CLASS X MID TERM EVALUATION

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1. The diagonals of a rhombus are 16cm and 12cm, in length. The side of rhombus in length is:

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2. If triangles ABC and DEF are similar and AB=4cm, DE=6cm, EF=9cm and FD=12cm, the perimeter of triangle is:

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3. A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

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4. In the figure if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD

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5. In the figure given below DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, the value of x is:

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6. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

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7. The distance of the point P (2, 3) from the x-axis is

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8. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

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9. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is

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10. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

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11. (sin30° + cos30°) – (sin 60° + cos60°)

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12. If cos A = 4/5, then tan A = ?

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13. If sin A + sin2 A = 1, then cos2 A + cos4 A = ?

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14. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

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15. If the height of a tower and the distance of the point of observation from its foot,both are increased by 10%, then the angle of elevation of its top

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16. sin 2A = 2 sin A is true when A =

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17. A circle can have _____parallel tangents at a single time

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18. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to

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19. The length of the tangent from an external point A on a circle with centre O is

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20. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

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

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In Δ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm . Determine the values of sin Q and cos Q.

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The angle of elevation of a tower at a point is 45°after going 40m towards the foot of the tower , the of elevation of the tower becomes 60°. Find the height of the tower.

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In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC, Prove that 9 AD2 =7 AB2

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Prove that

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A straight highway leads to the foot of the tower. A man standing at the top of the tower observes a car at an angle of depression of 30° , which is approaching to the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.Find the time taken by the car to reach the foot of the tower from this point

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CLASS X MID TERM EVALUATION

1. The diagonals of a rhombus are 16cm and 12cm, in length. The side of rhombus in length is:

2. If triangles ABC and DEF are similar and AB=4cm, DE=6cm, EF=9cm and FD=12cm, the perimeter of triangle is:

3. A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

4. In the figure if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD

5. In the figure given below DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, the value of x is:

6. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

7. The distance of the point P (2, 3) from the x-axis is

8. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

9. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is

10. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

11. (sin30° + cos30°) – (sin 60° + cos60°)

12. If cos A = 4/5, then tan A = ?

13. If sin A + sin2 A = 1, then cos2 A + cos4 A = ?

14. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

15. If the height of a tower and the distance of the point of observation from its foot,both are increased by 10%, then the angle of elevation of its top

16. sin 2A = 2 sin A is true when A =

17. A circle can have _____parallel tangents at a single time

18. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to

19. The length of the tangent from an external point A on a circle with centre O is

20. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

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

In Δ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm . Determine the values of sin Q and cos Q.

The angle of elevation of a tower at a point is 45°after going 40m towards the foot of the tower , the of elevation of the tower becomes 60°. Find the height of the tower.

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC, Prove that 9 AD2 =7 AB2

Prove that

Prove that the parallelogram circumscribing a circle is a rhombus

1. The diagonals of a rhombus are 16cm and 12cm, in length. The side of rhombus in length is:

2. If triangles ABC and DEF are similar and AB=4cm, DE=6cm, EF=9cm and FD=12cm, the perimeter of triangle is:

3. A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

4. In the figure if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD

5. In the figure given below DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, the value of x is:

6. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

7. The distance of the point P (2, 3) from the x-axis is

8. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

9. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is

10. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

11. (sin30° + cos30°) – (sin 60° + cos60°)

12. If cos A = 4/5, then tan A = ?

13. If sin A + sin2 A = 1, then cos2 A + cos4 A = ?

14. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

15. If the height of a tower and the distance of the point of observation from its foot,both are increased by 10%, then the angle of elevation of its top

16. sin 2A = 2 sin A is true when A =

17. A circle can have _____parallel tangents at a single time

18. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to

19. The length of the tangent from an external point A on a circle with centre O is

20. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

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

In Δ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm . Determine the values of sin Q and cos Q.

The angle of elevation of a tower at a point is 45°after going 40m towards the foot of the tower , the of elevation of the tower becomes 60°. Find the height of the tower.

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC, Prove that 9 AD2 =7 AB2

Prove that

Prove that the parallelogram circumscribing a circle is a rhombus