Mathematics Sample paper 7, Part- B for class 10th

 Mathematics Sample Paper

Part- B

19. Case Study III

Suppose there are two Windows in a house. A window of the house is at the height of 1.5 above the ground and the The other window is vertically above the lower window.

Anil and Sanjeev are sitting in the two Windows. At an instant, the angles of elevation of a balloon from these Windows are observed as 45° and 30° respectively.

a) Find the height of the balloon from the ground.

i. 8.6m

ii. 6.8m

iii. 9.4m

iv. 9.6m

b)  Among anil and Sanjeev, who is more closer to the balloon?

i. Sanjeev

ii. Anil

iii. Can't say

iv. None of the above

c) if the balloon is moving towards the building, then will both the angles of elevation remain same.

i. No

ii. Yes

iii. Can't say

iv. None of the above

d) If the height of any tower is double and the distance between the observer and foot of the tower is also doubled, then the angle of elevation

i. Remains same

ii. Become double

iii. Become triple

iv. None of the above

e) Suppose a tower and a pole is standing on the ground. And the angle of elevation from the bottom of pole is ø1 and elevation from top of pole to the top of tower is ø2.

Choose the correct option.

i. Ø1 >Ø2

ii. Ø1=Ø2

iii. Ø1<Ø2

iv. None of these

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20. Case Study IV

Flower Basket

In one corner of the drawing room, a flower basket is kept inside the glass, lies on the table. The basket is designed in such a way that every one pleases to see it.

The shape of flower basket is hemisphere with radius 60cm and upper shape is conical with height 120cm from the bottom surface.

a) Find the capacity of the glass.

i. 14.256/7m³

ii. 1.256/7m³

iii. 142.56/7m³

iv. 14.256/5m³

b) Find the volume of the cone.

i. 0.45m³

ii. 0.54m³

iii. 0.25m³

iv. 0.52m³

c) Find the curve surface area of hemisphere.

i. 0.102m²

ii. 0.104m²

iii. 0.201m²

iv. 0.401m²

d) The volume of two combined figure is equal to the sum of 

i. Two individual volumes

ii. Two individual curve surface area

iii. Volume and curve surface area

iv. None of the above

e) If the cost of painting the glass outside is Rs1.20per m², find the total cost of painting CSA of the glass.

i. Rs 57.02

ii. Rs 55.02 

iii. Rs 57

iv. Rs 55

Part-B(This is part B of Sample paper)

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

21. Solve the following system of equations by elimination method.

x+y=a-b

ax-by=a²+b²

Or

Solve the following pair of linear equations 7x-2y=1, 3x+4y=15

22. If cos alpha=1/2 and tan beeta =1/√3, then find sin(alpha+beeta), where alpha and beeta

are both acute angles.

Or

Find an acute angle ∅, when 

cosø-sinø/cosø+sinø=1-√3/1+√3

23. The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)?

24. Find the value of k, if the mean of the following distribution is 20.

25. If m times the mthterm of an AP is equal to n times it's nth term, then show that (m+n)th term of the AP is zero.

26. i. Name the type of the quadrilateral formed, if any, by the points (4,5), (7,6), (4,3) and (1,2).

ii. If diagonals of a quadrilateral are equal, then we say that it is a parallelogram. Is it true?

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

27. Prove that √5 is an irrational.

28. If alpha and beeta are zeroes of a quadratic polynomial x²-5, then form a quadratic polynomial whose zeroes are 1+alpha and 1+beeta.

Or

Can the quadratic polynomial x²+kx+k have equal zeroes for some odd integer k>1?

29. An aeroplane leaves an airport and flies due North at a speed of 1000km/hr. At the same time, another aeroplane leaves the same airport and flies due West at a speed of 1200km/hr. How far apart will be the two planes after 1 1/2hr?

Or

Two triangles ∆ABC and ∆DBC are on the same base BC and on the same side of BC in which angle A= angle D=90°. If CA and BD meet each other E, then show that

AE . EC= BE. ED

30. If sinø+ sin²ø=1, then find the value of cos12 ø+3cos10ø+3cos8ø+cos6 I+2cos⁴ø+2cos²ø-2.

31. From a well shuffled pack of 52 cards, few cards of same colour are missing. If P(drawing a red card)=2/3 and P (drawing a black card)=1/3, then which colour of cards are missing and how many?

32. A round table cover has six equal designs as shown in figure.

If the radius of the cover is 28cm, then find the cost of making the design at the rate of Rs 0.35per cm². (Take √3=1.73).

33. Solve the following system of linear equations graphically.

3x+y-11=0 and x-y-1=0

Also, find the area of the region bounded by these lines and the Y-axis.

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

34. Find the solution of the following equation by factorization method.

x+1/x-1- x-1/x+1=5/6, x≠1,-1

Or

Solve the quadratic equation

9x² - 9(a+b)x + (2a² + 5ab +2b²) =0 by factorization method.

35. Draw a circle with the help of circular solid ring. Construct a pair of tangents from a point P to the circle.

36. The mode of the following series is 36. Find the missing (x) frequency in it.

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Posted by :- Anuranjan Gadekar

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