9th class sample paper2015

Mock Test Papersth

(For Class 9 CBSE Summative Assessment-2 )

Apex Institute for IIT-JEE / PMT

Head Office : 62 Nitikhand -3 Indirapuram Cont. +91-9990495952, +91-9910817866, www.apexiit.co.in

Mathematics & Science

Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad: 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180, 9990495952 | www.apexiit.co.in/

Apex Institute Science & Mathematics Sample Paper: Class (IX)

MATHEMATICS-IX (Term-II) Time : 3 hours M.M. : 90

SECTION A (Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.) 1. In the given figure, PQRS is a rectangle. If ∠RPQ = 30°, then the value of (x + y) is : (a) 90° (b) 120° (c) 150° (d) 180° 2. In the figure, if area of parallelogram ABCD is 30 cm2, then ar (ADE) + ar (BCE) is equal to : (a) 20 cm2 (b) 30 cm2 (c) 15 cm2 (d) 25 cm2 3. In the figure, chord AB is greater than chord CD. OL and OM are the perpendiculars from the centre O on these two chords as shown in the figure. The correct relation between OL and OM is : (a) OL = OM (b) OL < OM (c) OL > OM (d) none of these 4. Ratio of the volume of a cone and a cylinder of same radius of base and same height is : (a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 1 : 4 5. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are written in ascending order. If median of data is 63, then x is : (a) 62 (b) 63 (c) 124 (d) 126 6. In the given figure, ABCD is a rhombus. If ∠OAB = 35°, then the value of x is : (a) 25° (b) 35° (c) 55° (d) 70° 7. If the slant height of a cone is 13 cm and the base radius is 5 cm, then the height of cone is : (a) 12 cm (b) 8 cm (c) 10 cm (d) 18 cm 8. If P(E) denotes the probability of an event E, then : (a) P(E) < 0 (b) P(E) >1 (c) 0 < P(E) < 1 (d) –1 < P(E) < 1

SECTION B (Question numbers 9 to 14 carry 2 marks each.)

9. The cost of 6 eggs is the same as the cost of one bread. Express this statement as a linear equation in two variables. (Take the cost of one egg to be Rs x and that of a bread to be Rs y). 10. In the figure, ABCD is a quadrilateral and BD is one of its diagonals. Show that ABCD is a parallelogram and find its area. 11. In the figure, ABCD is a rectangle. P and Q are the mid-points of AD and DC respectively. Find the length of PQ.

12. AOB is a diameter of a circle and C is a point on the circle. Check whether AC

2 + BC

2 = AB

2 is true or not.

OR For what value of x in the figure, points A, B, C and D are concyclic? 13. If the edge of a cube is doubled, what is the ratio of the volume of the first cube to that of the second cube? 14. A die is thrown 225 times and the results were as follows :

Outcome 1 2 3 4 5 6

Frequencies 34 50 16 71 24 30

Find the probability of getting a prime number. SECTION C

(Question numbers 15 to 24 carry 3 marks each.) 15. Draw the graph of the equation 2y – x = 7 and determine from the graph whether x = 3, y = 2 is its solution or not. 16. Determine the point on the graph of the linear

equation 2x + 5y = 19 whose ordinate is 3

2 times its

abscissa. 17. The angles between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram. OR ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. Show that the ratio of ar(ABFE) and ar(EFCD) is (3a + b) : (a + 3b). 18. Construct a triangle whose sides are 4.2 cm, 3.9 cm and 6.1 cm. Bisect its greatest angle and measure each part. 19. If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that

arcPXA arcPYB .

20. The total surface area of a solid cylinder is 462 cm2 and its curved surface area is one third of its total surface area. Find the radius of the cylinder. 21. A hemispherical vessel full of water is emptied in a cone. The radii of the vessel and the cone are 12 cm and 8 cm respectively. Find the height of the water in the cone. OR A shopkeeper has one spherical ladoo of the radius 5 cm. With the same amount of material, how many ladoos of radius 2.5 cm can be made? 22. Prepare a continuous grouped frequency distribution from the following data

Mid Point Frequencies

5 15 25 35 45

4 8

13 12 6

Also find the size of class intervals.



23. Show that if diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. 24. Find the mean of the following data

f 4 6 8 10 12

x 4 8 14 11 3

OR A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 and that of boys is 71. Find the mean score of the whole class.

SECTION D (Question numbers 25 to 34 carry 4 marks each.)

25. Draw the graph of the linear equation 2x + 3y = 12. At what points, the graph of the equation cuts the x-axis and the y-axis? 26. E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram. 27. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium. 28. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 29. A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 cm. (i) How many students can sit in the tent if a student on an average, occupies5/7 m

2 on the ground?

(ii) Find the volume of the cone. OR The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone. 30. Draw a histogram for the following data :

C.I. 25-29

30-34

35-39

40-44

45-49

50-54

Frequency 8 15 23 20 10 9

31. Show that the diagonals of a rhombus are perpendicular to each other. OR Show that a diagonal of a parallelogram divides it into two congruent triangles and hence prove that the opposite sides of a parallelogram are equal. 32. The parking charges of a car in a parking lot is Rs 30 for the first two hours and Rs 10 for subsequent hours. Taking total parking time to be x hours and total charges as Rs y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and read the charges for five hours. 33. Draw a frequency polygon for the following distribution

Class Interval Frequencies

10 - 19 20

20 - 29 15

30 - 39 45

40 - 49 60

50 – 59 12

60 - 69 6

70 - 79 15

34. Metal spheres, each of radius 2 cm are packed into a rectangular box of dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed in the box, it is filled with preservative liquid. Find the volume of this liquid to the nearest integer.

Director's Message

Dear Students/Parents

APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for

ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a

relentlessly motivating and competitive atmosphere.

As It is very important to discover the basic weaknesses and problems of students not succeeding in IIT-

JEE / PRE-MEDICAL exams. In fact, as question patterns are changing, now you need to have a different

approach for these exams. As far as ENGG. / PRE-MEDICAL preparations is concerned, students have

been wasting time and energy, studying Physics, Chemistry and Maths at different places. At APEX

INSTITUTE, the scope of the subject has been deliberately made all- inclusive to free them of this

burden. APEX INSTITUTE offers you complete preparation for IIT-JEE/PRE-MED. exams under one

roof.

Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject,

tricks of tackling the questions and above all enthusing students with self confidence, ambition and a

'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience. These

qualities, the APEX INSTITUTE ensures will be developed in students in full measure perhaps luck plays

some role in one's life and career. But it is also a universal truth that before proper grasps of subject.

Intelligent preparation and perservance even adverse luck does not stand a chance.

With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize

the Alchemist's dream of turning 'base metal' into 'gold'.

With best wishes.

S. Iqbal (Motivator & Mentor)



SCIENCE-IX (Term-II) Maximum Marks : 90 Maximum Time : 3 hours

SECTION A 1. In the figure given below, if the bob of the pendulum swings from P to Q, what is the kinetic energy at Q? [1] 2. What is ammonification? [1] 3. Name one control measure for overcoming the problem of ozone depletion. [1] 4. Draw a sketch of Bohr’s model of an atom with three shells. [2] 5. Name the group of plants with the following characters: [2] (a) Plants with seeds (b) Plants without roots, stem, leaves or flowers (c) Plants having seeds with two cotyledons (d) Plants visible with naked eye but having no chlorophyll. 6. Name and define the force experienced by a body when immersed in a fluid. What is the direction of this force? [2] 7. Why does the percentage of gases like oxygen, nitrogen and carbon dioxide remain almost the same in the atmosphere? [2] 8. What is the qualitative meaning of the symbol of chlorine (Cl) of atomic mass 35.5 u? [3] 9. (a) Mention the postulate of Dalton's Atomic Theory that explain the Law of Constant Proportion. [3] (b) Mention any two rules to write a chemical formula. (c) Write the chemical formulae of the following compounds : (i) Calcium hydroxide (ii) Ammonium sulphate 10. In the following table the mass number and the atomic number of certain elements are given.

Element A B C D E

Mass No 1 7 14 40 40

At. NO. 1 3 7 18 20

(a) Select a pair of isobars from the above table. (b) What would be the valency of element C listed in the above table? (c) Which two subatomic particles are equal in number in a neutral atom? 11. Which do you think is a more basic characteristic for classifying organisms—the place where they live or the kind of cells they are made of ? Why? [3] 12. (i) What do you mean by disease symptoms? [3] (ii) Suggest two lines of treatment given to patients suffering from infectious diseases. 13. What precautions will you take to justify “prevention is better than cure"? [3] 14. (a) Name any two air-borne diseases. How does the disease causing microbes spread through air? [3] (b) How does the immune system of our body function? 15. What happens when: (a) Buoyant Force exerted by the fluid is less than the weight of the body? [3]

(b) Buoyant Force exerted by the fluid is equal to the weight of the body? 16. (a) The potential energy of a freely falling object decreases progressively. What happens to its (i) kinetic energy (ii) total mechanical energy? State the law on which your answer is based. [3] (b) A household consumes 1 kWh of energy per day. How much energy is this in joule? 17. 50 sound waves pass through a point in 0.1 s. If the distance between one compression and the subsequent rarefaction is 0.34 m, calculate (a) frequency (b) wavelength (c) wave velocity of the longitudinal wave in air. [3] 18. Represent graphically by two separate diagrams in each case. [3] (i) Two sound waves having the same amplitude but different frequencies. (iii) Two sound waves having different amplitudes and also different wavelengths. 19. Explain with the help of a labelled diagram carbon cycle in nature. [3] 20. Give reasons for the following : [5] (a) 4040

18 20&CaAr are called isobars. (b) 'He' and 'Ne' have

zero valency. (c) An atom is neutral. (d) Nucleus is positively charged. (e) Isotopes have similar chemical properties.

OR (a) What are isobars? Give one example. (b) Write any two uses of isotopes. [5] (c) Write two differences between isobars and isotopes. 21. (a) Draw a well labelled diagram of Euglena. (b) Name the kingdom to which it belongs. [5] OR Pick the odd one out and justify your choice by giving reasons. (a) Moss, Fern, Pinus, Spirogyra. [5] (b) Sea cucumber, Octopus, Feather star, Star fish. 22. (a) Derive the formula of kinetic energy of an object of mass ‘m’ moving with a uniform velocity ‘v’. [5] (b) A force acting on a 20 kg mass changes its velocity from 5 m/s to 3m/s. Calculate the work done by the force.

OR (a) Define power. (b) State and define the S.I. unit of power. (c) A force applied on a body of mass 4 kg for 5 seconds changes its velocity from 10 m/s to 20 m/s. Find the power required. 23. (i) How the bats make use of ultrasonic waves to catch their prey? Explain. [5] (ii) A radar signal is reflected by an aeroplane and is received 2 × 10

–5 s after it was sent. If the speed of these

waves is 3 × 108 m/s, how far is the aeroplane?

OR (i) What causes reverberation of thunder sound? (ii) A SONAR device on a submarine sends a signal and receives an echo 5 s later.



Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m. 24. (a) How can we prevent the loss of top soil? Discuss. [5] (b) Why are root nodules useful for plants? OR (a) What is biogeochemical cycle? Describe the oxygen-cycle with the help of a labelled diagram.

SECTION B 25. Which of the following information is not conveyed by a chemical equation? [1] (a) The reactants taking part in the reaction (b) The products formed in the reaction (c) The speed of the reaction (d) The ratio of the weights of reactants and products taking part in the reaction 26. Observe the following pictures. The common feature that assigns them to the same phylum is : [1] (a) wings (b) three pairs of legs (c) jointed appendages (d) antennae 27. Which one of the following characteristics can be used to distinguish gymnosperms from angiosperms? [1] (a) Presence of pollen chamber in gymnosperms (b) Presence of naked ovules in gymnosperms (c) Presence of stomata in angiosperms (d) Absence of naked ovules in gymnosperms 28. Parallel venation is the characteristic feature of [1] (a) monocots (b) dicots (c) both (a) and (b) (d) none of these 29. In Pinus, the fertilisation takes place in the : [1] (a) 1st year cone (b) 2nd year cone (c) 3rd year cone (d) microsporangia 30. Scales are present in : [1] (a) fish (b) reptiles (c) both (a) and (b) (d) none of these 31. A female Anopheles lays the eggs about : [1] (a) one at a time (b) 5 at a time (c) 50 to 200 at a time (d) None of the above 32. The readings of the spring balance will be : [1] (a) equal to each other in all cases A, B and C (b) equal to each other in cases B and C only (c) equal to each other in cases A and C only (d) different in every case

33. The density of which of the following cannot be measured accurately using a spring balance and a measuring cylinder? [1] (a) A ball filled with a liquid having a leakage (b) A block of ice at 0°C

(c) A small porous solid (d) All of these 34. The principle of a spring balance is : [1] (a) the extension produced in spring is directly proportional to the square of the stretching force (b) the extension produced in spring is directly proportional to the stretching force (c) the extension produced in spring is inversely proportional to the stretching force (d) the extension produced in spring is inversely proportional to the square of the stretching force. 35. If the reflecting body is covered with a loose woollen cloth, the reflected sound : [1] (a) heard will be more louder (b) heard will be less louder (c) heard will be of the same loudness (d) will not be heard. 36. The figure given below shows a line diagram [1] for the verification of laws of reflection of a sound wave. The vibrating tuning fork should be held at : (a) A (b) B (c) D (d) C

37. It is easier to lift a heavy stone in water because : [1] (a) the stone loses its mass in water (b) the stone loses its weight in water (c) the stone experiences an up thrust equal to the volume of water displaced (d) the stone experiences an up thrust equal to the weight of water displaced. 38. During the formation of a pulse, most of the medium at any time is : [1] (a) in the state of rest (b) in the state of motion (c) some parts in the state of rest and some parts in the state of motion (d) none of the above. 39. A pulse travels through a slinky 10 m long from one end to the other end and then back to the point of origin in 3 s. The velocity of the pulse in the slinky is : [1] (a) 3.33 ms–1 (b) 4.5 ms–1 (c) 6.00 ms–1 (d) 6.66 ms–1. 40. In which case is the pressure exerted by the brick on the ground maximum? [1] (a) A (b) B (c) C (d) none of these 41. During sharpening of a knife we : [1] (a) decrease the surface area of the cutting edge (b) increase the surface area of the cutting edge (c) remove rust from the cutting edge (d) none of the above 42. The tuning fork in the experiment to prove laws of reflection of sound has to be placed with its prongs. [1] (a) Vertical near the tube (b) Horizontal near the tube



(c) Vertically or horizontally near the tube makes on difference (d) Inclined near the tube. ANSWERS 16. 3.6 × 10

6 J 17. 500 Hz, 0.68 m, 340 m/s 22. (b) 210 J OR

(c) 40 W 23. (ii) 3 km OR ((ii) 1450 m/s 25. (c) 26. (c) 27. (b) 28. (a) 29. (b) 30. (c) 31. (c) 32. (b) 33. (d) 34. (b) 35. (d) 36. (a) 37. (d) 38. (a) 39. (d) 40. (a) 41. (a) 42. (b)

Admission cum Scholarship Test

15th & 22nd March 2015

60%

Scholarship Upto

100%

Dhwani Jain is pursuing Chemical Engineering from N.U.S. (National university of Singapore) Ranked 2nd University in Asia. she was our two years classroom program Student.

Prakhar Goel is studying in Maulana Azad Medical College Delhi. He was our One year Dropper Batch Student

Prerna Kashyap is pursuing B.Tech (EC) fromNIT Kurukshetra. She was our Two years classroom program Student

Shubham Mukherjee is studying in IIT-Guwahati. He was our One year Dropper Batch Student

Shiddhant Rathore is pursuing B.Tech (Mechanical) from BITS Goa.He was our Three years Classroom Program Student.

AIR 427(GE)

Arindham Roy is pursuing B.Tech from NIT Patna. She was our Two years classroom program Student

AIR 1823(GE)

AIR 5982 (IITAdvanced)

Arindham Roy

AIR 521(GE)

9th class sample paper2015

Education

om b ol om c ol om d

value of x y

section b question numbers

section c question numbers

given figure

area of parallelogram

height of cone

linear equation