HOLI-DAY HOME WORK Class XI Chapter – Straight Lines 1. Show that the line joining (-2, 6) & (4, 8) is perpendicular to the line joining (8, 12) & (4, 24). 2. Find the equation of line passing through the intersection of lines x – 3y +1 = 0; 2x + 5y – 9 =0, and whose distance from origin is 2 units. 3. Using the concept of slope prove that (4, 4), (3, 5) and (-1,-1) forms a right triangle. 4. For the points (a, 0) (0, b) & (3, 4) write the condition of co- linearity. 5. Write the equation of a line cutting equal intercept on co-ordinate axes & passing through (2, 3). 6. Find the foot of perpendicular from (1, 2) on the line 3x + y + 1 = 0. 7. Transform the equation of line 3 x + y – 8 = 0 in (i) slope intercept form (ii) intercept form (iii) normal form. 8. Prove that equation of a line through (a,b) and parallel to Ax + By + C = 0 is A(x-a) + B(y-b)=0 9. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0. 10. The sides of a quadrilateral ABCD are given by x + 2y = 3, x = 1, x – 3y = 4, & 5x + y + 12 = 0 then find angle between diagonal AC & BD. 11. Find the equations of lines through (2, 5) & parallel & perpendicular to the line 2x – 3y = 7. 12. For what value of `p’ the lines 3x + y=2, px +2y – 3 = 0 & 2x – y – 3 =0 are concurrent? 13. Find the image of the point (-8, 12) in the line mirror 4x + 7y + 13 = 0. 14. A line is such that its segment between the lines 5x – y + 4 = 0 & 3x + 4y – 4 = 0 is bisected at (1, 5) find the line. 15. What point(s) on X-axis have perpendicular distance`4’ from the line 4x +3y = 12? 16. Obtain the equations of Medians for the triangle ART whose vertices are A (2, 5), R (-4, 9), T (-2,-1). 17. Is Origin at equidistance from the lines 3x – 4y + 10 = 0, 12x + 5y + 26 = 0 & 24x + 7y + 50 = 0? 18. If `p’ is the perpendicular distance from origin to the line bx + ay = ab, what relation-ship do `a’, `b’ & `p’ hold? 19. For what value of P lines Px + 3y = 4 & 3x – 4y = 7 are perpendicular? 20. Which line passes through (3, 2) making positive intercepts on axes in the ratio 3:4? Chapter –Conic- Sections 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Which circle passes through (0, 0), (0, 4) & (4, 0)? Write the co-ordinates of center and length of radius for a circle passing through (5,-8), (2,-9) & (2, 1). Write the equation of a circle which touches the Y-axis at origin and having center at (3, 0). Find the equation of circle passing through (0,-1) & (2,0) and whose center is on the line 3x + y = 5 Where does the line x + y = 5 touch the circle; x2 + y2 – 2x – 4y + 3 = 0? If parabola y2 = 4ax passes through (3, 4) write the vertex, focus, equation of directrix and length of LatusRectum. Write the vertex, focus, equation of directrix and length of Latus-Rectum for the parabola y = x2 – 2x + 3. Write the equation of parabola having Focus at (2, 3) and directrix x =4. Find the coordinate of a point on parabola y2 = 18x whose ordinate is 3 times the abscissa. If a parabolic reflector is 20cm in diameter and 5cm deep, find its focus. Write the equation of ellipse whose vertices are (±5,0) and foci at (±4,0). Find the equation of ellipse whose vertices are (0, ±5) and eccentricity is 0.8. An arch is in the form of semi-ellipse. It is 8m wide and 2m high at the centre. Find the height of arch at a point 2.5 m away from the centre. Find eccentricity, focus and length of Latus rectum for the ellipse 4x2 + 9y2 = 144. A man is running a race-course noticed that sum of his distances from two flag posts is always 10m and the flag posts are 8m apart. Find the equation of path he is running on. Use the definition of a conic section to find its equation when it is given that directrix is y = x + 3, focus is (-1, 1) and eccentricity is 3. Which conic section it is? Find eccentricity, focus and length of Latus rectum for the hyperbola 9x2 - 16y2 = 144. Find the equation of hyperbola whose conjugate axis is 5 and distance between foci is 13. Find the locus of all such points that difference of its distances from (±4, 0) is always 2. Show that the points (4, 3), (8,-3) & (0, 9) don’t lie on a circle. (C K JAIN) PGT Maths KV Deoli HOLI-DAY HOME WORK Class VIII Chapter- 11(Mensuration) 1. 2. 3. 4. Write the formula to find the area of a parallelogram and rhombus. Find the lateral surface area of a cube of edge 9 cm. 1 Liter = _______ cm3. The parallel sides of a trapezium are 12 m. and 8 m. and the distance between them is 6m. Find the area of the trapezium. 5. A cuboidal wooden block contains 144 cm3 of wood. If it is 8cm long and 6cm wide, find its height. 6. The height of a cylinder is 15 cm. and curved surface area is 660cm2. Find the radius of the cylinder. 7. The total surface area of a cube is 216m2. Find its volume. 8. The diagonals of a rhombus are of length 16 cm and 30 cm. Find its area. 9. The area of a trapezium is 84cm2and the distance between the parallel sides is 8cm. Find the length of the parallel sides if they are in the ratio 3:4. 10.Three cubes, each of edge 2cm long are placed together to form a cuboid. Find the total surface area of the cuboid so formed. 2 2 2 11.The rainfall on a certain day was 12 cm. How many liters of water fell on 3 hectares of land on that day? (1hactare =10000m2) 12.The diameter of a road roller is 80cm, & it is 140cm long. If it takes 600 revolutions to level a playground find the cost of leveling the ground at Rs. 3 per sq meter. 13.A rectangular sheet of aluminium foil is 44 cm. long and 20 cm. wide. A cylinder is made out of it, by rolling the foil along width. Find the volume of the cylinder. 20cm 20cm 44cm 14.The perimeter of the floor of a hall is 250 m. If the height is 4m, find the cost of painting the four walls at the rate of Rs. 12 per square meter. 15.By how many times do the volume and surface area of a cube increase if its edges get doubled? 16.If the edges of a cube are halved, then how many times its volume & TSA become? X Chetan Jain PGT Maths HOLI-DAY HOME WORK Class X Chapter:- Quadratic equations 1. Find the nature of the roots of the following quadratic equations. Also find them if they exists in real. (a) 2x2 – 4x + 3 = 0 1 (b) 3x2 – 2x + 3 = 0 (c) x2 – 9x + 18 = 0 Find the value of `k’ so that x2 + kx +64 = 0 & x2 – 8x + k = 0 has real roots. Two digits are added to give 11, while their squares are added to give 85, find them. If the roots of the equation (a2 + b2)x2 – 2 (ac + bd)x + (c2 + d2) = 0 are equal prove that ad = bc. If roots of the QE. (b – c)x2 + (c – a)x + (a – b) = 0 are equal prove that a,b & c are in A.P. If – 5 is a root of QE. 2x2 + px – 15 = 0 and the QE p(x2 + x) + k = 0 has equal roots, find k. If x2 – ax + 1 = 0 has two real and different roots, then a does not lie between (a) – 1 & 1 (b) -2 & 2 (c) 1 & 2 (d) – 1 & - 2 2 2 2 8. (x + 1) – x has (a) 4 real roots (b) 2 real roots (c) No real roots (d) 1 real root 9. Which is not true: (a) Every quadratic polynomial can have at most 2 zeros (b) Some quadratic polynomial do not have any zero (c) Some quadratic polynomials may have only one zero (d) Every quadratic polynomial has two zeros 10. If a student had walked 1km/hr faster, he would have taken 15 minutes less to walk 3 km. Find the rate at which he was walking. 3km/hr Chapter: - Arithmetic Progression 1. The sum of all natural numbers between 100 & 200 which are divisible by 4 is: (a) 15,000 (b) 10050 (c) 3600 (d)10500 2. If 18, a, b, - 3 are in A.P. what a + b = (a) 12 (b) 15 (c) 16 (d) 11 3. If S1, S2, S3 be the sum of first n, 2n, 3n terms of an A.P., then S3 = (a) 3S2 – S1 (b) S2 – 3S1 (c) 3(S2 – S1) (d) S2 – S1 4. The digits of a three digit number are in AP, their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Then the original number is (a) 285 (b) 528 (c) 852 (d) 825 5. Which is true: I. If the numbers a, b, c, d & e are in AP then a – 4b + 6c – 4d + e = 0 II. If the pth term of an AP is ‘q’ and qth term is ‘p’ then Tp+q = p + q III. 60th term of AP 3, 15, 27, 39, Is 132 more than its 54th term. (a) I only (b) II only (c) III only (d) none is true 6. Find the sum of numbers between 100 & 200 which are not divisible by 9. Ans: 13167 7. Find the sum of numbers between 1 & 200 which are multiple of 2 or 5. Ans: 12250 th th 8. The first term of an AP is 5 and 100 term is – 292. Find its 50 term. Ans: - 142 th th 9. 38 term of an AP is triple of 18 term. Which term is zero in this AP? Ans: 8th 10. Match items in column I to the items of column II correctly. Column I Column II (i) Number of terms in AP 7, 13, 19,…., 205? (a) 676 th (ii) 10 term of the AP 8, 10, 12,…, 126. From end (b) 51 (iii) 4 + 12 + 20 +…. + 100? (c) 108 (iv) T1 = -7, d= 6 and last term = 296 in an AP, then ‘n’ is (d) 34 2. 3. 4. 5. 6. 7. X C h e t a n J a in PGT M a th