE is parallel to BC.
AD 2
If  and AC =18 cm. Find AE.
BD 3
+
=
 
 
6 
 
 
 
 
 
 
8. Find X in the give n fig. if PT is tangent to the circle. 
 
 
2
9. and are zeros of 2 5( 2), then find the product of  and .
22
10. Find the perimeter of a quadrant of circle of radius 7cm( = ).
2
                                     SECTION-B
11. Find 31 term 
If x x a ß a ß
p
+ - of an AP whose 11 term is 38 and 16 term is 73.
12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). 
Also find the point of intersection.
13. Evaluate without using trignometric table
tan 50 sec 50
cos 40 cos 50
cot 40 cos 50
ec
ec
+
+
+
 
 
 
 
 
                                   OR 
 
sec 4 cos ( 20 ), where 4A is an acute angle, 
find the value of A.
If A ec A = - 
 
  
14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm.
 Find the perimeter of APQ. ? 
 
7 
 
 
15. If the mean of the following data is 18.
 find the missing frequency P.
 
 
X
i
 10 15 20 25 
f
i
 5 10 p 8 
 
2
3 2
SECT IO N-C
16. Find the zeros of polynom ial p(x)= 2 3 2 2 and 
verify the relationship betw een the zeros and co-efficients.
                                               OR
On dividing x -3x +x+2 by the 
x x - - polynomial g(x), the quotient
 and remainder w ere x-2 and -2x+4 respectively. Find g(x).
17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will
 have infinitely many solutions.
18. T he hypotenuse of a right triangle is 1 m less than tw ice the
 shortest side. If third side is 1 m m ore than the shortest side.
 Find the sides of the triangle.
 
Page 4


5 
 
SAMPLE PAPER 
CLASS-X 
 
General Instructions: 
 
1. All questions are compulsory. 
2. Section A consists of 10 questions of 1 mark each. 
     Section B consists of 5 questions of 2 marks each. 
     Section C consists of 10 questions of 3 marks each. 
     Section D consists of 5 questions of 6 marks each. 
3. There is no overall choice however internal choice has been provided. 
 
 
  SECTION-A
1. State fundam ental theorem of arithmatic.
2. O ne card is draw n at random from a well shuffled deck of 52 cards.
 Find the probability of getting a king of red suit.
3. If kx+y=7 and 3x-2y=11
o
 represent inte rsecting lines then find the 
value of K.
4.Find the 18th term of A.P. 2 , 3 2,5 2,........
5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A.
6.  If m ode of the following data is 15. Find K .
k
       10,15,17,15, 6,17, 20
2
7. In the given fig DE is parallel to BC.
AD 2
If  and AC =18 cm. Find AE.
BD 3
+
=
 
 
6 
 
 
 
 
 
 
8. Find X in the give n fig. if PT is tangent to the circle. 
 
 
2
9. and are zeros of 2 5( 2), then find the product of  and .
22
10. Find the perimeter of a quadrant of circle of radius 7cm( = ).
2
                                     SECTION-B
11. Find 31 term 
If x x a ß a ß
p
+ - of an AP whose 11 term is 38 and 16 term is 73.
12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). 
Also find the point of intersection.
13. Evaluate without using trignometric table
tan 50 sec 50
cos 40 cos 50
cot 40 cos 50
ec
ec
+
+
+
 
 
 
 
 
                                   OR 
 
sec 4 cos ( 20 ), where 4A is an acute angle, 
find the value of A.
If A ec A = - 
 
  
14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm.
 Find the perimeter of APQ. ? 
 
7 
 
 
15. If the mean of the following data is 18.
 find the missing frequency P.
 
 
X
i
 10 15 20 25 
f
i
 5 10 p 8 
 
2
3 2
SECT IO N-C
16. Find the zeros of polynom ial p(x)= 2 3 2 2 and 
verify the relationship betw een the zeros and co-efficients.
                                               OR
On dividing x -3x +x+2 by the 
x x - - polynomial g(x), the quotient
 and remainder w ere x-2 and -2x+4 respectively. Find g(x).
17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will
 have infinitely many solutions.
18. T he hypotenuse of a right triangle is 1 m less than tw ice the
 shortest side. If third side is 1 m m ore than the shortest side.
 Find the sides of the triangle.
 
8 
19.Construct a triangle of sides 4cm, 5cm & 6cm, and then a triangle 
2
similar to it whose sides are  of corresponding sides of first triangle.
3
20. Prove that:
(1+cotA+tanA)(sinA-cosA)=sinAtanA-cotAcosA
2
                            or
1 cos
(cosec -cot ) =
1 cos
21. he mid points of the sides of a triangle are (3,4), (4,6) and(5,7).
 Find the co-ordinates of the vertices of the triangle.
22. How many coin
T
?
? ?
?
- +
s 1.75 cm in diameter and 2mm thick must be melted 
to form a cuboid 11cm X 10 cmX 7cm.
23.Prove that 5 -3 2 is an irrational number.
24. In a trapezium ABCD, AB CD and CD=2 AB Cuts AD in F and BC in E, s 
BC 3
uch that .
EC 4
Diagonal BD intersect EF at G.
Prove that 7EF=10AB.
=
 
 
 
1 1
25. Prove that the points(a,0),(0,b) and (1,1) are collinear if 1.
a
                                              SECTION-D
26.Prove that the ratio of areas of two similar triangles is equal to the
b
+ =
 ratio
 of squares of their corresponding sides using the above theorem  do the
 following:
The area of two similar triangles ABC and PQR are in the ratio 9:16,. If BC=4.5 cm. 
Find the length of QR.
 
                                                       OR 
 
State and prove Pythagoras theorem. Using the above theorem, Prove the following. 
In the given figure PQR is a right triangle right angled at Q. If QS=SR, show that PR
2
=4PS
2
-3PQ
2
. 
 
 
Page 5


5 
 
SAMPLE PAPER 
CLASS-X 
 
General Instructions: 
 
1. All questions are compulsory. 
2. Section A consists of 10 questions of 1 mark each. 
     Section B consists of 5 questions of 2 marks each. 
     Section C consists of 10 questions of 3 marks each. 
     Section D consists of 5 questions of 6 marks each. 
3. There is no overall choice however internal choice has been provided. 
 
 
  SECTION-A
1. State fundam ental theorem of arithmatic.
2. O ne card is draw n at random from a well shuffled deck of 52 cards.
 Find the probability of getting a king of red suit.
3. If kx+y=7 and 3x-2y=11
o
 represent inte rsecting lines then find the 
value of K.
4.Find the 18th term of A.P. 2 , 3 2,5 2,........
5. If sec5A=cosec(A-36 ),where 5A is an acute angle. Find the value of A.
6.  If m ode of the following data is 15. Find K .
k
       10,15,17,15, 6,17, 20
2
7. In the given fig DE is parallel to BC.
AD 2
If  and AC =18 cm. Find AE.
BD 3
+
=
 
 
6 
 
 
 
 
 
 
8. Find X in the give n fig. if PT is tangent to the circle. 
 
 
2
9. and are zeros of 2 5( 2), then find the product of  and .
22
10. Find the perimeter of a quadrant of circle of radius 7cm( = ).
2
                                     SECTION-B
11. Find 31 term 
If x x a ß a ß
p
+ - of an AP whose 11 term is 38 and 16 term is 73.
12. Find the ratio in which the y-axis divides the join of (5,-6) and(-1,-4). 
Also find the point of intersection.
13. Evaluate without using trignometric table
tan 50 sec 50
cos 40 cos 50
cot 40 cos 50
ec
ec
+
+
+
 
 
 
 
 
                                   OR 
 
sec 4 cos ( 20 ), where 4A is an acute angle, 
find the value of A.
If A ec A = - 
 
  
14. If AB,AC and PQ are tangents in the given fig. and AB=5 cm.
 Find the perimeter of APQ. ? 
 
7 
 
 
15. If the mean of the following data is 18.
 find the missing frequency P.
 
 
X
i
 10 15 20 25 
f
i
 5 10 p 8 
 
2
3 2
SECT IO N-C
16. Find the zeros of polynom ial p(x)= 2 3 2 2 and 
verify the relationship betw een the zeros and co-efficients.
                                               OR
On dividing x -3x +x+2 by the 
x x - - polynomial g(x), the quotient
 and remainder w ere x-2 and -2x+4 respectively. Find g(x).
17. Find the value of K for which (k-3)x+3y=K, kx+ky=12 will
 have infinitely many solutions.
18. T he hypotenuse of a right triangle is 1 m less than tw ice the
 shortest side. If third side is 1 m m ore than the shortest side.
 Find the sides of the triangle.
 
8 
19.Construct a triangle of sides 4cm, 5cm & 6cm, and then a triangle 
2
similar to it whose sides are  of corresponding sides of first triangle.
3
20. Prove that:
(1+cotA+tanA)(sinA-cosA)=sinAtanA-cotAcosA
2
                            or
1 cos
(cosec -cot ) =
1 cos
21. he mid points of the sides of a triangle are (3,4), (4,6) and(5,7).
 Find the co-ordinates of the vertices of the triangle.
22. How many coin
T
?
? ?
?
- +
s 1.75 cm in diameter and 2mm thick must be melted 
to form a cuboid 11cm X 10 cmX 7cm.
23.Prove that 5 -3 2 is an irrational number.
24. In a trapezium ABCD, AB CD and CD=2 AB Cuts AD in F and BC in E, s 
BC 3
uch that .
EC 4
Diagonal BD intersect EF at G.
Prove that 7EF=10AB.
=
 
 
 
1 1
25. Prove that the points(a,0),(0,b) and (1,1) are collinear if 1.
a
                                              SECTION-D
26.Prove that the ratio of areas of two similar triangles is equal to the
b
+ =
 ratio
 of squares of their corresponding sides using the above theorem  do the
 following:
The area of two similar triangles ABC and PQR are in the ratio 9:16,. If BC=4.5 cm. 
Find the length of QR.
 
                                                       OR 
 
State and prove Pythagoras theorem. Using the above theorem, Prove the following. 
In the given figure PQR is a right triangle right angled at Q. If QS=SR, show that PR
2
=4PS
2
-3PQ
2
. 
 
 
9 
 
 
                                                     
27. A sailor can row a boat 8 km downstream and return back to the starting 
point in 1 hr. 40min. If speed of stream is 2 km/hr. Find the speed of boat in
 still water.
28. An aeroplane when 3000m high, passes vertically above another 
aeroplane at an instant when the angles of elevation of the two 
aeroplanes from the same point on the ground are 6
0 0
0 and 45 respectively. 
Find the vertical distance between two aeroplanes.
29. A solid in the form of right circular cylinder, with hemisphere at one 
end and a cone at other end. the radius of the common base is 3.5 cm and 
the heights of the cylindrical & conical portion are 10cm amd 6 cm respectively.
22
 Find the total surface area of the (use = )
7
p
 
 
 
 
 
30. Calculate Medians of the following data: 
Marks obtained No. of students 
Less than 20 0 
Less than 30 4 
Less than 40 16 
Less than 50 30 
Less than 60 46 
Less than 70 66 
Less than 80 82 
Less than 90 92 
Less than 100 100 
 
 
 
 
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