Students and Teachers Forum

1. If a+b+c =0, prove that
 1xb+c×1xc+a×1xa+b=1

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2. It is easy to open the lid of a can by using a spoon. Give reason.

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3. Iron cutting scissors have short cutting edges whereas cloth cutting scissors have long edges. Why?

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4. What is wedge? 
What is screw?

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5. What is an inclined plane?

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6. What is pulley? What is its function?

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7. In which class of lever is the effort arm always smaller than the load arm?

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8. If abc = 1, prove that:
 11+a+b-1+11+b+c-1+11+c+a-1=1

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9. What is lever? Give two examples.

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10. What will be the mass of body when 20 N of force is applied on it so that it produces an acceleration of 4 m/s2?

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11. How much force is required to produce an acceleration of 2 m/s2 on a car of mass 1000 kg?

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12. If 20N force is required to lift a 5 kg mass. Find the acceleration produced on the body.

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13. Find the acceleration of car, if its velocity increases from 20 m/s to 50 m/s in 5 seconds.

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14. A bus starts to move from the rest with an acceleration of 0.25 m/s2 . Find its final velocity after 3 minutes.

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15. Bina leaves home on a bicycle and reaches her school in 30 minutes. If the school is 25 km far from her home, calculate the average speed of her bicycle.

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16. Ram takes 2 minutes to cover a distance of 500 meter. Calculate his speed.

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17. In the given figure, ABCD is a cyclic quadrilateral. If ∡FAB = (x+20)⁰ and ∡BCE= (x-20)⁰, find the value of x.

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18. In the given figure, BC = 20cm ∡ABC = 30⁰ and area of ∆ABC is 75 cm2, find the length of AB.

Given, Area of △ABC = 75 cm2  CB = 20 cm AB = ?  Now, Area of △ABC = ( 1 / 2 ) x CB x AB x sinB or, 75 = ( 1 / 2 ) x 20 x AB x sin30o or, 150/20 = AB x ( 1 / 2 ) (∴ sin30o = 1/2) ∴ AB = 15 .....

19. Find the unknown angle:

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20. Find the unknown angle:

Here, ∡PSQ = ∡PRQ = 35o ( angles on the same arc PQ) ​​​​​​​∡PQR = 90o ( inscribed angle made by lines extending from diameter ) In △PRQ x + y + 90o =180o ( sum of interior angles of a triangle .....

21. Find the unknown angle:

In the given circle, Triangle COB is an isosceles triangle because OC = OB ( radius of the circle ) ∡CAB = ∡CDB = 65o ( angles of an isosceles triangle ) ∡CAB + ∡CDB + ∡COB = 180o ( sum of interior angles .....

22. Find the size of unknown angle in the following figures.

Here,  Exterior angle AOB + Interior angle AOB = 360o (complete angle) ∴  Exterior angle ∡AOB = 360o - 140o = 220o Now, ∡ACB = ( 1 / 2 ) of Exterior angle ∡AOB ( circumference angle is half of the centre .....

23. What kind of  object is said to be stationary and what kind of objects is said to be moving?

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24. If the veloctiy of a vehicle starting from rest reaches 5 m/s in 2 second, is the veloctiy of the vehicle uniform? Explain.

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25. In the given diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. If ∡ABC =65⁰ and ∡CED =75⁰, find the value of ∡DCE.


 

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26. A car starts from rest. If the acceleration of the car remains 2 m/s2 for 2 seconds, calculate the final velocity of the car. 

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27. In the given figure, O is the centre of circle. ∡XOY =50⁰, find the value of ∡XZY.

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28. In the given figure, AB =8cm and ∡APB =60⁰. PA and PB are tangents to the circle. Find the length of PA and PB.

Here,  PA = PB ( tangents to the circle originating from the same point are equal ) ∴△PAB is an isosceles triangle so, ∡PAB = ∡PBA = y In △PAB, ∡PAB + ∡PBA + ∡APB = 180o ( sum of interior .....

29. In the given figure, find the area of ∆DCE in which AB//DE, AD//BE, AB =8cm, DC = 8cm and ∡CDE = 30⁰.

Given, DC = 8 cm DE = 8 cm  ∡CDE = 30o ∴ Area of triangle DCE = ( 1 / 2 ) x DC x DE x sin(∡CDE)                                       .....

30. If a car travels 5 km in 5 minutes, what distance does it travels in 1 second?

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31. Find the value of x and y of the circle.

From the figure, OB = OC ( radius of a circle) ∴ OBC is an isosceles triangle i.e ∡OBC =  ∡OCB In ▲OBC, x + 64o + 64o  = 180o (sum of interior angles of a triangle) or, x = 180o - .....

32. Find the area of the given figure.

The above figure consists of two shapes: A triangle at left and a rectangle at right. First for the triangle: Base ( b ) = 11 - 9 = 2 cm. Height ( h ) = 6 cm. Area of the triangle = 1/2 x b x h               .....

33. What is a variable motion? Explain it with an example.

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34. Find the area of the given quadrilateral ABCD in which ∡DBC = 60o, AB = AD, BC = CD = 8 cm and AC = 12 cm.

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35. In the figure, I is the centre of the circle. PM and PN are two circle. PM and PN are two tangents. If ∡MIN =158⁰, find ∡MPN.

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36. Write down the difference between vector quantity and scalar quatity with example.

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37. In the given diagram, ABCD is a parallelogram. AB = 8 cm, BF =5 cm ∡ADC = 100⁰ and ∡CBF = 20⁰. Find the area of parallelogram ABCD.

 

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38. Why is speed called a scalar quantity?

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39. What are the various effects of the force? Explain.

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40. Define:
a. Velocity                     b. Uniform-velocity
c. Variable-velocity       d. Objects at rest
e. Object in motion

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41. How does friction occur?

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42. Why can the moon not escape from the earth?

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43. What is relative velocity?

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44. In the given figure, ABCD is a kite. If the diagonals AC and BD intersect each other at O making 90o, find area of the kite ABCD.

 

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45. Find the volume of the figure given below.

Height of pyramid ( hp ) = 15 cm. Height of cuboid ( hc ) = 6 cm Length of cuboid ( lc ) = breadth of cuboid ( bc ) = 12 cm  Volume of upper pyramid ( Vp ) = ( 1 / 3 ) x length x breadth       .....

46. What are rest and motion?

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47. The volume of water in a measuring cylinder is 100cm3. On immersing a brick compeletely in water, the level rises to 120cm3. Calculate the volume of the brick.

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48. In the given figure, two circles are intersecting at M and N. PQ and RS pass through M. If R, P, S and Q are joined to N, prove that ∠PNR =∠SNQ.
 
 

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49. Explain an experiment to measure the volume of an irregular solid.

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50.  Line segments TQ and TR are equal in length. Prove that PQ = SR and PR = QS.

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