SAMPLE PAPER CLASS X

MATHS

Time: 3hrs. Marks : 80

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections A, B, C and D.

(iii) Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each.

Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks

each.

(iv) There is no overall choice. However, an internal choice has been provided in four questions of 3

marks each and three questions of 4 marks each. You have to attempt only one of the

alternatives in all such questions.

(v) (v) Use of calculators is not permitted.

SECTION-A

1 Without performing the actual long division find if 395

1050will have terminating or non

terminating (repeating decimal expansion).

395

1050

|

2 If = 2 is a solution of P 2 + 2 4 = 0, then find the value of P.

= 2, P 2 + 2 4 = 0 P |

3 If nth term of an A.P. is 7 4. Find its common difference d.

n 7 4 d |

4 Find the distance between the lines 3 + 6 = 0 7 = 0.

3 + 6 = 0 7 = 0 |

5 In given figure, ST || RQ, PS=3cm and SR=4cm. Find the ratio of the area of PST to the area

of PRQ.

ST || RQ, PS=3cm SR=4cm | PST PRQ

|

6 If cosA=2

5 , then find the value of 4+4tan2A.

cosA=2

5 4+4tan2A |

SECTION-B

7 If n is a positive odd integer then show that n2-1 is divisible by 8.

n n2-1, 8 |

8 If the sum of first n terms of an A.P. is Sn= 5n2+3n then find out the 10th term of the A.P.

n Sn= 5n2+3n |

9 Find out the value(s) of for which the pair of linear equations + = and + = 1

have infinitely many solutions.

k + = + = 1 |

10 Find out the value of p for which the points (2,1) , (p,-1) and (-1,3) are collinear.

p (2,1) , (p,-1) (-1,3) ?

11 Two dice are rolled simultaneously. Find the probability that the sum of the two numbers

appearing on the two dice is a perfect square.

|

|

12 In a non leap year, what is the probability of 53 Mondays?

53 ?

SECTION C

13 Prove that 5 is an irrational number.

5 |

14 If and are the zeros of the polynomial 6y2-7y+2, find a quadratic polynomial whose

zeroes are 1

and

1

.

6y2-7y+2 1

1

|

15 Solve the following pair of equations for and . 5

1+

1

2= 2

6

1

3

2= 1 ; 1 , 2

5

1+

1

2= 2

6

1

3

2= 1 ; 1 , 2

16 Find the ratio in which the point P(x,2) divides the line segment joining the points A(12,5)

and B(4,-3). Also find the value of x.

P(x,2) A(12,5) B(4,-3)

| x |

OR

If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a parallelogram taken in order then

find its area.

A(-5,7), B(-4,-5), C(-1,-6) D(4,5)

|

17 In given figure if 1= 2 and NSQ MTR, then prove that PTS PRQ.

1= 2 NSQ MTR, PTS PRQ.

OR

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that

ABE CFB.

ABCD AD E BE CD F

| ABE CFB.

18 A quadrilateral ABCD is drawn to circumscribe a circle prove that

AB+CD = AD+BC

ABCD |

AB+CD = AD+BC

19 If tan + sin = m and tan - sin=n. Show that m2-n2 =4

tan + sin = m tan - sin=n m2-n2 =4

OR

Evaluate ( )

+

++

20 The median of the following distribution is 14.4. Find out the values of x and y if the total frequency is

20.

Class Interval 0-6 6-12 12-18 18-24 24-30 Total

Frequency 4 x 5 y 1 20

14.4 x y 20 |

0-6 6-12 12-18 18-24 24-30 Total

4 x 5 y 1 20

21 In the given figure. ABCD is a square of side 14cm with centres A,B,C and D, four circles are drawn

such that each circle touch externally two of the remaining three circles find the area of the shaded

portion.

ABCD 14cm | A, B, C, D

|

|

22 How many silver coins, 1.75cm in diameter and of thickness 2mm, must be melted to form a cuboid of

dimensions 5.5cm x 10cm x 3.5cm.

5.5cm x 10cm x 3.5cm 1.75cm 2mm

?

OR

A bucket of height 30cm is in the form of frustum of a cone with radii of its lower and upper ends as

10cm and 20cm respectively. Find the capacity of the bucket. Also find the cost of milk which can

completely fill the container at the rate of Rs. 25 per liter. (take = 3.14)

30 cm | 10cm

20cm | 25

| ( = 3.14 )

SECTION-D

23 An aeroplane starts late by 30 minutes to reach the destination which is 1500 km away. The pilot

increases the speed by 250km/hour just to reah on time. Find the original speed of the aeroplane.

30 | 1500 km

250 / |

|

OR

If the equation (1+m2)x

2+ 2mcx + c

2-a

2=0 has equal roots, then prove that c

2 = a

2(1+m

2)

(1+m2)x

2+ 2mcx + c

2-a

2=0 c

2 = a

2(1+m

2).

24 The sum of first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161 find the 28th

term of

this A.P.

7 63 7 161 | 28

|

25 Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their

corresponding sides.

|

OR

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct

points, the other two sides are divided in the same ratio.

|

26 Draw a triangle ABC with side BC=6cm, B =30o and A =120o. Then construct a triangle whose

sides are 5

4 times the corresponding sides of ABC.

ABC BC=6cm, B =30o A =120o |

ABC 5

4 |

27 Prove that ( )

+ 1

+ 1=

1

28 An aeroplane at an altitude of 200m has angles of depression at opposite points on the two banks of

the river as 45oand 60

o. Find the width of river.

200 |

45o 60

o | |

29 A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone

at other and their diameter is 4.2cm. The height of cylindrical and conical portions are 24cm and

14cm respectively. Find the volume of the toy.

|

4.2cm : 24cm 14cm |

|

30 The following distribution shows the daily pocket allowance of children of a locality. The mean pocket

allowance is Rs. 18. Find the missing frequency k.

Rs. 18

k |

Daily Pocket Allownace

11-13 13-15 15-17 17-19 19-21 21-23 23-25

Number of children

03 06 09 13 K 05 04

OR

Following table shows the rainfall in a city in 60days.

Draw a more than type Ogive for given data and find the median with the help of curve.

60 |

|

Rainfall (cm)

(cm)

0-10 10-20 20-30 30-40 40-50 50-60

Number of Days

16 10 08 15 05 06