Download Formula Book for Class 10 Maths and Sciece

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2

                                                        Section A

1.Determine whether the given value of x is a solution of the given quadratic equation or not:
6X2 – x – 1 = 0; x =1/2.

2.Find 15th term of the AP with second term 11 and common difference 9.

3.Find the coordinates of the point which divides the line segment joining the points (3, 5) and (7, 9) internally in the ratio 2 : 3.

4.In a circle of radius 21 cm, an arc subtends an angle of 60 ° at the centre. Find the length of the arc.

                                                          Section B

5.Using quadratic formula, solve the following quadratic equation: 2X2 – 7x + 3 = 0

6.Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

7.A point P is 18 cm from the centre of a circle. The radius of the circle is 12 cm. Find the length of the tangent drawn to the circle from the point P.

8.In a box, there are 800 bulbs, out of which 20 bulbs are defective. One bulb is taken out at random. Find the probability that the bulb is not defective.

9.The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of these two circles.

10.A rectangular solid metallic cuboid 18 cm x 15 cm x 4.5 cm is melted and recast into solid cubes each of side 3 cm. How many solid cubes can be made?

                                                                     Section C

11.Divide 39 into two parts such that their product is 324.

12.Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

13.Solve for x:(1/  x + 4 )-(1/x-7 )=11/30,  (x not equal to  -4, 7 )

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

15. 21 cards are numbered 1, 2, …, 20, 21 and placed in a box. The cards are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) an even                                                                     (ii) a prime number                                                                           (iii) divisible by 4

16.A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.

17.Find the value of k if the points A(2,3), B(4, k) and C(6, -3) are collinear.

18.Find the value of k, if the point P(2,3) is equidistant from the points A{k, 1) and B(7, k).

19.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.  (Take pi =22/7)

20.A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 14 cm, find the area of material used for  making it. (Take pi =22/7)

                                                                  Section D

21. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age in  years. Find their present ages.

22. A manufacturer of TV sets produced 600 units in the third year and 700 units in the 7th year. Assuming that  the production increases uniformly by a fixed number every year, find
(i) the production in the first year,     (ii) the production in the 10th year,
(iii) the total production in 7 years

23.A circle is inscribed in AABC having sides AB = 8 cm, BC = 7 cm and AC = 5 cm. Find AD, BE and CF
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-40jpg_Page1

24.In figure, given below, XP and XQ are tangents from X to the circle with centre O and ARB is tangent at point R. Prove that XA + AR = XB + BR
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-41jpg_Page1

25.If O be the centre of a circle and tangents drawn to the circle at the points A and B of the circle intersect each other at P, then prove that angle AOB + angle APB = 180 °.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-42jpg_Page1

26.An electric pole is 12 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 60 ° with the horizontal through the foot of the pole, find the length of the wire. (Take root 3 =73)

27.The angle of elevation of the top of a tower from a point on the ground is 45 °. On walking 30 metres towards the tower, the angle of elevation becomes 60 °. Find the height of the tower and the original distance from the foot of the tower. (Take root 3 = 1.73)

28.Find the length of the median through the vertex A(5, 1) drawn to the triangle ABC where other two vertices are B(l, 5) and C(-3, -1).

29.Find the area of the shaded region in figure if ABCD is a square of side 20 m and APD and BPC are semicircles. (Take pi =22/7)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-43jpg_Page1
If shaded region is used by society for planting trees, then what value is reflected?

30.A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm respectively and the height of the cylindrical part of the solid is 3.5 cm, find the volume  of the solid. (Take pi =22/7)

31.A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height  of the toy is 15.5 cm. Find the total surface area of the toy. (Take pi =22/7)

Answers

                                                                Section A

1.Determine whether the given value of x is a solution of the given quadratic equation or not:  6X2 – x – 1 = 0; x =1/2.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-1

2.Find 15th term of the AP with second term 11 and common difference 9.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-2jpg_Page1

3.Find the coordinates of the point which divides the line segment joining the points (3, 5) and (7, 9) internally in the ratio 2 : 3.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-3jpg_Page1

4.In a circle of radius 21 cm, an arc subtends an angle of 60 ° at the centre. Find the length of the arc.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-4jpg_Page1

                                                          Section B

5.Using quadratic formula, solve the following quadratic equation: 2X2 – 7x + 3 = 0
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-5jpg_Page1

6.Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-6jpg_Page1

7.A point P is 18 cm from the centre of a circle. The radius of the circle is 12 cm. Find the length of the tangent drawn to the circle from the point P.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-7jpg_Page1

8.In a box, there are 800 bulbs, out of which 20 bulbs are defective. One bulb is taken out at random. Find the probability that the bulb is not defective.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-8jpg_Page1

9.The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of these two circles.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-9jpg_Page1

10.A rectangular solid metallic cuboid 18 cm x 15 cm x 4.5 cm is melted and recast into solid cubes each of side 3 cm. How many solid cubes can be made?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-10jpg_Page1

                                                                     Section C

11.Divide 39 into two parts such that their product is 324.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-11jpg_Page1

12.Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-12jpg_Page1

13.Solve for x:(1/  x + 4 )-(1/x-7 )=11/30,  (x not equal to  -4, 7 )
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-13jpg_Page1

14.Draw a triangle ABC with side BC = 7 cm, B = 45 °, A = 105 °. Then construct a triangle whose sides are 4/3  times the corresponding sides of triangle ABC.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-14jpg_Page1

15. 21 cards are numbered 1, 2, …, 20, 21 and placed in a box. The cards are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) an even                                                                     (ii) a prime number                                                                           (iii) divisible by 4
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-15jpg_Page1

16.A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-16jpg_Page1

17.Find the value of k if the points A(2,3), B(4, k) and C(6, -3) are collinear.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-17jpg_Page1

18.Find the value of k, if the point P(2,3) is equidistant from the points A{k, 1) and B(7, k).
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-18jpg_Page1

19.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.  (Take pi =22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-19jpg_Page1

20.A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 14 cm, find the area of material used for  making it. (Take pi =22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-20jpg_Page1

                                                                  Section D

21. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age in  years. Find their present ages.
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-21jpg_Page1
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-21ajpg_Page1

22. A manufacturer of TV sets produced 600 units in the third year and 700 units in the 7th year. Assuming that  the production increases uniformly by a fixed number every year, find
(i) the production in the first year,     (ii) the production in the 10th year,
(iii) the total production in 7 years
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-22jpg_Page1

23.A circle is inscribed in AABC having sides AB = 8 cm, BC = 7 cm and AC = 5 cm. Find AD, BE and CF
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-40jpg_Page1
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-23jpg_Page1
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-23ajpg_Page1

24.In figure, given below, XP and XQ are tangents from X to the circle with centre O and ARB is tangent at point R. Prove that XA + AR = XB + BR
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-41jpg_Page1
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-24jpg_Page1

25.If O be the centre of a circle and tangents drawn to the circle at the points A and B of the circle intersect each other at P, then prove that angle AOB + angle APB = 180 °.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-42jpg_Page1
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-25jpg_Page1

26.An electric pole is 12 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 60 ° with the horizontal through the foot of the pole, find the length of the wire. (Take root 3 =73)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-26jpg_Page1

27.The angle of elevation of the top of a tower from a point on the ground is 45 °. On walking 30 metres towards the tower, the angle of elevation becomes 60 °. Find the height of the tower and the original distance from the foot of the tower. (Take root 3 = 1.73)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-27jpg_Page1
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-27ajpg_Page1

28.Find the length of the median through the vertex A(5, 1) drawn to the triangle ABC where other two vertices are B(l, 5) and C(-3, -1).
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-28jpg_Page1

29.Find the area of the shaded region in figure if ABCD is a square of side 20 m and APD and BPC are semicircles. (Take pi =22/7)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-q-43jpg_Page1
If shaded region is used by society for planting trees, then what value is reflected?
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-29jpg_Page1

30.A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm respectively and the height of the cylindrical part of the solid is 3.5 cm, find the volume  of the solid. (Take pi =22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-30jpg_Page1
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-30-ajpg_Page1

31.A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height  of the toy is 15.5 cm. Find the total surface area of the toy. (Take pi =22/7)
Ans.
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2-31jpg_Page1

Class 10 MathsScienceSocial ScienceSanskritEnglishEnglish CommunicativeComputer ScienceHindi

(Download Questions PDF)

Download (PDF, 2.41MB)

(Download Solutions PDF)

Download (PDF, 5.71MB)