CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 7

Section A

1.Rohan’s mother is 26 years older than him. The product of their ages (in years) after 3 years from now will be 360. We would like to find Rohan’s present age.
Represent above situation in the form of quadratic equation.

2.The first and last terms of an AP are 1 and 11 respectively. If the sum of its terms is 36, find the number of terms.

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3.Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (-1, -4).

4.An arc of a circle is of length 5n cm and the sector it bounds has an area of 20tt cm². Find the radius of the circle.

Section B

6.The sum of four numbers in an AP is 0 and their product is 9. Find the numbers.

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

8.Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is more than 8.

9.In the given figure, find the area of the shaded region, where AC = 13 cm, AB = 12 cm, O is centre of the circle and triangle ABC = triangle DAB = 90°.(Use pi =3.14)

10.The diameter of a spherical cannonball is 42 cm. It is melted and recast into a right circular mould, the base of which is 28 cm in diameter. Find the height of the cone

Section C
11.For what value of k, are the roots of the quadratic equation (k – 4)x2 + (k – 4) x + 4 = 0 equal?

12.Solve for x :(x-2/x-4)+(x-6/x-8) = 6 2/3, (x not equal to 4,8)

13.Find the sum of all multiples of 7 lying between 103 and 999.

14.Draw a circle of radius 5 cm. From a point, 12 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

15.Three coins are tossed together. Find the probability of:
(i) getting at most one tail.
(ii) getting at least one tail.

16.Cards marked with numbers 5 to 100 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is:
(i) a perfect square.
(ii) a multiple of 7.
(iii) a prime number less than 25.

17.Determine the ratio in which the point C(p, -3) divides the join of A(-6, 3) and B(2, -9). Also find the value of p.

18.The line segment PQ joining the points P(2, -4) and Q(5, 2) is trisected at the points R(3, a) and S(b, 0). Find the values of a and b.

19.A steel wire when bent in the form of a square encloses an area of 196 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. (Use pi = 22/7)

20.A hemispherical bowl of internal diameter 60 cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 10 cm and height 12 cm. Find the number of bottles necessary to empty the bowl.

Section D
21.Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

22. Sahil repays the total loan of Rs 2,36,000 by paying every month starting with the first instalment of Rs 2000. He increases the instalment Rs 200 every month.
(a)What amount would he pay as the last instalment of loan?
(b)On 5th of every month the amount of instalment is directly transferred from his bank account. Therefore, Sahil ensures sufficient funds in his bank account before 5th of every month. What values are depicted by Sahil in this act?

23.In figure, OP is equal to diameter of the circle. Prove that triangle APB is an equilateral triangle.

24.PAQ is a tangent to the circle with centre O at a point A as shown in figure. If OBA = 35°, find the value of angle BAQ and angle ACB.

27.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where to top touches the ground is 8 m. Find the height of the tree.

28.If the points A(l, -2), B(2, 3), C(-3, 2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.

29.The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in two days (48 hours). [Take pi = 22/7]

30.A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i water displaced out of the cylindrical vessel.
(ii) water left in the cylindrical vessel. [Take pi = 22/7]

31.The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per square metre.

Answers

Section A

1.Rohan’s mother is 26 years older than him. The product of their ages (in years) after 3 years from now will be 360. We would like to find Rohan’s present age.
Represent above situation in the form of quadratic equation.
Ans.

2.The first and last terms of an AP are 1 and 11 respectively. If the sum of its terms is 36, find the number of terms.
Ans.

3.Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (-1, -4).
Ans.

4.An arc of a circle is of length 5n cm and the sector it bounds has an area of 20tt cm². Find the radius of the circle.
Ans.

Section B

Ans.

6.The sum of four numbers in an AP is 0 and their product is 9. Find the numbers.
Ans.

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

Ans.

8.Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is more than 8.
Ans.

9.In the given figure, find the area of the shaded region, where AC = 13 cm, AB = 12 cm, O is centre of the circle and triangle ABC = triangle DAB = 90°.(Use pi =3.14)

Ans.

10.The diameter of a spherical cannonball is 42 cm. It is melted and recast into a right circular mould, the base of which is 28 cm in diameter. Find the height of the cone
Ans.

Section C
11.For what value of k, are the roots of the quadratic equation (k – 4)X² + (k – 4) x + 4 = 0 equal?
Ans.

12.Solve for x :(x-2/x-4)+(x-6/x-8) = 6 2/3, (x not equal to 4,8)
Ans.

13.Find the sum of all multiples of 7 lying between 103 and 999.
Ans.

14.Draw a circle of radius 5 cm. From a point, 12 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Ans.

15.Three coins are tossed together. Find the probability of:
(i) getting at most one tail.
(ii) getting at least one tail.
Ans.

16.Cards marked with numbers 5 to 100 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is:
(i) a perfect square.
(ii) a multiple of 7.
(iii) a prime number less than 25.
Ans.

17.Determine the ratio in which the point C(p, -3) divides the join of A(-6, 3) and B(2, -9). Also find the value of p.
Ans.

18.The line segment PQ joining the points P(2, -4) and Q(5, 2) is trisected at the points R(3, a) and S(b, 0). Find the values of a and b.
Ans.

19.A steel wire when bent in the form of a square encloses an area of 196 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. (Use pi = 22/7)
Ans.

Section D
21.Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Ans.

22. Sahil repays the total loan of Rs 2,36,000 by paying every month starting with the first instalment of Rs 2000. He increases the instalment Rs 200 every month.
(a)What amount would he pay as the last instalment of loan?
(b)On 5th of every month the amount of instalment is directly transferred from his bank account. Therefore, Sahil ensures sufficient funds in his bank account before 5th of every month. What values are depicted by Sahil in this act?
Ans.

23.In figure, OP is equal to diameter of the circle. Prove that triangle APB is an equilateral triangle.

Ans.

24.PAQ is a tangent to the circle with centre O at a point A as shown in figure. If OBA = 35°, find the value of angle BAQ and angle ACB.

Ans.

Ans.

28.If the points A(l, -2), B(2, 3), C(-3, 2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of the parallelogram.
Ans.

29.The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in two days (48 hours). [Take pi = 22/7]
Ans.

30.A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i water displaced out of the cylindrical vessel.
(ii) water left in the cylindrical vessel. [Take pi = 22/7]
Ans.

31.The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per square metre
Ans.

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