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**CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 11**

** Section A**

1.Find the value of p which will make the product of 2p – 5 and p – 4 equal in value to p + 8.

2.Which term of the AP 21, 18, 15, … , is zero?

3.Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

4.If the circumference of a circle exceeds the diameter by pi units, then find the diameter of the circle.

** Section B**

6.Which term of the sequence 25, 22, 19, … is the first negative term?

7.The incircle of an isosceles triangle ABC, with AB = AC, touches the sides AB, BC and CA at D, E and F respectively. Prove that E bisects BC.

8.Find the probability of getting 53 Mondays in a leap year.

10.A solid cube is cut into eight cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of one small cube.

** Section C**

12.The cost price of an article is Rs x and is sold at a profit of (x + 20)%. Find the cost price of the article, if its selling price is Rs (1.4x – 48).

13.Find the sum of all the three-digit numbers each of which leaves a remainder 3, when divided by 7.

14.Construct an isosceles triangle whose base is 6 cm and altitude 5 cm and then another triangle whose sides are 4/3 times the corresponding sides of the isosceles triangle.

15.All jacks, queens, kings and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is

(i) red face card (ii) a card of spade.

16.A child’s game has 12 triangles of which 4 are blue and rest are green. 8 rectangles of which 5 are green and rest are blue, 10 rhombus of which 7 are blue and rest are green. One piece is lost at random. Find the probability that it is

(i) a rectangle

(it) a triangle of green colour

(iii)a rhombus of blue colour.

17.If P(5, -7), Q(4, 7) and R(6, -3) are the vertices of triangle PQR, M is mid point of QR and A is a point on PM joined PA/PM = 2, find the coordinates of A.

18.If (a, 0), (0, b) and (3, 2) are collinear, show that 2a + 3b – ab = 0

20.A cone of height 48 cm has a curved surface area of 2200 cm^{2.} Find its volume.[use pi=22/7]

** Section D**

21. Solve for x :(2x/x – 3 )+( 1/ 2x + 3) +(3x + 9/(x – 3) (2x + 3))=0 x not equal to 3,-3/2

22.Along a road lies an odd number of stones placed at intervals of 20 metres. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 6 km. Find the number of stones.

23.If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.

24.QR is a tangent at Q. PR || AQ where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.

25.In figure tangents PQ and PR are drawn to a circle such that RPQ = 30 °. A chord RS is drawn parallel to the tangent PQ. Find triangle RQS.

[Hint : Draw a line through Q perpendicular to QP.]

26.At the foot of a mountain, the elevation of its summit is 45 °. After ascending 1000 m towards the mountain up a slope of 30 ° inclination, the elevation is found to be 60 °. Find the height of the mountain.

27.The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certian instant the angles of elevation of a balloon from these windows are observed to be 60 ° and 30 ° respectively. Find the height of the balloon above the ground.

28.Coordinates of houses of Sonu and Labhoo are (7, 3) and (4, 3) respectively. The coordinates of their school are (2, 2). If both leave their house at the same time in the morning and also reach school in time then (a) who travel faster and (b) which value is depicted in the question?

29.From a thin metallic piece, in the shape of a trapezium ABCD in which AB || CD and ZBCD = 90 °, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining(shaded) part of the metal sheet. [Use pi = 22/7]

30.The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?

31.The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section made?

**Answers**

** Section A**

**1.Find the value of p which will make the product of 2p – 5 and p – 4 equal in value to p + 8.**

**Ans.**

**2.Which term of the AP 21, 18, 15, … , is zero?**

**Ans.**

**3.Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).**

**Ans.**

**4.If the circumference of a circle exceeds the diameter by pi units, then find the diameter of the circle.**

**Ans.**

** Section B**

**Ans.**

**6.Which term of the sequence 25, 22, 19, … is the first negative term?**

**Ans.**

**7.The incircle of an isosceles triangle ABC, with AB = AC, touches the sides AB, BC and CA at D, E and F respectively. Prove that E bisects BC.**

**Ans.**

**8.Find the probability of getting 53 Mondays in a leap year.**

**Ans.**

**Ans.**

**10.A solid cube is cut into eight cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of one small cube.**

**Ans.**

**Ans.**

** Section C**

**12.The cost price of an article is Rs x and is sold at a profit of (x + 20)%. Find the cost price of the article, if its selling price is Rs (1.4x – 48).**

**Ans.**

**13.Find the sum of all the three-digit numbers each of which leaves a remainder 3, when divided by 7.**

**Ans.**

**14.Construct an isosceles triangle whose base is 6 cm and altitude 5 cm and then another ****triangle whose sides are 4/3 times the corresponding sides of the isosceles triangle.**

**Ans.**

**15.All jacks, queens, kings and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is**

**(i) red face card (ii) a card of spade.**

**Ans.**

**16.A child’s game has 12 triangles of which 4 are blue and rest are green. 8 rectangles of which 5 are green and rest are blue, 10 rhombus of which 7 are blue and rest are green. One piece is lost at random. Find the probability that it is**

**(i) a rectangle**

**(it) a triangle of green colour**

**(iii)a rhombus of blue colour.**

**Ans.**

**17.If P(5, -7), Q(4, 7) and R(6, -3) are the vertices of triangle PQR, M is mid point of QR and A is a point on PM joined PA/PM = 2, find the coordinates of A.**

**Ans.**

**18.If (a, 0), (0, b) and (3, 2) are collinear, show that 2a + 3b – ab = 0**

**Ans.**

**Ans.**

**20.A cone of height 48 cm has a curved surface area of 2200 cm ^{2.} Find its volume.[use pi=22/7]**

**Ans.**

** Section D**

**21. Solve for x :((2x/x) – 3 )+( (1/ 2x) + 3) +((3x + 9)/(x – 3) (2x + 3))=0 x not equal to 3,-3/2**

**Ans.**

**22.Along a road lies an odd number of stones placed at intervals of 20 metres. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 6 km. Find the number of stones.**

**Ans.**

**23.If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.**

**Ans.**

**24.QR is a tangent at Q. PR || AQ where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.**

**Ans.**

**25.In figure tangents PQ and PR are drawn to a circle such that RPQ = 30 °. A chord RS is drawn parallel to the tangent PQ. Find triangle RQS.**

**[Hint : Draw a line through Q perpendicular to QP.]**

**Ans.**

**26.At the foot of a mountain, the elevation of its summit is 45 °. After ascending 1000 m towards the mountain up a slope of 30 ° inclination, the elevation is found to be 60 °. Find the height of the mountain.**

**Ans.**

**27.The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certian instant the angles of elevation of a balloon from these windows are observed to be 60 ° and 30 ° respectively. Find the height of the balloon above the ground.**

**Ans.**

**28.Coordinates of houses of Sonu and Labhoo are (7, 3) and (4, 3) respectively. The coordinates of their school are (2, 2). If both leave their house at the same time in the morning and also reach school in time then (a) who travel faster and (b) which value is depicted in the question?**

**Ans.**

**29.From a thin metallic piece, in the shape of a trapezium ABCD in which AB || CD and ZBCD = 90 °, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining(shaded) part of the metal sheet. [Use pi = 22/7]**

**Ans.**

**30.The barrel of a fountain-pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?**

**Ans.**

**31.The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section made?**

**Ans.**

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