Mathematics Sample Paper 10, Part-B for class 10th

 Mathematics Sample paper

 Part-B 

19. Case Study III

Dice Game

In two dice game, the player take turns to roll both dice , they can roll as many times as they want in one turn. A player scores the sum of the two dice thrown and gradually reaches a higher score as they continue to roll. If a single number 1 is thrown on either die, the score for that whole turn is lost. Two dice are thrown simultaneously.

a) Find the probability of getting the sum as an even number.

i. 3/4

ii. 1/2

iii. 1/4

iv. 5/8

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b) Find the probability of getting the sum as a prime number.

i. 5/12

ii. 1/6

iii. 7/12

iv. 11/12

c) Find the probability of getting the sum of at least 10

i. 5/12

ii. 5/6

iii. 1/6

iv. 7/12

d) Find the probability of getting a doublet of even number.

i. 1/12

ii. 5/12

iii. 11/12

iv. 7/12.

e) In a right throw of a dice, if the dice falls in tilt position, then what is the probability?

i. 0

ii. 1/2

iii. 1

iv. Can't determine

20. Case Study IV

Hexagone Dice

Suppose we have a hexagonal three dimension dice. We cut the dice in three parts and the images of there part is shown in the coordinates axis.

a) Find the coordinates of point E and B of a rectangle ABED

i. (3,2), (7,8)

ii. (4,2), (7,8)

iii. (4,2), (6,8)

iv. None of these

b) Find the length AE of a ∆AEF.

i. 5

ii. 6

iii. 4

iv. 3

c) Find the area of ∆BCD.

i. 6 sq unit

ii. 5 sq unit

iii. 7 sq unit

iv. 8 sq unit

d)  Find the perimeter of a rectangle ABDE.

i. 16

ii. 17

iii. 19

iv. 18

e) Find the coordinates of intersection point of diagonals.

i. (11/2,6)

ii. (11/2, 5)

iii. (11/3, 5)

iv. None of these

Part- B

Directions ( Q.nos. 21-26 are of 2 marks each)

21. An army contingent of 616 members is to March behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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22. If the points P(4,3) and Q(x,5) are on the circle with centre O(2,3). Then, find the value of x.

23. In a rhombus of side 10cm, one of the diagonals is 12cm long. Find the length of the second diagonal.

Or 

In the given figure, if DE\\AQ and DF\\AR, then prove that EF\\QR.

24. Jio has launched two new mobile hand sets: set A and set B, set A is cheaper as compared to set B but set B has built in device to recharge the battery with auto cut power supply when it is fully charged. In a lot, there are 250 pieces of set A and 100 pieces of set B. If a mobile is picked at radom, then

i. Find the probability of getting set A

ii. Find the probability of getting set B

25. If cos alpha/cos beeta =m and cos alpha/sun beeta=n, show that (m² + n²)cos²beeta=n²

Or

Find acute angle A and B, if sin(A+2B)=√3/2

and cos(A+4B)=0, A>B.

26. Solve the following equation 

x+3/x-2 - 1-x/x=17/4

Directions (Q.nos. 27-33  are of 3 marks each) 

27. Write that denominator of the rational number 257/5000 in the form 2^m × 5^n, where m and n are non- negative integers. Hence, write the decimal expansion, without actual division.

Or

Find the greatest number that will divide 445, 572 and 699 leaving remainders 4,5 and 6, respectively.

28. Solve the following equations for x and y.

7^x + 5^y=74 and 7^x+1 - 5^y+1=218

Or

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work and also that taken by 1 man alone.

29. In the given figure, ∆ABC is an equilateral triangle inscribed in a circle of radius 4cm. Find the area of shaded region. 

30. An incomplete distribution is given as follows 

The median value is 35 and the sum of all the frequencies is 170. Using the median formula,fill up the missing frequencies.

31. If tan∅-cot∅ = a and cos∅ + sin∅=b,then show that(a²+4) (b²-1)²=4.

32. The given figure shows two parallel tangents XY and X'Y' at the points A and B, respectively to the circle with centre O.

Another tangents CD is drawn parallel to AB at the point P. Show that a circle with P as centre and OP as radius will pass through C and D.

33. Find the zeroes of the quadratic polynomial pgx²+ (pr+qs) x + rs and verify the relationship between the zeroes and coefficients.

Directions ( Q.nos. 34-36 are of 5 marks each) 

34. Draw a circle of radius 3 cm. From a point P, 7 cm away from it's centre draw two tangents to the circle. Measure the length of each tangeny.

35. A spherical glass vessel has a cylindrical neck 8cm long,2cm in diameter and the diameter of the spherical part is 8.5cm. By measuring the amount of water it holds, a girl finds it's volume to be 345³. Check whether she is correct , taking the above as the inside measurements. (Take the=3.14)

36. Three positive integers a1, a2 and a3 are in AP such that a1 + a2 + a3 =33 and a1×a2×a3=1155. Find the integers a1, a2 and a3.

Or

The 10th term of an AP is 52 and 16th term is 82. Find the 

i. 32nd term of an AP

ii. General term of an AP

iii. Sum of the first 20 terms of an AP

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Posted By:- Anuranjan Gadekar

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