Practice Assignment For CBSE Class X Mathematics Board Examination 2009-10

Practice Assignment No. 3

Q. 1. Prove that √2 is irrational.

Q. 2. Divide 2x⁴ + x³ -14x²-19x-6 by x² +3x +2 and verify the division logarithms.

Q. 3. For what value of k, the following pair of linear equations has infinite many solutions

10x +5y-(k-5) = 0,, 20x + 10y –k = 0

Q. 4. The sum of a two digit no. and no. obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

Q. 5. Solve the following quadratic equation :  ax² + (4a² – 3b)x-12ab = 0

Q. 6. The sum of n terms of A.P. is 5n^2- 3n.Find the A.P it’s nth term and find its 10^th term.

Q. 7. State and prove Pythagoras Theorem.

Q. 8. In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9AD² = 7AB².

Q. 9. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).

Q. 10. Find the area of the triangle formed by joining the midpoints of the sides of the    triangle whose vertices are (0,-1), (2, 1) and (0, 3).Find the ratio of the triangle formed to area of the given triangle.

Q. 11. Evaluate :  (Sin²25 + Sin²65) +√3(tan 5 tan 15 tan 30 tan 75 tan 85)

Q. 12. Prove  :  (1 + cot θ - cosec θ)(1+ tan θ + sec θ) = 2

Q. 13. From a point on a bridge across a river, the angles of depression of the banks on opposite sides of rivers are 30 and 45 respectively. If the bridge is at a height of 3 meter from the banks. Find the width of the river.

Q. 14. Draw a pair of tangents to a circle of radius 4 cm and which are inclined to each other at 60º.

Q. 15. Water in a canal 30dm wide and 12m deep is flowing velocity of 10 km/hr. How much area will it irrigate if 8 cm of standing water is required for irrigation?

Q. 16. A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the circles, it is just immersed as shown in figure .What friction of water flows over?

Q. 17. Draw both type of Olive Curve on the same graph paper and then determine the median

Q. 18. Two dices are thrown simultaneously. Find the probability of getting:

1. sum more than 7
2. a sum less than 7
3. a doublet.

Q. 19. What is the distance between two parallel tangents of a circle of radius 4 cm?

Q. 20. Find the area of quadrant of a circle whose circumference is 49 cm.