KENDRIYA VIDYALAYA HVF AVADI 2014-15
CLASS: X HOLIDAY HOME WORK (QUADRATIC EQUATIONS)
1. Find the roots of (a)
(b)
(c)
2. Using quadratic equation solve (a)
(b)
(c)
3. Without solving find the nature of the roots of the following quadratic equations.
(a)
(b)
(c)
4. For what value of p the given quadratic equation have equal roots?
(a)
(b)
(c)
5. The sum of the squares of two consecutive positive integers is 265. Find the integers.
6. Sum of ages of a mother and her son is 30 years. And product of their ages is 125. Find their ages.
7. The hypotenuse of a right triangle is 4 meter less than twice the shortest side and the third side is 4 meter more than the shortest side, find the sides of the triangle.
8. The speed of the boat in still water is 11km/hr. It can go 12km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.
9. The denominator of a fraction is one less than twice the numerator. If the sum of the fraction and its reciprocal is , find the fraction.
10. The diagonal of a rectangular field is 10m more than the shorter side. If the longer side is 5m more than the shorter side, Find the sides of the field.
ARITHMETIC PROGRESSION
1. If the 8th term of an AP is 31 and 15th term is 16 more than the 11th term. Find the AP.
2. Which term of the AP 5,15,25……will be 130 more than its 31st term.
3. If the 10th term of an AP is 52 and 17th term is 20 more than the 13th term. Find the AP.
4. The sum of 5th and 9th terms of an AP is 72 and the sum of 7th and 12th term is 97. Find the AP.
5. If the pth term of an AP is q and qth term is p, prove that its nth term is (p+q-n).
6. Find the sum of all 3 digit natural numbers which are divisible by 7.
7. How many terms of the series 54,51,48….be taken so that their sum is 513. Explain the double answer.
8. Find the 6th term from the end of the AP 121,117,113,……-40.
9. Which term of the AP 121,117,113,… is its 1st negative term?
10. Find the sum of all 3 digit numbers which leave reminder 3 when divided by 5.
11. If the 5th term is 0, show that its 33rd term is 4 times its 12th term.
12. The sum of the 1st n terms of an AP is given by = 3n2 - 4n. Determine 12th term of the AP.
AREAS RELATED TO CIRCLES
1. Four circular cardboard pieces of radii 7cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
2. An archery target has three regions formed by three concentric circles as shown in fig. if the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.
Fig i Fig ii Fig iii
3. In the fig i given above, find the perimeter of the shaded region where ADC,AEB and BFC are semicircles on diameters AC,AB and BC respectively.
4. In the fig ii given above, ABC is a right triangle right angled at A. Semicircles are drawn on AB,AC and BC as diameters. Find the area of the shaded region.
5. In the fig iii given above, triangle ABC is right angled at B, AB=28cm, BC=21 cm. With AC as diameter semicircle is drawn and BC as diameter a quarter circle is drawn. Find the area of the shaded region.
Fig iv Fig v Fig vi
6. In the fig iv given above, AB=BC=CD and AD=84 cm. Find the area of shaded portion.
7. In the fig v given above, triangle ABC is right angled at A. Find the area of shaded region if AB=6cm, BC=10cm and O is the centre of the in-circle of triangle ABC. (Use π=3.14)
8. In the fig vi given above, if the area of four sectors having same radius is 616 sq.cm. What is the radius?
Fig vii Fig viii
9. In the fig vii given above, if ABCD is a square of side 14√2 cm, find the area of the shaded region.
10. In the fig viii given above, a circular table cover of radius 32cm, a design is formed leaving an equilateral triangle ABC in the middle. Find the area of the design.