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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