MONTH: AprilD.A.V.PUBLIC SCHOOL, THERMAL COLONY PANIPAT ASSIGNMENT NO 1 CLASS: IX TOPIC: NUMBER SYSTEM NAME:M.M 1: Find 5 rational numbers between 3 and 4. 2: Find 3 rational numbers lying between - 3 and –1 7 7 3: Classify the following numbers as rational or irrational: (i) 2 -√5 (ii) (√2 +√3) (√2 -√3) (iii) 2π (iv) (3√3) (2√27) 4: Represent 2 +√ 3 on the number line. 5: Find the three different irrational numbers between 5 and 9 7 11 6.: Represent √ 9.37 on the number line. 7.: Express 2√2 + 3√3 with rational denominator. 2- √2 +√3 8.: Solve for x and y (i) (25) x = 5y-1 and (32) y = 4× 8x (ii) (3)4x+1 = 1 x+1 9 9.: Find the value √a + 1 when a = 7 - 4√3 √a 10: If x = √3 +√2 and y = √3 - √2 , determine x2 + y2 √3 - √2 √3 +√2 11.Express the following with rational denominator. 1 √6 + √5 - √11 12.If ax = by =cz and b2 = ac, prove that 1 + 1 = 2 x z y V. find the value of y. 14 Which of the following points will lie on x-axis and y-axis? A(1. find k. Find one more solution. 5 For what value of k is 2x3+10x2+11x+k+3 is exactly divisible by 2x –1.0). x ≠ -2. 3 If the polynomials ax3+4x2+3x-4 and x3-4x+a leave the same remainder when divided by (x-3).D. 2 2 (361) – (361 × 139) + (139) 12 Factorise using factor theorem: (i) x3 + 6x2 + 11x + 6 (ii) x3 – 8x2 + 17x – 10 13 Draw a quadrilateral whose vertices are (i) (1.-1). THERMAL COLONY PANIPAT ASSIGNMENT NO 2 CLASS IX TOPIC: POLYNOMIAL & LINEAR EQUATION IN TWO VARIABLES MONTH: May NAME: M. (2. find the values of a & b 7 Give possible expressions for length and breadth of the following rectangles.-2) and (-4.0). H(0. when y = -7x 6 4 9 2 (ii) x + 5x + 6 = 3x + 1.M 1 Factorise: (i) m8-11m4n4-80n8 (iii) x4 + 17x2y2 – 84y4 (v) m6 + n6 (vii) x4 + x2 + 1 (ix) 1 p3 – 8q3 216 (xi) (p –q) 3 + (q-r)3 + (r-p)3 (ii) 8(a+1)2 + 2(a+1)(b+2) –15(b+2)2 (iv) (x2+x)2 + 4(x2+x)-12 (vi) a3 – b3 + 1 + 3ab (viii) x4 + 2x3y – 2xy3 – y4 (x) a3 – 8b3 +64c3 +24abc 2 If (x –1) is a factor of p(x) = 2x2 +kx +√2.2) (-6. (i) Area: 25a2 – 35a+12 (ii) area: 35y2+13y-12 3 3 3 8 If a + b +c = 3abc and a + b + c = 0.-7). C(0.-6).(i) If x + 5 – x + 3 = x + 1. 6 If ax3+bx2+x-6 has x+2 as a factor and leaves a remainder 4 when divided by (x – 2).A. Find the co. (8.1). y = 1] as well as [x = 4. How many such solutions can we find? 16 Draw a graph of the line 3x + y = 6.1). B(1. 15 Show that [x = 1. if x – y = 10 and xy = 5 9 3 10 Prove that if p = 2-a then a3 + 6ap +p3 – 8 = 0 11 Evaluate: (361)3 + (139)3 .4). 4 For what values of a & b.ordinate of the points at which axes 17 Draw a graph of: (i) x – 10 = y – 3 (ii) y – 2 = x + 5 3 7 18 Solve for x:.1).-2).0). y = -1] is a solution of the equation 2x + y = 7.1). (-4. E(-1.4) and (10. G(4.PUBLIC SCHOOL. show that (b+ c)2 + (c + a)2 + (a + b)2 = 1 3bc 3ac 3ab 9 Find the value of x3 – y3. find the value of a. the polynomial x4+ax3+2x2-3x+b is exactly divisible by (x-1) and (x+1). (ii) (-2.0). F(0. D(0. 2 x2 + 4x +4 5x – 2 5 this line intersects the . A. Find ∠ POQ.∠ C 2.∠ B. find ∠ A. 8 . TRIANGLES CLASS : IX SUB: MATHS NAME: M. PO & OQ are angle bisectors of ∠ BPQ & ∠ DQP respectively. AB║CD . S is any point on the side QR. Show that PQ + QR + RP >2PS. A P B O C Q 3 . 6. PQRS is a quadrilateral in which diagonals PR and QS intersects in O. Prove that the other sides of the quadrilateral are equal.Prove that in a triangle. angles opposite to equal sides are equal.PUBLIC SCHOOL. THERMAL COLONY PANIPAT ASSIGNMENT NO: 3 TOPIC: LINES & ANGLES .MONTH: July D. prove that the bisectors of the interior angles intersect each other at right angles.If two parallel lines are intersected by a transversal. If in ∆ ABC .In given fig. In the given figure .M 1. In ∆ PQR.V.points M and N of opposite sides AB and DC of quadrilateral ABCD is perpendicular to both these sides.The side BC of ∆ ABC is produced. 2 Q R D T S 4 . If the bisector of the vertical angle of a triangle bisects the base of the triangle. 2 ∠ A =3 ∠ B = 6 ∠ C . 10. Prove that AD < ( AB + BC + CA) . such that D is on ray BC.PQ is the transversal . 11 . D is any point on BC. M A B N 9.∠ R).In given figure the line segment joining the mid. Show that: (i) PQ + QR + RS + SP > PR + QS (ii) PQ +QR+RS +SP< 2 (PR + QS) D C . 5 . Prove that ∠ ABC +∠ ACD = 2∠ ALC.Using above theorem show that each angle of an equilateral triangle is of 60°. The bisectors of ∠ A meets BC in L. then the triangle is isosceles. In the given figure. if PS is bisector of ∠ QPR and PT ⊥QR. show that : P ∠ TPS = 1 (∠ Q . A B D C 7 . point of CD. 5. If L is the mid-point of BC. P is the mid-point of side AB of a parallelogram ABCD. THERMAL COLONY PANIPAT ASSIGNMENT NO: 4 TOPIC: QUADRILATERALS CLASS: IX SUB: MATHS MONTH:AUGUST NAME: M. CP ║ AB and AP is the bisector of exterior ∠ CAD of ∆ ABC. Q and R are. 6. 2 2.M 1. AO and BO are the bisectors of ∠ A and ∠ B respectively. Prove that (i) AR = 2BC (ii) BR = 2BQ.D. Prove that the angle bisectors of a parallelogram form a rectangle.PUBLIC SCHOOL. A line through B parallel to PD meets DC at Q and AD produced at R. prove that P is the mid. P is a point on AD such that AP = 1 AD and Q is a point such that CQ = 1 BC. 11. BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. 4. CR and PQ meet at Y. 2 A B E F D C 10. ABCD is a trapezium in which side AB is parallel to side DC and E is the mid-point of side AD. 3 3 . Prove that ∠ APB = 90° . P. respectively the mid – points of sides BC. prove that LM = LN. Prove that XY = 1 BC 4 7. ABC is an isosceles triangle in which AB = AC.In a parallelogram ABCD . 3. ABCD is a parallelogram. Prove that EF = 1 ( AB + DC).A. If the bisectors AP and BP of the angles A and B respectively meet at P on CD. Prove that ∠ AOB = 1 ( ∠ C + ∠ D). the bisectors of adjacent angles A and B intersect each other at P. 9. .V. In parallelogram ABCD. D A B B C 8. such that EF is parallel to side DC. If F is a point on the side BC. Prove that AD = 2AB. In the given figure. In a quadrilateral ABCD. CA and AB of a triangle ABC. the bisector of ∠ A also bisects BC at X. PR and BQ meet at X. ABCD is a parallelogram and ∠ DAB = 60°. Prove that ∠ PAC = ∠ BCA and ABPC is parallelogram. Prove that AQCP is a parallelogram. 75% or above (iv) less than 65% marks . 92. if 5 is subtracted from each number.MONTH: August D. 87. Determine the class size. 35. Convert it into a frequency distribution table Marks Below 45 Below 60 Below 75 Below 90 Below 105 Below 120 No of students 0 8 23 48 85 116 4 Find the arithmetic mean and median of first ten prime numbers.20 20 -25 No of students 2 6 13 17 11 Prepare a cumulative frequency table. 2. find the new mean. (ii) Marks between 70% and 80% (iii) A distinction i. THERMAL COLONY PANIPAT ASSIGNMENT NO . the class limits and the true class limits. 2. 4. 11 A die is thrown 1000 times with the following frequencies for the outcomes 1. Find p and q. 8 Find p. 8.15 15 . If 92 is replaced by 99 and 41 by 43. 5. 14 from their mean. 52. 64. 57.A. x 15 17 19 20 + p 23 f 2 3 4 5p 6 9 The mean of 1. 4 and 4 is m. 3. 62. 3. 3.PUBLIC SCHOOL. 33. 90. Outcome No head One head Two head Three head Frequency 14 38 36 12 compute the probability of (i) 2 heads coming up (ii) 3 heads coming up (iii) At least one head coming up (iv) getting more heads then tail (v) getting more tails then heads 13 The percentage of marks obtained by a student in monthly unit test are given below: Unit test I II III IV V % of marks 58 64 76 62 85 Find the probability that the student gets: (i) A first class i. at least 60% marks.e. 2. Find the correct mean.72. 4. 25 – 30 4 3 A cumulative frequency distribution is given below.G 1 The class marks of a distribution are: 47. 55. 10 Find the median of the following observations: 46. 58. Later on it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. 67. 3 and p have mean (m – 1) and median q.7 TOPIC: STATISTICS & PROBABILITY CLASS: IX NAME: R. 6 The mean of 10 numbers is 20.V. The observations 3. 41. 5 Find the sum of the deviations of the variety values 3. find the new median. 77. 6.5 5 – 10 10 . 4. 7.e. 5 and 6 as given Below: Outcome 1 2 3 4 5 6 Frequency 179 150 157 149 175 190 Find the probability of (i) A prime number (ii) An even number (iii) An odd number (iv) A composite number 12 Three coins are tossed simultaneously 100 times with the following frequencies . 7 The mean of 200 items was 50. if the mean of the following distribution is 20. 2 The marks scored by 55 students in a test are given below: Marks 0 . M 1. 3 .5cm and ∠ B = 45° 12 Construct a right-angled triangle whose perimeter is equal to 10cm and one acute angle equal to 60° .PQ and RS are two parallel chords of a circle whose center is O and radius is 10cm. find the distance between PQ and RS. The cost paint 1cm2 of the surface is 7paise.A.5 CLASS: IX TOPIC: AREA.PUBLIC SCHOOL. Given ∠ CBE = 65°. 15 .point of AB. THERMAL COLONY PANIPAT ASSIGNMENT NO . 9 . CIRCLE AND CONSTRUCTION NAME:M. EBCF is a parallelogram and D is the mid-point of BC.circular sheet of metal of diameter 28cm is bent into an open conical cup. If PQ = 16cm.Chord ED is parallel to diameter AC of the circle..V. Show that BC is the radius of the circumcircle of ∆ ABC. Find its volume.ABC is an equilateral triangle in which ∠ BAC = 30°. if they lie (i) On the same side of the center (ii) On the opposite side of center 7 . 13. Show that ar (∆ BPQ) = 1 ar(∆ ABC) 2 6 . (Take π = 22/7) 14 . 11 Construct a ∆ ABC in which BC = 3. D is the mid. 4 . Find the depth and capacity of the cup. P is any point on BC.The internal and external diameter of a hemi. If ar ( ∆ ADC) = 20 cm2. calculate ∠ DEC.In fig. E F 2. AB – AC = 1. A cone of height 24cm has a curved surface area 550cm2.In the fig. CQ║PD meets AB in Q. ∠ P = 45° and∠ Q = 60°. show that ar(∆ AGB) = ar(∆ AGC) = ar(∆ BGC) = 1 ar(∆ ABC) 3 5 .Show that the area of a rhombus is half the product of the lengths of its diagonals.4cm. If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. Find the total cost to paint . RS = 12cm.find area of parallelogram EBCF.What is the measure of x ? C A B 10 Construct a triangle PQR whose perimeter is equal to 14cm.AOB is a diameter of the circle . whose center is O.spherical vessel is 24cm and 25cm respectively.MONTH: October D.If the medians of ∆ ABC intersect at G.A semi. 8 .In ∆ ABC. 60 per m2 is Rs 179.D. The area of the base is 154cm2. find the outer and inner radii of pipe. Find the cost of white washing its curved surface at the rate of Rs 210 per 100m2the vessel all over. 175.An iron pipe 20cm long has exterior diameter equal to 25cm. cm. find the dimensions of the room.A solid cube is cut into two cuboids of equal volumes. 2. find the length of the perpendicular on the side of length 50dm from the opposite vertex. Find the cost of tiling the floor at the rate of Rs 6. The cost of painting is Rs. 9 . Find the difference of their surface area. From inside. find the whole surface of the pipe. If two of its side is 78dm and 50dm. Find the cost of painting the vessel all over. 11 . 6 . 5 . if the sum of their radii is 7. 17.The perimeter of triangular field is 240dm. Find the area of the curved surface.A field in the shape of trapezium whose parallel sides are 25m and 10m. If the pipe is made of 99cm3 of metal.) 16 . 3m wide and 2. 10 . The slant height and base diameter of a conical tomb are 25m and 14m respectively.PUBLIC SCHOOL. 3. If 1 door and 2 windows occupy 8m2. 7 . The non-parallel sides are 14m and 13m.2 per sq. If the thickness of the pipe is 1cm.A. Find the extent to which the level of the field has been raised. . A pit 6m long. If the cost of white washing is Rs 2 per m2 Find the inside surface area of the dome and volume of the air inside the dome.M 1. 8 . The cost of white washing the walls at the rate Rs 1.25 per m2 is Rs.5m deep is dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field.The radius and height of a cone are in the ratio 4:3.6 TOPIC: MENSURATION MONTH: November NAME: M. Find the ratio of the total surface area of the given cube and that one of the cuboids.The difference between outside and inside surfaces of a cylindrical metallic pipe 14cm long is 44cm2.A dome of a building is in the form of a hemisphere. it was whitewashed at cost of Rs 498.The external and internal diameters of a hollow hemispherical vessel are 12cm and 10cm respectively.20.96.80.40 per m2 is Rs 240. The cost of carpeting the room at Rs 3.An agricultural field is in the form of a rectangle of length 20m and width 14m. THERMAL COLONY PANIPAT ASSIGNMENT NO .A room is half as long again as it is broad.Find the radius of a sphere whose surface area is 154 sq. 12.50 and the cost of papering the walls at Rs 1.m.Length of a class room is two times its height and its breadth is 1½ times its height. 4. Find the area of the field.The volume of the two spheres is in the ratio 64:27.V.75 per m2. CP ║ AB and AP is the bisector of exterior ∠ CAD of ∆ ABC. ABCD is a parallelogram and ∠ DAB = 60°. In a quadrilateral ABCD. 9. If diagonals of a quadrilateral bisect each other at right angles. then prove that it is a rhombus. Prove that the angle bisectors of a parallelogram form a rectangle. If the bisectors AP and BP of the angles A and B respectively meet at P on CD.In a parallelogram ABCD . Prove that EF = 1 ( AB + DC). ABC is an isosceles triangle in which AB = AC. Prove that ∠ PAC = ∠ BCA and ABPC is parallelogram.point of CD.M 1. If F is a point on the side BC.A. In parallelogram ABCD. Show that AB + BC + CD + DA > AC + BD.PUBLIC SCHOOL. such that EF is parallel to side DC. 2 2. AO and BO are the bisectors of ∠ A and ∠ B respectively. THERMAL COLONY PANIPAT ASSIGNMENT NO: 4 TOPIC: QUADRILATERALS CLASS: IX SUB: MATHS MONTH:AUGUST NAME: M. 6. the bisector of ∠ A also bisects BC at X. 5. Prove that AD = 2AB. 2 A B E F D C 10. the bisectors of adjacent angles A and B intersect each other at P.V. 4. prove that P is the mid. Prove that ∠ APB = 90° . In the given figure. In quadrilateral ABCD diagonals intersect at O . ABCD is a trapezium in which side AB is parallel to side DC and E is the mid-point of side AD. D A B B C 8.D. Prove that ∠ AOB = 1 ( ∠ C + ∠ D). 3. . where P is power. Work and Energy? 3Q: What is the commercial unit of energy? 4Q:Two bodies have their masses m1/m2 =3 and their kinetic energy E1/E2=1/3 .The ratio of their velocities are? 5Q:Prove that P=F * v . The Power of the motor is? 7Q:State Work Energy theorem? DAV PUBLIC SCHOOL THERMAL POWER COLONY ASSIGNMENT TOPIC.PREETI PANWAR CLASS-9th 1Q: A coolie carries a load of 50kg on his head and walks on a level road up to 100m.A. The Power of the motor is? 7Q:State Work Energy theorem? D.What is the work done by him? 2Q: Give units of Power. ENERGY AND POWER SUBJECT TEACHER . F is force and v is velocity? 6Q:An electric motor creates a tension of 4500N in hoisting a cable and reels at a rate of 2m/s. where P is power. TEACHER.WORK .D. F is force and v is velocity? 6Q:An electric motor creates a tension of 4500N in hoisting a cable and reels at a rate of 2m/s.The ratio of their velocities are? 5Q:Prove that P=F * v .V PUBLIC SCHOOL THERMAL COLONY PANIPAT ASSIGNMENT TOPIC.WORK .IX SUB.What is the work done by him? 2Q: Give units of Power. Q2: A force of 15N is uniformly distributed over an area of 150m2. Find pressure In Pascal? Q3: Differentiate between mass and weight? Q4: What is the relation between thrust and pressure? Q5: What is the relation between acceleration due to gravity and Gravitational Constant? Q6: What happens to a body when the density of a body is equal to the density .PREETI PANWAR Q1:What is density? Give its units. ENERGY AND POWER SUBJECT TEACHER . Work and Energy? 3Q: What is the commercial unit of energy? 4Q:Two bodies have their masses m1/m2 =3 and their kinetic energy E1/E2=1/3 .GRAVITATION CLASS.A.PREETI PANWAR CLASS-9th 1Q: A coolie carries a load of 50kg on his head and walks on a level road up to 100m.V PUBLIC SCHOOL THERMAL COLONY PANIPAT ASSIGNMENT TOPIC. WORK .Of the liquid? Q7: A body of mass 2kg floats in a liquid.PREETI PANWAR CLASS-9th 1Q: A coolie carries a load of 50kg on his head and walks on a level road up to 100m. Q9: A ship sends out ultrasound that results from the seabed and is detected After 3. what is the distance of the sea bed from the ship? D. also discuss the speed of fastest one In solids.The ratio of their velocities are? 5Q:Prove that P=F * v . Explain. infrasonic and ultrasonic waves? Q6: Can sound waves travel through vacuum? Q7: Does the sound of a bomb explosion travel faster than the sound produced By a humming bee? Q8: If an observer places his ear at the end of a long pipe. where P is power. TEACHER. he can hear two Distinct echoes when the pipe is hammered at the other end. liquids and solids? Q3: A source of wave produces 20 crests and 20 troughs in 0. If the speed of ultrasound through sea water is 1531m/s. F is force and v is velocity? 6Q:An electric motor creates a tension of 4500N in hoisting a cable and reels at a rate of 2m/s. frequency and wavelength? Q2: Which travels faster sound of light.42s.A.IX SUBJECT. ENERGY AND POWER SUBJECT TEACHER .PHYSICS SUB. The Power of the motor is? . . what is the buoyant force on the body? DAV PUBLIC SCHOOL THERMAL POWER COLONY ASSIGNMENT TOPIC.What is the work done by him? 2Q: Give units of Power. Find the Frequency of the wave? Q4: Will a vibrating source always produce sound? Q5: What are supersonics.PREETI PANWAR Q1: What is the relation between speed of sound.2s. Work and Energy? 3Q: What is the commercial unit of energy? 4Q:Two bodies have their masses m1/m2 =3 and their kinetic energy E1/E2=1/3 .V PUBLIC SCHOOL THERMAL COLONY PANIPAT ASSIGNMENT TOPIC.SOUND CLASS. WORK .A. where P is power. –2 CLASS-IX SUB.FORCE AND LAWS OF MOTION Q1: When two bodies A and B interact with each other A exerts a force of 10 N on B towards east.PREETI PANWAR CLASS-9th 1Q: A coolie carries a load of 50kg on his head and walks on a level road up to 100m.V PUBLIC SCHOOL THERMAL COLONY PANIPAT ASSIGNMENT TOPIC. Work and Energy? 3Q: What is the commercial unit of energy? 4Q:Two bodies have their masses m1/m2 =3 and their kinetic energy E1/E2=1/3 . ENERGY AND POWER SUBJECT TEACHER . F is force and v is velocity? 6Q:An electric motor creates a tension of 4500N in hoisting a cable and reels at a rate of 2m/s. What would be the acceleration if the force were doubled? Q6: If a body is at rest. TEACHER.PREETI PANWAR TOPIC.01s.What is the work done by him? 2Q: Give units of Power. The nail stops the hammer in a very short time of 0. The Power of the motor is? 7Q:State Work Energy theorem? DAV PUBLIC SCHOOL THERMAL COLONY PANIPAT ASSIGNMENT NO. What is the force of the nail on the hammer? Q5: What would be the force required to produce the acceleration of 2m/s2 in a Body of mass 12kg?.THERMAL COLONY PANIPAT ASSINGNMENT :1st(PHYSICS) Sub Teacher: Mr.7Q:State Work Energy theorem? D.A.Ravi kant Sharma CLASS:9th Unit :1st .V PUBLIC SCHOOL.The ratio of their velocities are? 5Q:Prove that P=F * v .s second law of motion gives measure of which physical quantity? Q3: A gun of mass 5kg fires a 50gm bullet with a velocity of 200m per second calculate the recoil velocity of the gun? Q4: A hammer of mass 500gm moving with 50m/s strikes a nail. What is the force exerted by B on A? Q2: Newton. What will be its momentum? Q7: What is the relation of force with momentum and acceleration? Q8: With what acceleration an object moves when a force of 1N acts on a mass Of 1kg and is free to move? D. Q:5A ball is gently dropped from a height of 20m. if its velocity increase uniformly at the rate of 10m/s2.V PUBLIC SCHOOL. Q:7A standing train in which we are sitting appears to move. Can it have zero displacement ? Support your answer with an example. Q:8Can the average speed of a moving body be zero? D. if its velocity increase uniformly at the rate of 10m/s2. Q:8Can the average speed of a moving body be zero? .Ravi kant Sharma CLASS:9th Unit :1st Q:1 What is the nature of the distance time graph for uniform and non uniform motion of an object? Q:2 A bus starts from rest and moves with a uniform acceleration of 1m/s2 for 5 minutes. Q:4A train starting from a railway station and moving with a uniform acceleration attains a speed of 40km/h in 10 minute. Calculate(1)the speed acquired and (2) the distance traveled by the bus.can it have zero displacement ? Support your answer with an example. Q:3 An object has moved through a distance. Calculate(1)the speed acquired and (2) the distance traveled by the bus.Explain Why.Wheather the walls of a class room are at rest or in motion. Q:4A train starting from a railway station and moving with a uniform acceleration attains a speed of 40km/h in 10 minute.THERMAL COLONY PANIPAT ASSINGNMENT :1st(PHYSICS) Sub Teacher: Mr. Find the acceleration.Q:1 What is the nature of the distance time graph for uniform and non uniform motion of an object? Q:2 A bus starts from rest and moves with a uniform acceleration of 1m/s2 for 5 minutes. Q:7A standing train in which we are sitting appears to move.Explain Why. Q:3 An object has moved through a distance. with what velocity will it strikes the ground? Q:6Explain. Find the acceleration.Wheather the walls of a class room are at rest or in motion.A. Q:5A ball is gently dropped from a height of 20m. with what velocity will it strikes the ground? Q:6Explain.