Mathematics Previous year Sample paper, Part- B for class 10th

 Mathematics Sample Paper

Part- B

Section- C

Directions (Q.nos. 27 to 34 are of 3 marks each)

27. Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2y-x=8, 5y-x=14 and y-2x =1

Or

If 4 is a zero of the cubic polynomial x³-3x²-10x+24, find it's other two zeroes.

28. Find the area of ∆PQR formed by the points P(-5,7), Q(-4,-5) and R(4,5).

Or

If the point C(-1,2) divides internally the line segment joining A (2,5) and B(x,y) in the ratio 3:4, find the coordinates of B.

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29. Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) =ax² +bx +c, a≠0, c≠0.

Or

Divide the polynomial 

f(x) =3x²-x³-3x +5 by the polynomial g(x)=x-1-x² and verify the division algorithm.

30. In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle.

31. A cone of base radius 4cm is divided into two parts by drawing a plane through the mid points of it's height and parallel to it's base. Compare the volume of two parts.

32. A man can row a boat downstream 20km in 2 h and upstream 4km in 2 h. Find his speed of rowin in still water. Also find the speed of stream.

33. In the given figure, two circles touch each other at the point C. Prove that the common tangents to the circles at C, bisects the common tangent at P and Q.

34. Prove that 

cot∅ + cosec∅-1/cot∅-cosec∅+1=

1+cos∅/sin∅

Section- D

Directions (Q.nos. 35 to 40 are of 4 marks each)

35. The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village:

Change the distribution to a more than type distribution and draw it's ogive.

Or

The median of the following data is 525. Find the value of x and y, if total frequency is 100.

36. A bucket in the form of a frustum of a cone of height 30 cm with radii of it's lower and upper ends as 10 cm and 20cm, respectively. Find the capacity of the bucket. Also find the cost of milk which can completely fill the bucket at the rate of Rs 40 per litre. (Use π= 22/7)

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37. Show that the square of any positive integer can't be of the form (5q+2) or (5q+3) for any integer q.

Or

Prove that one of every three consecutive positive integers is divisible by 3.

38. The sum of four consecutive numbers in AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms 7:15. Find the numbers.

Or

Solve:

1+4+7+10+.....+x=287

39. Draw a ∆ABC with BC=7cm, angle B=45° and angle A =105°. Then, construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.

40. From the top of a 7m high building the angle of elevation of the top of a tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

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Posted by:- Anuranjan Gadekar

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