**CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 6**

** Section A**

2.If the sum of first m terms of an AP is 2m^{2} + 3m, then what is its second term?

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3.Find the value of a so that the point (3, a) lies on the line represented by 2x – 3y – 5.

4.If the diameter of a semicircular protractor is 14 cm, then find its perimeter, [pi = 22/7]

** Section B**

5.For what value of p, does the quadratic equation 25 X^{2} + 10 px + 9 = 0 have equal roots?

6.If 5th term of an AP is zero, show that 33rd term is four times its 12th term.

7.In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P,tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

8.21 cards numbered, 1, 2, 3, … 21 are put in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card is a perfect square.

9.Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 28 cm x 14 cm. Find the area of the remaining cardboard. (Use pi = 22/7)

10.A granary is in the shape of a cuboid of size 10 m x 8 m x 4 m. If a bag of grain occupies a space of 0.75 m^{3}, how many bags can be stored in granary?

** Section C**

11.300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

12.Solve for x : 12X^{2} – 6(a^{2} + b^{2})x + 3a^{2}b^{2} = 0.

13.In an AP the sum of first ten terms is -150 and the sum of its next ten terms is -550. Find the AP.

14.Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then construct another triangle whose sides are 3/4 times the corresponding sides of the isosceles triangle.

15.A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is

(i) a card of heart or a king.

(ii) a black queen.

(iii) neither an ace nor a jack.

(iv) either an ace or a jack.

16.Card marked with numbers 1, 2, 3, … 23 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that

(i) number on the card is divisible by 4 (ii) number is divisible by 3 and 2.

17.If the points (-1, 2), (p, q) and (5, 0) are collinear and p – q – 2 then find the values of p and q.

18.Find the coordinates of two points which divide the line segment joining (1, -4) and (-5, -7) into three equal parts.

19.Find the area of the shaded region in fig, if AB = 80 cm, BC = 60 cm and O is the centre of the circle. (Use pi = 3.14)

20.A hemispherical bowl of internal radius 18 cm is full of water. Its contents are emptied in a cylindrical vessel of internal radius 12 cm. Find the height of water in the cylindrical vessel.

** Section D**

21.A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ? 90, find the number of articles produced and the cost of each article.

22.315 logs are stacked in the following manner. 25 logs in the bottom row, 24 in the next row, 23 in the row next to it and so on. In how many rows the 315 logs are placed and how many logs are in the top row?

23.In the figure, a circle is inscribed in a quadrilateral ABCD in which B = 90°. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r) of the circle.

24.AB is a diameter of a circle. AH and BK are perpendicular from A and B respectively to the tangent at P. Prove that AH + BK = AB.

25.For the inauguration of the Eco friendly week in a school, badges were given to volunteers. Neelu made these badges in the shape of a triangle with a circle inscribed in it (as shown in figure). A message supporting tree plantation was written in the circle. If BD = 6 cm, CD = 8 cm and AE = 3 cm,

(a)find the length of AB and AC.

(b)what values are imbibed by having such week in the school?

26.A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.

27.Two boats approach a lighthouse in mid-sea from opposite directions. The angles of elevations of the top of the lighthouse from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the lighthouse.

28.The three vertices of a parallelogram ABCD are A(3, -4), B(-1, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of ABCD.

29.Find the area of the shaded region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre.

30.A tent consists of a frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)

31.A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it and spread all around to a width of 5 m to form an embankment. Find the height of embankment.

**Answers**

** Section A**

**Ans.**

**2.If the sum of first m terms of an AP is 2m ^{2} + 3m, then what is its second term?**

**Ans.**

**3.Find the value of a so that the point (3, a) lies on the line represented by 2x – 3y – 5.**

**Ans.**

**4.If the diameter of a semicircular protractor is 14 cm, then find its perimeter, [pi = 22/7]**

**Ans.**

** Section B**

**5.For what value of p, does the quadratic equation 25 X ^{2} + 10 px + 9 = 0 have equal roots?**

**Ans.**

**6.If 5th term of an AP is zero, show that 33rd term is four times its 12th term.**

**Ans.**

**7.In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P,tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.**

**Ans.**

**8.21 cards numbered, 1, 2, 3, … 21 are put in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card is a perfect square.**

**Ans.**

**9.Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 28 cm x 14 cm. Find the area of the remaining cardboard. (Use pi = 22/7)**

**Ans.**

**10.A granary is in the shape of a cuboid of size 10 m x 8 m x 4 m. If a bag of grain occupies a space of 0.75 m ^{3}, how many bags can be stored in granary?**

**Ans.**

** Section C**

**11.300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.**

**Ans.**

**12.Solve for x : 12X ^{2} – 6(a^{2} + b^{2})x + 3a^{2}b^{2} = 0.**

**Ans.**

**13.In an AP the sum of first ten terms is -150 and the sum of its next ten terms is -550. Find the AP.**

**Ans.**

**14.Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then construct another triangle whose sides are 3/4 times the corresponding sides of the isosceles triangle.**

**Ans.**

**15.A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is**

**(i) a card of heart or a king.**

**(ii) a black queen.**

**(iii) neither an ace nor a jack.**

**(iv) either an ace or a jack.**

**Ans.**

**16.Card marked with numbers 1, 2, 3, … 23 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that**

**(i) number on the card is divisible by 4 (ii) number is divisible by 3 and 2.**

**Ans.**

**17.If the points (-1, 2), (p, q) and (5, 0) are collinear and p – q – 2 then find the values of p and q.**

**Ans.**

**18.Find the coordinates of two points which divide the line segment joining (1, -4) and(-5, -7) into three equal parts.**

**Ans.**

**19.Find the area of the shaded region in fig, if AB = 80 cm, BC = 60 cm and O is the centre of the circle. (Use pi = 3.14)**

**Ans.**

**20.A hemispherical bowl of internal radius 18 cm is full of water. Its contents are emptied in a cylindrical vessel of internal radius 12 cm. Find the height of water in the cylindrical vessel.**

**Ans.**

** Section D**

**21.A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ? 90, find the number of articles produced and the cost of each article.**

**Ans.**

**22.315 logs are stacked in the following manner. 25 logs in the bottom row, 24 in the next row, 23 in the row next to it and so on. In how many rows the 315 logs are placed and how many logs are in the top row?**

**Ans.**

**23.In the figure, a circle is inscribed in a quadrilateral ABCD in which B = 90°. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r) of the circle.**

**Ans.**

**24.AB is a diameter of a circle. AH and BK are perpendicular from A and B respectively to the tangent at P. Prove that AH + BK = AB.**

**Ans.**

**25.For the inauguration of the Eco friendly week in a school, badges were given to volunteers. Neelu made these badges in the shape of a triangle with a circle inscribed in it (as shown in figure). A message supporting tree plantation was written in the circle. If BD = 6 cm, CD = 8 cm and AE = 3 cm,**

**(a)find the length of AB and AC.**

**(b)what values are imbibed by having such week in the school?**

**Ans.**

**26.A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.**

**Ans.**

**27.Two boats approach a lighthouse in mid-sea from opposite directions. The angles of elevations of the top of the lighthouse from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the lighthouse.**

**Ans.**

**28.The three vertices of a parallelogram ABCD are A(3, -4), B(-1, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of ABCD.**

**Ans.**

**29.Find the area of the shaded region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre.**

**Ans.**

**30.A tent consists of a frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)**

**Ans.**

**31.A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it and spread all around to a width of 5 m to form an embankment. Find the height of embankment.**

**Ans.**