Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

Question Bank Age Group 14-15 - III

1. A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 meters, what is the width of the river?

2. If 4tanθ = 5, evaluate

.

3. The variance of 65 scores is 64. If each of them is divided by 2, find the Standard Deviation and Variance of the new scores.

4. A natural number less than or equal to 25 is chosen.  What is the probability that it is a multiple of 5?

5. Prove that the angle bisectors of the angles of a triangle are concurrent.

6. In triangle ABC, angle C is a right angle, P is a point on AB and N is a point on BC. If AP=3 cms, PB=4 cms, CN=x cmx and PN=y cms, show that

.

7. Two dices are cast together. Find the probability of the two digit number formed with the numbers turning up on their faces is a multiple of 7 or 5.

8. Prove that

.

9. If cosec A = √2, show that

.

10. Find the equation of the line through the point of intersection of the lines 2x+y-5 = 0, x+y-3 = 0 and bisecting the line segment joining the points (3,-2) and (-5,6).

11. Find the circumcenter of the triangle whose vertices are A(4,2), B(3,1), and C(3,3).

12. Find the equation of the line passing through (-3,10) and making intrcepts a,b on the X, Y axis respectively whose sum is 8.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.