10th class sample paper2015

Mock Test Papersth

(For Class 10 CBSE Summative Assessment-2 )

Apex Institute for IIT-JEE / PMT

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Mathematics & Science

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

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

SECTION A (Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four alternative choices have been provided of which only one is correct. You have to select the correct choice) 1. If the quadratic equation 2x

2 – kx + 3 = 0 has equal

roots, then the value of k is

5 6 2 6 3 2a b c d

2. 51 + 52 + 53 +........ + 100 is equal to (a) 3775 (b) 4025 (c) 4275 (d) 5050 3. In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle, then length of OP is : (a) 30 cm (b) 28 cm (c) 25 cm (d) 31 cm 4. If two tangents inclined at angle of 60° are drawn to a

circle of radius 3 cm, then length of each tangent is equal

to

2

3 2 3 3 33

a b c d

5. Two circles touch each other externally at C and AB is a

common tangent to the circles. Then, ∠ACB is

(a) 60° (b) 45° (c) 90° (d) 180°

6. To divide a line segment AB in the ratio 4 : 7, a ray AX is

drawn first such that ∠BAX is an acute angle and then

points A1, A2, A3, ........ are located at equal distances on

the ray AX and the point B is joined to

(a) A12 (b) A11 (c) A10 (d) A9

7. The area of the sector which subtends an angle of 60° at the centre of a circle is 4.4 cm

2, then area of the circle is :

(a) 36 cm2

(b) 26.4 cm2

(c) 36.6 cm2 (d) 30 cm

2

8. Volume of the largest right circular cone that can be cut

out from a cube of edge 4.2 cm is

(a) 9.7 cm3

(b) 77.6 cm3

(c) 58.2 cm3 (d) 19.4 cm

3

9. The ratio of the length of a rod and its shadow is 1: 3

. The altitude of the sun is

(a) 30° (b) 45° (c) 60° (d) 90°

10. If two dice are thrown simultaneously, then the

probability of getting a doublet is

5 1 1 1

36 18 9 6

a b c d

SECTION B

(Question numbers 11 to 18 carry 2 marks each)

11. Using quadratic formula solve the following quadratic

equation for x: x2 – 4ax + 4a

2 – b

2 = 0

12. Split 207 into three parts such that these are in A.P.

and the product of the two smaller parts is 4632.

13. In the figure, CP and CQ are tangents to a circle

with centre O. ARB is another tangent touching the circle

at R. If CP = 11 cm and BC = 7 cm, then find the length of

BR.

14. Find the area of the shaded region in the figure below, if AB = 12 cm, BC = 5 cm.

15. A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed. 16. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9). 17. Find the ratio in which the line segment joining the points (–3, 10) and (6, –8) is divided by (–1, 6). 18. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. A ball is drawn at random from the bag. Find the probability that it is not green. OR From a well-shuffled pack of cards, a card is drawn at random. Find the probability that the card drawn is a black queen.

SECTION C (Question numbers 19 to 28 carry 3 marks each)

19. solve for x 1 3 10

; 2,42 4 3

x xx

x x

OR The sum of the squares of two consecutive odd numbers is 394. Find the numbers. 20. Find the 31st term of an A.P. whose 11th term is 38 and 16th term is 73. 21. In the given figure, there are two concentric circles with centre O and of the radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP?

OR

Prove that the lengths of the tangents drawn from an external point to a circle are equal. 22. Construct a triangle with sides 5 cm, 6 cm and 7 cm and

then construct another triangle whose sides are 7

5of the

corresponding sides of the first triangle.



23. In the figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region 24. Two cones with the same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

OR A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π. 25. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building. 26. Find the area of a rhombus if its vertices are (3, 0), (4, 5) (–1, 4) and (–2, –1) taken in order. 27. If the vertices of a ΔABC are A(1, m), B(4, –3) and C(–9, 7) and its area is 15 sq. units, find the value of m. 28. Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that number on the taken out card is (i) a prime number less than 10. (ii) a number which is a perfect square.

SECTION D (Question numbers 29 to 34 carry 4 marks each) 29. Two years ago, a man’s age was three times the square of his son’s age. In three years, his age will be four times his son’s age. Find their present ages.

OR If –5 is a root of the quadratic equation 2x

2 + px – 15 = 0

and the quadratic equation p(x2 + x) + k = 0 has equal

roots, find the value of k. 30. A sum of Rs 700 is to be used to give seven cash prizes to students to a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes. 31. A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary. 32. In Radhika’s house there is a flower pot. The sum of radii of circular top and bottom of the flower pot is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circular top and bottom. 33. A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base, find the ratio of the volumes of two parts.

OR A well of diameter 3 m, dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

34. The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 10 seconds, the angle of elevation changes to 30°. If the jet is flying at a speed of 432 km/hour, find the constant height at which the jet is flying.

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SCIENCE X TERM-II Maximum Marks: 80 Maximum Time: 3hours

SECTION A 1. Name the compound formed when ethanol is warmed with ethanoic acid in the presence of a few drops of conc. H2SO4. [1] 2. What happens to the image distance in the eye when we increase the distance of an object from the eye? [1] 3. Construct an aquatic food chain showing four trophic levels. [1] 4. Where is the ozone layer located? [1] 5. Nitrogen (atomic number 7) and phosphorus (atomic number 15) belong to group 15 of the Periodic Table. Write the electronic configuration of these elements. Which of these will be more electronegative? Why? [2] 6. State two main properties of elements on which Mendeleev’s periodic classification was based. Why no fixed position could be assigned to hydrogen in his periodic table. [2] 7. Mention two functions of the human ovary. [2] 8. Why is DNA copying an essential part of the process of reproduction? [2] 9. The image of an object is formed on itself when placed at a distance of 30 cm from a concave mirror. What is the focal length of the concave mirror? [2] 10. Draw a neat labelled diagram showing the course of a ray of light through an equilateral glass prism and show clearly the angle of incidence and angle of deviation.[2] 11. Why is the sunlight reaching the earth yellowish? [2] 12. Give two changes which we can adopt in our daily life or habits to reduce the use of fossil fuel. [2] 13. Why must we conserve our forests? List any two causes for deforestation taking place. [2] 14. How were the following defects of original Mendeleev’s Periodic Table resolved in the modified Mendeleev’s Period Table? [3] (i) Problem of anomalous pairs. (ii) Position of rare earths (iii) Position of isotopes. 15. Name the reaction which is commonly used in the conversion of vegetable oils to fats. Explain the reaction involved in detail. [3] 16. Draw a diagram of a flower to show its male and female reproductive parts. Label on it : (a) ovary (b) anther (c) filament (d) stigma [3] 17. How is the equal genetic contribution of male and female parents ensured in the progeny? [3] 18. Explain the importance of fossils in deciding evolutionary relationships. [3] 19. A man with blood group A marries a woman with blood group O and their daughter has blood group O. Is this information enough to tell you which of the traits — blood group A or O — is dominant? Why or why not? [3] 20. A concave lens has a focal length 15 cm. At what distance should an object 10 cm long be placed so that it

forms an image 10 cm from the lens? Find the nature and size of the image formed. [3] 21. Draw a ray diagram showing the path of rays of light when it enters with oblique incidence. [3] (i) from air into water (ii) from water into air 22. Make a diagram to show how hypermetropia is corrected. The near point of a hypermetropic eye is 1m. What is the power of lens required to correct this defect? Assume that the near point of the normal eye is 25 cm. [3] 23.

Elements A B C D

Electronic configuration 1 2, 1 2, 4 2, 8, 7

The table above shows the electronic configuration of elements from A to D. By drawing dot diagrams show the formation of compounds between: (i) A and B (ii) A and D (iii) A and C (iv) B and C (v) B and D (vi) C and D

OR Define combustion. [5] (ii) Why is the flame of an unsaturated hydrocarbon sooty? (iii) Give a reaction other than oxidation which is a characteristic of saturated hydrocarbons. (iv) Which of the following hydrocarbons undergo addition reactions? Support your answer by a chemical equation. C2H6, C3H8, C2H2 and CH4 24. (i) Only through labelled diagrammatic epresentations, represent the process of budding as seen in Hydra. (ii) What is vegetative propagation? Classify giving suitable examples. OR (i) What is the structure of the embryo sac? [5] (ii) What is the importance of the menstrual cycle? 25. (i) A beam of light is incident through the holes on side A and emerges out of the hole on the other face of the box as shown in the figure. [5]

What type of lens is present inside the box? (ii) Two thin lenses of power + 2.5 D and –1.5 D are placed in contact with each other. Calculate: (a) power of the combination, (b) focal length of the combination.

OR (i) One half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer and explain your observation. (ii) P1 and P2 are the power of two thin lenses. What is the power P when both lenses are placed in contact with one another? [5]



SECTION B 26. A bright nail is placed in a beaker containing aqueous copper sulphate solution. When the iron nail is taken out of copper sulphate solution after 15 minutes, its surface is coated with: [1] (a) Reddish deposit (b) greenish deposit (c) black deposit (d) white deposit 27. Zinc granules were added to zinc sulphate, copper sulphate, aluminium sulphate and iron sulphate solutions as shown below. You would observe the deposition of metal on zinc granules in the beakers :

(a) I and III (b) II and IV (c) I and II (d) III and IV 28. Ethanoic acid reacts with sodium bicarbonate: [1] (a) Vigorously with lot of effervescence (b) slowly (c) at a moderate rate without effervescence (d) none of these 29. 5 ml each of acetic acid and water are mixed together and shaken well: [1]

The resulting mixture would appear as in : (a) I (b) II (c) III (d) IV 30. The odour of acetic acid resembles that of : [1] (a) rose (b) burning plastic (c) vinegar (d) kerosene 31. A student determines the focal length of a device X, by focussing the image of a far off object on the screen positioned as shown in the figure below. The device X is a : (a) Convex lens (b) Concave lens (c) Convex mirror (d) Concave mirror 32. The focal length of the concave mirror in the experimental set up, shown below, equals: (a) 10.3 cm (b) 11.0 cm (c) 11.7 cm (d) 12.2 cm 33. A student performs an experiment on finding the focal length of a convex lens by keeping a lighted candle on one end of a laboratory table, a screen on its other end and the lens between them as shown in

the figure. The positions of the three are adjusted to get a sharp image of the candle flame on the screen. [1] If now the candle flame were to be replaced by a distant lamp on a far away electric pole, the student would be able to get a sharp image of this distant lamp on the screen by moving: (a) the screen in the direction of the lens or the lens in the direction of the screen. (b) the screen in the direction of the lens or the lens away from the screen. (c) The screen away from the lens or the lens in the direction of the screen. (d) Neither the screen nor the lens. 34. Which one of the following is the best set-up for tracing the path of a ray of light through a rectangular glass slab? [1]

(a) I (b) II (c) III (d) IV 35. A ray of light travelling through medium A enters medium B, such that it bends away from the normal at the surface of separation. From this observation, we can say that medium B is : [1] (a) denser than medium A (b) rarer than medium A (c) of the same optical density as A (d) none of these 36. The diagram given alongside illustrates [1] (a) bud formation in yeast (b) binary fission in Amoeba (c) formation of daughter cells in yeast (d) pseudopodia formation in Amoeba 37. A student is given a permanent slide showing binary fission in Amoeba. Following are the steps in focussing the object under the microscope: [1] (i) Place the slide on the stage; look through the eye piece and adjust the mirror and diaphragm to get even illumination. (ii) Look through the eye piece and raise the objective using coarse adjustment until the object is focused. (iii) Make the focus sharp with the help of fine adjustment. (iv) Look through the eye piece and move the slide until the object is visible. The proper sequence of steps is (a) (i), (iii), (iv), (ii) (b) (ii), (iii), (iv), (i) (c) (iv), (iii), (ii), (i) (d) (i), (iv), (ii), (iii) 38. Following are the sketches made by some students.

The sketch not illustrative of budding in yeast is (a) A (b) B (c) C (d) D



39. A student soaked 5 grams of raisins in 25 ml of distilled water in each of the two beakers A and B. Beaker A was maintained at 25ºC and beaker B at 50ºC. After one hour, the student observed that the water absorbed by the raisins was: [1] (a) same in case of A and B (b) less in case of A than in B (c) exactly double in A, of that in B (d) exactly four times in A, of that in B 40. When kept in 10% sugar solution raisins swell up due to: [1] (a) endosmosis (b) exosmosis (c) plasmolysis (d) diffusion 41. If ‘x’ is the initial weight of raisins and ‘y’ is the final weight (after soaking), percentage of water absorbed by the raisins is given by : [1]

100 100 100 100x y y x x y y x

a b c dx y y x

ANSWERS

9. 15 cm 20. (i) –30 cm, 3.33 cm 22. + 3D 25. (a) + 1.0 D (b) 1 m 26. (a) 27. (b) 28. (a) 29. (c) 30. (c) 31. (d) 32. (b) 33. (b) 34. (d) 35. (b) 36. (b) 37. (d) 38. (c) 39. (b) 40. (a) 41. (d)

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10th class sample paper2015