10th class sample paper2015

Mock Test Papersth
(For Class 10 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 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 3
3
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 cm
2
(b) 26.4 cm
2
(c) 36.6 cm
2
(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 cm
3
(b) 77.6 cm
3
(c) 58.2 cm
3
(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: x
2
– 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
19. solve for x
1 3 10
; 2,4
2 4 3
x x
x
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
5
of 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
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(x
2
+ 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]
       100 100 100 100
x y y x x y y x
a b c d
x 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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