1 Model Question Papers

Govt. QUESTION PAPER - SEPTEMBER 2020

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - I 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.

1. If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, then state which of the following statement
is true?
a) (A×C) Ì (B×D) b) (B×D) Ì (A×C) c) (A×B) Ì (A×D) d) (D×A) Ì (B×A)
2. Let f (x) = x2 – x, then f (x – 1) – f (x + 1) is
a) 4x b) 2 – 2x c) 2 – 4x d) 4x – 2
3. Using Euclid’s division lemma, if the cube of any positive integer is divided by 9, then the possible
remainders are
a) 0, 1, 8 b) 1, 4, 8 c) 0, 1, 3 d) 1, 3, 5
4. If A = 265 and B = 264 + 263 + 262 + ....... + 20, which of the following is true?
a) B is 264 more than A b) A and B are equal
c) B is larger than A by 1 d) A is larger than B by 1
a2 b2
5. + =
a 2 - b2 b2 - a 2
a) a – b b) a + b c) a2 – b2 d) 1
6. Transpose of a column matrix is
a) unit matrix b) diagonal matrix c) column matrix d) row matrix
7. In DLMN, ÐL=60°, ÐM = 50°. If DLMN ~ DPQR, then the value of ÐR is
a) 40° b) 70° c) 30° d) 110°
8. In the figure, if PR is tangent to the circle at
P and O is the centre of the circle, then ÐPOQ is
a) 120° b) 100°
c) 110° d) 90°
9. The straight line given by the equation x = 11 is
a) Parallel to x-axis b) Parallel to y-axis
c) Passing through the origin d) Passing through the point (0, 11)
10. If tanθ + cotθ = 2, then the value of tan2θ + cot2θ is
a) 0 b) 1 c) 2 d) 4
11. A child reshapes a cone made up of clay of height 24 cm and radius 6 cm into a sphere, then the
radius of sphere is
a) 24 cm b) 12 cm c) 6 cm d) 48 cm
12. A sphericl ball of radius r1 units is melted to make 8 new identical balls each of radius r2 units.
Then r1 : r2 is
a) 2 : 1 b) 1 : 2 c) 4 : 1 d) 1 : 4
13. The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all
deviations is
a) 40000 b) 160900 c) 160000 d) 30000
10th Std - Mathematics 2
14. If a letter is chosen at random from the English alphabets (a, b, c, ...., z), then the probability that
the letters chosen precedes x, is
12 1 23 3
a) b) c) d)
13 13 26 26

PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. If A × B = {(3, 2) (3, 4) (5, 2) (5, 4)}, then find A and B.

16. Show that the function f: N ® N defined by f (m) = m2 + m + 3 is one-one function.
17. If m, n are natural numbers, for what values of m, does 2n × 5m end in 5?
ì n2 if nis odd
ï
18. Find the 3rd and 4th terms of a sequence, if an = í n 2
ï if nis even
î2
19. Find the value of 12 + 22 + 32 + ...... + 102 and hence deduce 22 + 42 + 62 + ..... + 202.
20. Find the value of k for which the equation 9x2 + 3kx + 4 = 0 has real and equal roots.
æ 7 -3ö
ç ÷
21. If A = ç - 5 2 ÷ then find the transpose of –A.
ç ÷
è 3 -5ø
22. Check whether AD is bisector of ÐA of DABC in the following:
AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm.
23. Find the slope of a line joining the points (14, 10) and (14, –6).
1 + sin q
24. Prove = secθ + tanθ
1 - sin q
25. Find the diameter of a sphere whose surface area is 154 m2.
26. If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area.
27. Find the range and coefficient of range of the data.
63, 89, 98, 125, 79, 108, 117, 68.
28. Find the volume of the iron used to make a hollow cylinder of height 9 cm and whose internal and
external radii are 3 cm and 5 cm respectively.

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

PART - III
Answer any 10 questions. Question No. 42 is compulsory. 10×5=50
29. Let A = The set of all natural numbers less than 8
B = The set of all prime numbers less than 8
C = The set of even prime number. Verify that (AÇ B) × C = (A × C) Ç (B × C)
30. Let A = {1, 2, 3, 4} and B = {2, 5, 8, 11, 14} be two sets. Let f : A ® B be a function given by
f (x) = 3x – 1. Represent this function i) by arrow diagram ii) in a table form iii) as a set of ordered
pairs iv) in a graphical form.
31. Find the sum of all natural numbers between 100 and 1000 which are divisible by 11.
32. Solve: 6x + 2y – 5z = 13; 3x + 3y – 2z = 13; 7x + 5y – 3z = 26
33. Find the GCD of the polynomials, x4 + 3x3 – x – 3 and x3 + x2 – 5x + 3.

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 3 Model Question Papers
34. Find the square root of 64x4 − 16x3 + 17x2 − 2x + 1
æ 2 -1ö
æ 1 2 1ö
35. If A = ç and B = ç -1 4 ÷ show that (AB)T = BTAT.
è 2 -1 1÷ø ç ÷
è 0 2ø
36. State and prove Angle Bisector theorem.
37. Find the value of k, if the area of a quadrilateral is 29 sq. units, whose vertices are
(–4, –2), (–3, k), (3, –2) and (2, 3).
38. From the top of a tower 60 m high, the angles of depression of the top and bottom of a vertical lamp post
are observed to be 38° and 60° respectively. Find the height of the lamp post.
(tan 38° = 0.7813, 3 = 1.732)
39. A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small non-hollow cylindrical
metal of radius 5 cm and height 4 cm is immersed in it completely. Calculate the rise of water in the glass.
40. The scores of a cricketer in 7 matches are 70, 80, 60, 50, 40, 90, 95. Find the standard deviation.
41. Two unbiased dice are rolled once. Find the probability of getting:
i) a doublet (equal numbers on both dice) ii) the product as a prime number
iii) the sum as a prime number iv) the sum as 1
42. A straight line AB cuts the co-ordinate axes at A and B.
If the mid-point of AB is (2, 3), B (0, y)
find the equation of AB.
A (x, 0)

PART - IV
Note: Answer all the questions. 2×8=16
6
43. a) Construct a triangle similar to a given triangle ABC with its sides equal to of the corresponding
6 5
sides of the triangle ABC. æç scale factor ö÷
è 5ø
(OR)
b) Draw two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also
measure the lengths of the tangents.
44. a) Graph the quadratic equation x2 – 8x + 16 = 0 and state the nature of their solution.
(OR)
b) A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw
the graph for the relation between the Marked Price and the Discount.
Hence find,
(i) the marked price when a customer gets a discount of ` 3250 (from graph)
(ii) the discount when the marked price is ` 2500.
***
10th Std - Mathematics 4

PTA MODEL QUESTION PAPER - 1

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - III 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.
1. If {(a, 8), (6, b)} represents an identity function, then the value of a and b are respectively
1) (6, 8) 2) (8, 6) 3) (8, 8) 4) (6, 6)
2. 74k ≡ ---------- (mod 100).
1) 4 2) 3 3) 2 4) 1
3. A system of three linear equations in three variables is inconsistent if their planes
1) intersect only at a point 2) intersect in a line
3) coincides with each other 4) do not intersect
4. In then adjacent figure ÐBAC = 90° and AD ^ BC then,
1) BD.CD = BC2 2) AB.AC = BC2
2
3) BD.CD = AD 4) AB.AC = AD2
5. The straight line given by the equation x = 11
1) Passing through the origin 2) Passing through the point (0, 11)
3) Parallel to X - axis 4) Parallel to Y - axis
6. If (sinα + cosecα)2 + (cosα + secα)2 = k + tan2α + cot2α then the value of k is equal to
1) 3 2) 5 3) 7 4) 9
7. The total surface area of a cylinder whose radius is 1/3 of its height is
8p h 2 9p h 2 56p h 2
1) sq.units 2) sq. units 3) sq. units 4) 24πh2 sq. units
9 8 9
8. Which of the following is incorrect?
1) P(A) + P(A) =1 2) P(φ) = 0 3) 0 ≤ P(A) ≤ 1 4) P(A) > 1
9. The sequence –3, –3, –3 … is
1) an A.P. only 2) a G.P only
3) neither A.P nor G.P 4) both A.P and G.P
10. The L.C.M of x3 – a3 and (x – a)2 is
1) (x3 – a3) (x + a) 2) (x3 – a3) (x – a)2 3) (x–a)2 (x2+ax+a2) 4) (x+a)2 (x2+ax+a2)
11. In n(A) = p, n(B) = q then the total number of relations that exists between A and B is
1) 2p 2) 2q 3) 2p+q 4) 2pq
12. If the HCF of 65 and 117 is expressible in the form of 65m – 117 than, the value of m is
1) 1 2) 3 3) 2 4) 4
13. The sum of all deviations of the data form its mean is
1) always positive 2) always negative 3) zero 4) non-zero integer
14. The angle of elevation and depression are usually measured by a device called
1) Theodolite 2) Kaleidoscope 3) Periscope 4) Telescope

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 5 Model Question Papers
PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots.
Find the number of completed rows and how many flower pots are left over
16. Solve: x4 – 13x2 + 42 = 0
17. If A is of order p × q and B is order q × r what is the order of AB and BA?
18. A relation ‘f ’ is defined by f (x) = x2 – 2 where, x Î{–2, –1, 0, 3}
i) List the elements of f ii) Is f a function?
19. Show that ∆PST ~ ∆ PQR
P
2 4
T
S 2
1
R
Q
20. A tower stands vertically on the ground. From a point on the ground, which is 48m away from the foot
of the tower, the angle of elevation of the top of the tower 30°. Find the height of the tower.
21. The volume of a solid right circular cone is 11088 cm3. If its height is 24 cm then find the radius of the
cone.
2 2 1
22. If P(A) = , P(B) = and P(A B) = then find P(A∩B).
3 5 3
23. Find A × B and A × A if A = {m, n}; B = f
24. Find the middle terms of an A.P. 9, 15, 21, 27, ..., 183.
25. The product of Kumaran’s age (in years) two years ago and his age four years from now is one more than
twice his present age. What is his present age?
7
26. Find the equation of a line passing through the point (–4, 3) and having slope – .
5
27. The standard deviations of 20 observations is 6 . If each observation is multiplied by 3, find the standard
deviation and variance of the resulting observations.
28. An organization plans to plant saplings in 25 streets in a town in such a way that one sapling for the first
street, three for the second, nine for the third and so on. How many saplings are needed to complete the
work?

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by
9
t(C) = F where (F = C+32). Find (i) t(0) (ii) t(28) (iii) t(–10) (iv) the value of C when t(C) = 212 (v)
5
the temperature when the Celsius value is equal to the Farenheit value.
30. Rekha has 15 square colour papers of sizes 10cm, 11 cm, 12 cm, …. 24 cm. How much area can be
decorated with these colour papers?
æ 1 1ö æ 1 2ö æ -7 6ö
31. If A = ç ÷ ,B= ç , C= ç verify that A(B+C) = AB + AC.
è -1 3ø ÷
è -4 2ø è 3 2÷ø
32. State and Prove Pythagoras Theorem.
33. As observed from the top of a 60m high light house from the sea level, the angles of depression of two
ships are 28° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the
distance between the two ships. (tan28° = 0.5317).
34. Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular
cylinder of height 10 cm and diameter 4.5 cm.
10th Std - Mathematics 6
35. The marks scored by the students in a slip test are given below.
x 4 6 8 10 12
f 7 3 5 9 5
36. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The
set of even prime number. Verify that A × (B – C) = (A × B) – (A × C)
37. If Sn = (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ….. n terms then

prove that (x – y) Sn =
(
x2 xn - 1 ) - y (y
2 n
-1 ).
x -1 y -1

1 1 1 1 1 1 1 1 4 2
38. Solve: + - = ; = ; - + =2
2 x 4 y 3z 4 x 3 y x 5 y z 15
39. A funnel consists of a frustum of a cone attached to a cylindrical portion 12 cm long attached at the
bottom. If the total height be 20 cm, diameter of the cylindrical portion be 12 cm and the diameter of the
top of the funnel be 24 cm. Find the outer surface area of the funnel.
40. In a class of 50 students, 28 opted for NCC, 28 opted for NSS and 10 opted both NCC and NSS. One of
the students is selected at random, Find the probability that
i) The student opted for NCC but not NSS.
ii) The student opted for NSS but not NCC.
iii) The student opted for exactly one of them.
41. The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq.cm then find its
base and altitude
42. The area of a triangle is 5 sq.units. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y)
where y = x + 3. Find the coordinates of the third vertex.

PART - IV
Note: Answer all the questions. 2×8=16

Draw the graph of y = x2 + x – 2 and hence use it to solve the equation x2 + x – 2 = 0.

43. a) 
(OR)
b) Solve: 2x + y + 4x = 15, x – 2y + 3z = 13, 3x + y – z = 2
6
44. a) Construct a triangle similar to a given triangle ABC with its sides equal to of the corresponding
5
6
sides of the triangle ABC. (Scale Factor )
5
(OR)
b) ABC is a triangle with B = 90°, BC = 3 cm and AB = 4 cm. D is a point on AC such that
AD = 1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

***

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 7 Model Question Papers

PTA MODEL QUESTION PAPER - 2

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - I 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.
1. If f : A→B is a bijective function and if n(B) = 7, then n(A) is equal to
1) 1 2) 49 3) 14 4) 7
2. If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B
is
1) 2 2) 3 3) 4 4) 8
3 1 1 1
3. The next term of the sequence , , , ,….. is
16 8 12 18
2 1 1 1
1) 2) 3) 4)
3 24 27 81
4. Which of the following should be added to make x4 + 64 a perfect square?
1) 4x2 2) 8x2 3) –8x2 4) 16x2
x3 + 8
5. The excluded value of the rational expression is
x2 - 2 x - 8
1) 8 2) 2 3) 4 4) 1
6. Graph of a linear equation is a
1) straight line 2) circle 3) parabola 4) hyperbola
7. A Tangent is perpendicular to the radius at the
1) centre 2) infinity 3) point of contact 4) chord
8. The area of triangle formed by the points(–5, 0), (0, –5 )and (5, 0) is
1) 0 sq.units 2) 5 Sq .units 3) 25 sq.units 4) none of these
9. The point of intersection of 3x – y = 4 and x + y = 8 is
1) (3, 5) 2) (2, 4) 3) (5, 3) 4) (4, 4)
5 1
10. If 5x =secθ and = tanθ then, x2 – 2 is equal to
x x
1
1) 1 2) 5 3) 25 4)
25
sin (90 - q ) cos (90 - q )cosq
11. + =
tanq cotq
1) tanθ 2) 1 3) –1 4) sin θ
12. The height and radius of the cone of which the frustum is a part are h1 units and r1 units respectively.
Height of the frustum is h2 units and radius of the smaller base is r2 units if h2 : h1 = 1:2 then r2:r1
is
1) 1 : 2 2) 2 : 1 3) 1 : 3 4) 3 : 1
13. The range of the first 10 prime numbers is
1) 9 2) 20 3) 27 4) 5
14. The average of first ‘n’ natural numbers is
n(n + 1) n n +1
1) 2) 3) 4) n
2 2 2
10th Std - Mathematics 8
PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. A relation R is given by the set {(x, y) / y = x + 3, x Î{0, 1, 2, 3, 4, 5}. Determine its domain and range.
16. If f (x) = x2 – 1, g (x) = x – 2, find a if g o f (a) = 1
17. If A and B are two mutually exclusive events of a random experiment and P (not A) = 0.45,
P(A È B) = 0.65, then find P(B).
x-7
18. If a polynomial P(x) = x2 – 5x – 14 is divided by another polynomial q(x) we get find q(x).
x+2
æ 7 -3ö
ç ÷
19. If A = ç - 5 2 ÷ then find the transpose of –A.
ç ÷
è 3 -5ø
20. If ∆ABC is similar to DEF such that BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm2. Find the area
of ∆DEF.
21. Find the slope of a line joining the points (sinθ, –cosθ) and (–sinθ, cosθ)
22. The hill in the form of a right triangle has its foot at (19, 3). The inclination of the hill to the ground is
45°. Find the equation of the hill joining the foot and top.
23. Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric progression.
24. If 1 + 2 + 3 +…+ n = 666 then find n.
25. Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from
the foot of a tower of height 10 3 m.
26. The ratio of the radii of two right circular cones of same height is 1:3. Find the ratio of their curved
surface area when the height of each cone is 3 times the radius of the smaller cone.
27. If two positive integers p and q are written as p = a2b3 and q = a3b; a, b are prime numbers, then verify
LCM (p, q) × GCD (p, q) = pq.
28. Find the number of spherical lead shots, each of diameter 6 cm that can be made from a solid cuboid of
lead having dimensions 24 cm × 22 cm × 12 cm.

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. In the figure, the quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of
the patio.
30. State and Prove Basic Proportionality Theorem (BPT) or Thales Theorem.
31. If f (x) = x – 4 , g (x) = x2 and h (x) = 3x – 5 then Show that (f o g) o h = f o (g o h).
32. Find the least positive value of x such that (i) 67 + x ≡ 1 (Mod 4) (ii) 98 ≡ (x+4) (Mod 5)
33. The houses of a street are numbered from 1 to 49. Senthil’s house is numbered such that the sum of
numbers of the houses prior to Senthil’s house is equal to the sum of numbers of the houses following
Senthil’s house. Find Senthil’s house number?
34. A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two
consecutive heads.
35. The temperature of two cities A and B in a winter season are given below.
Temperature of city A (in degree Celsius) 18 20 22 24 26
Temperature of city B (in degree Celsius) 11 14 15 17 18
Find which city is more consistent in temperature changes?

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 9 Model Question Papers
36. A = {x Î W / x < 2}, B = {x Î N / 1< x ≤ 4} and C = {3, 5}. Verify that A × (B È C)= (A×B) È (A×C).
37. Vani, her father and her grandfather have an average age of 53. One - half of her grand father’s age plus
one-third of her father’s age plus one fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was
four times as old as Vani then how old are they all now?
écos q 0 ù ésin q 0 ù 2 2
38. If A = ê ú B= ê ú then show that A + B = 1.
ë 0 cos q û ë 0 sin q û
39. A metallic sheet in the form of a sector of a circle of radius 21 cm has central angle of 216°. The sector
is made into a cone by bringing the bounding radii together. Find the volume of the cone formed.
40. A shuttle cock used for playing badminton has the shape of a frustum of a cone is mounted on a hemisphere.
The diameters of the frustum are 5 cm and 2 cm. The height of the entire shuttle cock is 7 cm. Find its
external surface area.
41. A motor boat whose speed is 18 km/hr in still water lakes 1 hour more to go to 24 km upstream than to
return downstream to the same spot. Find the speed of the stream.
42. A 1.2 m tall girl Jasmine spots a balloon moving with the wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the baloon from the eyes of the girl at an instant is 60°. After
some time the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the
interval.

PART - IV
Note: Answer all the questions. 2×8=16

43. a) Draw the graph of y = x2 – 5x – 6 and hence solve x2 – 5x – 14 = 0.

(OR)
b) Find the values of a and b if 16x – 24x + (a–1)x2 + (b+1)x + 49 is a perfect square.
4 3

44. a) Take a point which is 11cm away from the centre of a circle of radius 4cm and draw two tangents to
the circle from the point.
(OR)
b) In a figure ÐQPR = 90°. PS is its bisector. If ST PR, Prove that ST × (PQ + PR) = PQ × PR
***
10th Std - Mathematics 10

PTA MODEL QUESTION PAPER - 3

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - III 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.

1. A ={a, b, p}, B ={2, 3}, C ={p, q, r, s}, then n[(AÈ C) × B] is -----------.

1) 8 2) 12 3) 16 4) 20
x
2. Given f(x) = (–1) is a function from N to Z. Then the range of f is
1) {1} 2) N 3) {1, –1} 4) Z
3. The value of (13 + 23 + 33 + …. + 153) – (1 + 2 + 3 + ….. + 15) is
1) 14200 2) 14280 3) 14400 4) 14520
4. If 2 + 4 + 6 + … + 2k = 90, then the value of k is
1) 8 2) 9 3) 10 4) 11
5. A Straight line has equation 8y = 4x + 21, Which of the following is true?
1) The slope is 0.5 and the y intercept is 1.6
2) The slope is 0.5 and the y intercept is 2.6
3) The slope is 5 and the y intercept is 2.6
4) The slop is 5 and y intercept is 1.6
6. GCD of 6x2y, 9x2yz, 12x2y2z is
1) 36xy2z2 2) 36x2y2z 3) 36x2y2z2 (4) 3x2y
7. In ∆ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1cm then the length of
AE is
1) 1.05 cm 2) 1.2 cm 3) 1.4 cm 4) 1.8 cm
1
8. The slope of the line joining (1, 2, 3), (4, a) is The value of a is
8
1) 1 2) 2 3) 4 4) –5
9. (2, 1) is the point of intersection of two lines.
1) x + 3y – 3 = 0; x – y – 7 =0 2) 3x + y = 3; x + y =7
3) x + y = 3; 3x + y = 7 4) x – y – 3 = 0; 3x – y – 7 = 0
10. The value of tanθ cosec2θ – tanθ is equal to
1) cotθ 2) cot2θ 3) sinθ 4) secθ
11. The total surface area of a hemi-sphere is how much times the square of its radius.
1) 4π 2) 3π 3) 2π 4) π
12. If the volume of sphere is 36π cm3, then its radius is equal to
1) 3 cm 2) 2 cm 3) 5 cm 4) 10 cm
13. The range of the data 8, 8, 8, 8, 8, …., 8 is
1) 8 2) 3 3) 1 4) 0
14. If a letter is chosen at random from the English alphabets (a, b, .…, z) then the probability that
the letter chosen precedes x?
1 12 3 23
1) 2) 3) 4)
13 13 26 26

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 11 Model Question Papers
PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. Let f be a function and f : N → N be defined by f (x) = 3x + 2, x N.

Find the pre-image of 29, 53.
16. Is 7 × 5 × 3 × 2 + 3, a composite number? Justify your answer.
17. If 3 + k, 18 – k, 5k + 1 are in A.P, then find k.
18. If 13 + 23 + 33 + ...... k3 = 16900, then find 1 + 2 + 3 + .....+ k.
æ 7 8 6ö æ 4 11 -3ö
19. If A = ç 1 3 9 ÷ , B = ç -1 2 4 ÷ then find 2A + B
ç ÷ ç ÷
è -4 3 -1ø è 7 5 0ø
20. If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k.
a 2 + 3a - 4 2
21. If x = 2
and y = a + 2a - 8 find the value of x2y–2
3a - 3 2a 2 - 2a - 4
22. In ∆ABC, AD is the bisector of Ð A meeting side BC at D, if AB = 10 cm, AC = 14 cm and BC = 6 cm,
find BD and DC.

23. What is the inclination of a line whose slope is 1?

24. A player sitting on the top of a tower of height 20m observes the angle of depression of a ball lying on
the ground as 60°. Find the distance between the foot of the tower and the ball.( 3 = 1.732)
25. A cone of height 24cm is made up of modeling clay. A child reshapes it in the form of a cylinder of same
radius as cone. Find the height of the cylinder.
26. If A is an event of a random experiment such that P(A) : P( A) = 17: 15 and n(S) = 640 then find
(i) P( A) (ii) n(A) .
27. The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.
28. Show that the straight lines 3x – 5y + 7 = 0 and 15x + 9y + 4 = 0 are perpendicular.

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. Let A = {1, 2, 3, 4} and B = {2, 5, 8, 11, 14} be two sets. Let f : A → B be a function given by f (x) =
3x – 1. Represent this function. (i) by arrow diagram (ii) in a table form (iii) as a set of ordered pairs
(iv) in a graphical form
30. The distance S an object travels under the influence of gravity in time t seconds is given by
1
S(t) = gt2 + at + b where, (g is the acceleration due to gravity), a, b are constants.
2
Check if the function S(t) is one – one.
10th Std - Mathematics 12
31. A = {x Î W / 0 < x < 5}, B = {x Î W / 0 ≤ x ≤ 2} and C = { x Î W / x < 2}
Verify that A × (B ∩ C) = (A × B) ∩ (A × C).
32. Find the sum of the Geometric Series 3 + 6 + 12 + .... + 1536
33. Find the sum of all 3 digit natural numbers which are divisible by 9.
4 x 2 20 x 30 y 9 y 2
34. Find the square root of the expression + + 13 - + 2
y2 y x x
5x + 7
35. Solve the following quadratic equation by completing the square method = 3x + 2.
x -1
æ1 7 ö
æ 5 2 9ö
36. A = ç and B = ç 1 2 ÷ verify that (AB)T = BTAT
è 1 2 8÷ø ç ÷
è 5 -1ø
37. The hypotenuse of a right triangle is 6 m more than twice of the shortest side the third side is 2 m less
than the hypotenuse, find the sides of the triangle.
38. Find the equation of a straight line joining the point of intersection of 3x + y + 2 = 0 and x – 2y – 4 = 0
to the point of intersection of 7x – 3y = –12 and 2y = x + 3.
3tan q - tan 3 q
39. If 3 sinθ – cosθ = 0, then show that tan 3θ =
1 - 3tan 2 q
40. The radius of a conical tent is 7 m and the height is 24 m. Calculate the length of the canvas used to make
the tent if the width of the rectangular canvas is 4 m?
41. A card is drawn from a pack of 52 cards. Find the probability of getting a King or a Heart or a Red card.
42. Find the coefficient of variation of 18, 20, 15, 12, 25.

PART - IV
Note: Answer all the questions. 2×8=16

43. a) Draw the graph of y = 2x2 and hence solve 2x2 – x – 6 = 0.

(OR)
b) 
The following table shows the data about the number of pipes and the time taken to fill the same tank.
No. of pipes (x) 2 3 6 9
Time Taken (in min) (y) 45 30 15 10
Draw the graph for the above data and hence
(i) find the time taken to fill the tank when five pipes are used.
(ii) find the number of pipes when the time is 9 minutes.

44. a) D raw ∆PQR such that PQ = 6.8 cm, vertical angle is 50° and the bisector of the vertical angle meets
the base at D where PD = 5.2 cm.
(OR)
3
b) Construct a triangle similar to a given triangle PQR with its sides equal to of the
5
3
corresponding sides of the triangle PQR. (scale factor < 1)
5

***

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 13 Model Question Papers

PTA MODEL QUESTION PAPER - 4

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - I 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.

1. The range of R={(x, x2) | x is a prime number less than 13} is

1) {4, 9, 25, 49, 121} 2) {1, 4, 9, 25, 49, 121}
3) { 2, 3, 5, 7} 4) {2, 3, 5, 7, 11}
2. Let A = {1, 2, 3, 4}, B = {4, 8, 9, 10}. A function f : A→B given by
f ={(1, 4), (2, 8), (3, 9), (4, 10)} is a
1) Many–one function 2) Identity function 3) One to One function 4) Into function
3. If 6 times of 6 term of an A.P., is equal to 7 times the 7 term, then the 13th term of the A.P. is
th th

1) 0 2) 6 3) 7 4) 13
4. The sum of the exponents of prime factors in the prime factorization of 1729 is
1) 4 2) 3 3) 2 4) 1
5. If a and b are two positive integers where a>0 and b is a factor of a, then HCF of a and b is
a
1) b 2) a 3) 3ab 4)
b
2 2
6. If (x – 6) is the HCF of x – 2x – 24 and x – kx - 6 then the value of k is
1) 8 2) 6 3) 5 4) 3
7. If a polynomial is a perfect square then its factors will be repeated ______ number of times.
1) Odd 2) Zero 3) Even 4) None of the above
8. If ∆ABC-is an isosceles triangle with ÐC = 90°and AC = 5cm, then AB is
1) 5 2 cm 2) 10 cm 3) 2.5 cm 4) 5 cm
9. When proving that a quadrilateral is a trapezium ,it is necessary to show
1) Two parallel and two non-parallel sides 2) Two sides are parallel.
3) Opposite sides are parallel 4) All sides are of equal length
10. The equation of a line passing through the origin and perpendicular to the line
7x – 3y + 4 = 0 is
1) 7x – 3y + 4 = 0 2) 3x – 7y + 4 = 0 3) 7x – 3y = 0 4) 3x + 7y = 0
11. If sinθ = cosθ and 2tan2 θ + sin2θ – 1 is equal to
3 3 2 2
1) 2) – 3) 4) –
2 2 3 3
12. In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its
height is 20 cm, the volume of the material in it is
1) 56π cm3 2) 3600π cm3 3) 5600π cm3 4) 11200π cm3
13. Which of the following is incorrect?
1) P(A) + P(A) =1 2) P(φ) = 0 3) 0 ≤ P(A) ≤ 1 4) P(A) > 1
14. Probability of getting 3 heads or 3 tails in tossing a coin 3 times is
1 1 3 1
1) 2) 3) 4)
8 4 8 2
10th Std - Mathematics 14
PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. Find k if f o f (k) = 5 where f (k) = 2k – 1.

16. Let A = {1, 2, 3, ...... 100} and R be the relation defined as “is cube of “ on A. Find the domain and the
range of R.
17. In a theatre, there are 20 seats in the front row and 30 rows were allotted. Each successive row contains
two additional seats than its front row. How many seats are there in the last row?
1 1
18. In a G.P , – , 1, –2,..... Find t10.
4 2
2
3
19. Which rational expression should be subtracted from x + 6 x + 8 to get 2
3
x +8 x - 2x + 4
æ 3 ö
20. Determine the quadratic equations , whose sum and products of roots are çè - 2 , - 1÷ø
21. State Pythagoras Theorem.
BE BC
22. In a figure DE || AC and DC || AP Prove that = .
EC CP
23. Show that the points P(–1.5, 3), Q(6, –2) and R(–3, 4) are collinear.
cot A - cos A cos ec A - 1
24. Prove that =
cot A + cos A cos ec A + 1
25. The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3.
Find the ratio of heights.
26. The range of a set of data is 13.67 and the largest value is 70.08. Find the smallest value.
27. Write the sample space for selecting two balls from a bag containing 6 balls numbered
1 to 6 using tree diagram (with replacement).
28. Find the sum and product of the roots of equation 8x2 – 25 = 0.

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height.
Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y
= ax + b, where a, b are constants
Length x of forehand (in cm) Height ‘y’ (in inches)
35 56
45 65
50 69.5
55 74
i) Check if this relation is a function ii) Find a and b.
iii) Find the height of a woman whose forehand length is 40 cm.
iv) Find the length of forehand of a woman if her height is 53.3 inches.
30. A function f : [–5, 9] → R is defined as follows.
ì 6 x + 1 -5 £ x < 2
ï 2 2 f (-2) - f (6)
f (x) = í5 x - 1 2 £ x < 6 . Find (i) f (7) – f (1) and (ii)
ï 3x - 4 6 £ x £ 9 f (4) + f (-2)
î

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 15 Model Question Papers
31. Find the sum to n terms of the series 5 + 55 + 555 + .... .
32. A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find
their present ages.
33. Find the non-zero values of x satisfying the matrix equation
æ 2x 2 ö æ 8 5x ö æ x 2 + 8 24 ö
xç +
÷ ç2 ÷ = 2 ç ÷
è 3 x ø è 4 4x ø è 10 6x ø
34. Find the values of a and b if the following polynomials are perfect squares
4x4 – 12x3 + 37x2 + bx + a
35. State and Prove Alternate Segment Theorem.
36. Find the Equation of a straight line through the point of intersection of the lines
8x+3y = 18, 4x+5y = 9 and bisecting the line segment joining the points (5, –4) and (–7, 6).
37. A building and a statue are in opposite side of a street from each other 35m apart. From a point on the
roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of
the statue of 34°. Find the height of the statue.
(tan24° = 0.4452, tan 34° = 0.6745)
38. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand completely. This
bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap
is 24 cm, find the radius and slant height of the heap.
39. The consumption of number of guava orange on a particular week by a family are given below.
Number of Guavas 3 5 6 4 3 5 4
Number of Oranges 1 3 7 9 2 6 2
Which fruit is consistently consumed by the family?
40. In a class of 50 students, 28 opted for NCC, 30 opted for NSS and 1 opted both NCC and NSS. 8 One
of the students is selected at random, Find the probability that
i) The student opted for NCC but not NSS.
ii) The student opted for NSS but not NCC.
iii) The student opted for exactly one of them.
41. By using slopes, show that the points (1, –4), (2, –3) and (4, –7) form a right angled triangle.
42. A man saved ` 16,500 in ten years. In each year after the first he saved 100 more than he did in the
preceding year. How much did he save the first year?

PART - IV
Note: Answer all the questions. 2×8=16

43. a) Draw the graph of y = 2x2 and hence solve 2x2 – x – 6 = 0.

(OR)
1
b) Graph the following linear function y = x. Identify the constant of variation and verify it with the
2
graph. Also (i) find y when x = 9 (ii) find x when y = 7.5.
44. a) D raw a ∆PQR such that PQ = 6.8 cm, vertical angle is 50° and the bisector of the vertical angle meets
the base at D, where PD = 5.2 cm.
(OR)
b) Draw a ∆PQR in which QR = 5cm, ÐP = 40° and the median PG from P to QR is 4.4 cm. Find the
length of the altitude from P to QR.
***
10th Std - Mathematics 16

PTA MODEL QUESTION PAPER - 5

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - I 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.
1. f (x) = (x + 1)3 – (x – 1)3 represents a function which is
1) Quadratic 2) cubic 3) linear 4) reciprocal
2. Using Euclids’ division lemma, if the cube of any positive integer is divided by 9 then the possible
remainders are
1) 1, 3, 5 2) 1, 4, 8 3) 0, 1, 3 4) 0, 1, 8
3. An A.P. consists of 31 terms. if its 16th term is m, then the sum of all the terms of this A.P. is
31
1) 16 m 2) 62 m 3) m 4) 31 m
2
3y - 3 7y -7
4. ¸ is
y 3 y2
9 y3 9y 2 7 ( y 2 - 2 y + 1)
1) 2) 3) 21y - 423 y + 21 4)
( 21y - 21) 7 3y y2
5. The solution of x2 – 25 = 0 is
1) No real roots 2) Real and equal roots
3) Real and unequal roots 4) Imaginary roots
é1 3 5 ù T
6. For the given matrix A = ê ú the order of the matrix (AT) is
ë 2 4 6 û
1) 2 × 3 2) 3 × 2 3) 3 × 4 4) 4 × 3
7. The perimeters of two similar triangles ∆ABCand ∆PQR are 36 cm and 24 cm respectively. If PQ
= 10 cm, then length of AB is
2 2 10 6
1) 6 cm 2) 66 cm 3) cm 4) 15 cm
3 3 3
8. If (5, 7), (3, p) and (6, 6) are collinear, then the value of, p is
1) 9 2) 12 3) 3 4) 6
9. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order
then the value of p is
1) –7 2) 7 3) 6 4) – 6
10. acotθ + bcosecθ = p and bcotθ + acosecθ = q then , p2 – q2 is equal to
1) a2 + b2 2) a2 – b2 3) b2 – a2 4) b – a
11. The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same
height is
1) 1 : 2 : 3 2) 3 : 1 : 2 3) 2 : 1 : 3 4) 1 : 3 : 2
12. C.S.A of solid sphere is equal to
1) T.S.A of solid sphere 2) T.S.A of hemisphere 3) C.S.A of hemisphere 4) None of these
13. Variance of first 20 natural numbers is
1) 32.25 2) 33.25 3) 44.25 4) 30
14. Which of the following is incorrect?
1) P(A) + P( A) = 1 2) P(φ) = 0 3) 0 ≤ P(A) ≤ 1 4) P(A) > 1

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 17 Model Question Papers
PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f (x) = x3 then,

i) Find the range of f ii) Identify the type of function.
16. If 3 + k, 18 – k, 5k + 1 are in A.P, then find k.
17. Find the geometric progression whose first term and common ratios are given by a = –7, r = 6.
144a8b12 c16
18. Find the square root of
81 f 12 g 4 h14
19. Which term of an A.P 21, 18, 15,…. is –81? State with reason is there any term 0 in this A.P?
20. A relation R is given by the set {(x, y)/y = x + 3, x Î{0, 1, 2, 3, 4, 5}. Determine its domain and range.
æ 0 4 9ö æ 7 3 8ö
21. A = ç and B = ç find the value of 3A – 9B.
÷
è 8 3 7ø è 1 4 9÷ø
22. From the figure, AD is the bisector of ÐA. If BD = 4 cm,
DC = 3 cm and AB = 6 cm, find AC.
23. Show that the straight lines x – 2y + 3 = 0 and 6x + 3y + 8 = 0 are perpendicular.

24. Prove that sec q - tan q = 1 - sin q

sec q + tan q cos q
25. Find the sum of the following series 103 + 113 + 123 + ...... + 203
26. Find the range of the following distribution.
Age (in Years) 16 – 18 18 – 20 20 – 22 22 – 24 24 – 26 26 – 28
Number of students 0 4 6 8 2 2
27. Three fair coins are tossed together. Find the probability of getting
i) Atleast one tail ii) Atmost one head
1
28. Find the value of p, when px2 + ( 3 – 2 )x – 1 = 0 and x = is one root of the equation.
3
PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. Let A = {x Î W / x < 2}, B = {x Î N / 1 < x ≤ 4} and C = {3, 5}.

Verify that A × (B ∩ C) = (A × B) ∩ (A × C).
30. If f(x) = 2x + 3, g(x) = 1 – 2x and h(x) = 3x. Prove that f o (g o h) = (f o g ) o h.
31. A man repays a loan of ` 65,000 by paying ` 400 in the first month and then increasing the payment by
` 300 every month. How long will it take for him to clear the loan?
32. If the radii of the circular ends of a frustum which is 45 cm high are 28 cm and 7 cm, find the volume of
the frustum.
33. Solve the following system of linear equations in three variables
x + y + z = 5, 2x – y + z = 9, x – 2y + 3z = 16.
34. Find the square root of 289x4 – 612x3 + 970x2 – 684x + 361.

é1 -1ù
35. If A = ê ú then, Prove that A2 – 4A + 5I2 = 0
ë2 3 û
36. State and Prove Angle Bisector Theorem.
10th Std - Mathematics 18
37. Find the value of k, if the area of quadrilateral is 28 sq.units, whose vertices are (–4, –2), (–3, k), (3, –2)
and (2, 3).
38. Two ships are sailing in the sea on either sides of a light house. The angle of elevation of the top of the
lighthouse as observed from the ships are 30° and 45° respectively. If the lighthouse is 200m high, find
the distance between the two ships. ( 3 = 1.732)
39. A right circular cylindrical container of base radius 6cm and height 15 cm is full of ice cream. The ice
creams to be filled in cones of height 9cm and base radius 3 cm, having a hemispherical cap. Find the
number of cones needed to empty the container.
40. A well of diameter 3 m is 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 4m to form an embankment. Find the height of the embankment.
41. The time taken by 50 students to complete a 100 meter race are given below. Find its standard deviation.
Time taken (sec) 8.5 – 9.5 9.5 – 10.5 10.5 – 11.5 11.5 – 12.5 12.5 – 13.5
Number of students 6 8 17 10 9
42. A card is drawn from a pack of 52 cards. Find the probability of getting a Queen or a diamond or a black
card.

PART - IV
Note: Answer all the questions. 2×8=16

43. a) A company initially started with 40 workers to complete the work by 150 days. Later, it decided to
fasten up the work increasing the number of workers as shown below.
Number of workers (x) 40 50 60 75
Number of days (y) 150 120 100 80
(i) Graph the above data and identify the type of variation.
(ii) From the graph, find the number of days required to complete the work if the company decides
to opt for 120 workers?
(iii) If the work has to be completed by 30 days, how many workers are required?
(OR)
b) Draw the graph of y = x + 3x – 4 and hence use it solve x2 + 3x – 4 = 0
2

44. a) C  onstruct a triangle ∆PQR such that QR = 5 cm, ÐP = 30° and the altitude from P to QR is of length
4.2 cm.
(OR)
b) Draw the two tangents from a point which is 10cm away from the centre of a circle of radius 5cm.
Also, measure the lengths of the tangents.

***

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 19 Model Question Papers

PTA MODEL QUESTION PAPER - 6

Time: 3 hrs
CLASS: X MATHEMATICS Marks: 100

Note: (i) Answer all the 14 questions.

PART - I 14×1=14
(ii) Choose the most suitable answer from the given four alternative and write the option code
with the corresponding answer.

1. If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function given by g(x)= αx + β then the values of α and β are
1) (1, 2) 2) (–1, 2) 3) (2, –1) 4) (–1, –2)
2. The given diagram represents
1) an onto function 2) a constant function 3) an one-one function 4) not a function
3. If A = 265 and B = 264 + 263 + 262 + …. + 20 which of the following is true?
1) B is 264 more than A 2) B is larger then A by 1
3) A and B are equal 4) A is larger then B by 1
a-b
4. If a, b, c are in A.P then is equal to
b-c
a b a
1) 2) 3) 4) 1
b c c
1
5. y2 + is not equal to
y2
2 2 2
é 1ù é 1ù é 1ù y4 + 1
1) ê y - ú + 2 2) ê y + –2 3) ê y + 4)
ë yû ë y úû ë y úû y2

æ 1 3ö æ 5 7ö
6. Find the matrix x if 2X + ç ÷ = ç
è 5 7ø è 9 5÷ø
æ 2 1ö æ 1 2ö æ -2 -2ö æ2 2 ö
1) ç 2) ç 3) ç 4) ç
è 2 2÷ø è 2 2÷ø è 2 -1÷ø è 2 -1÷ø

x 2 - 25 x+5
7. On dividing by 2 is equal to
x+3 x -9
1) (x – 5) (x – 3) 2) (x – 5) (x + 3) 3) (x + 5) (x – 3) 4) (x + 5) (x + 3)
8. In a ∆ABC, AD is the bisector of, ÐBAC If AB = 8cm BD = 6 cm and DC = 3 cm. The length of the
side AC is
1) 3 cm 2) 4 cm 3) 6 cm 4) 8 cm
9. In a given figure, PR = 26 cm, QR = 24 cm ÐPAQ = 90°, PA = 6cm, QA = 8 cm. Find ÐPQR
1) 90° 2) 85° 3) 80° 4) 75°
10. If slope of the line PQ is 1 , then slope of the perpendicular bisector of PQ is
3
1
1) 0 2) 3 3) – 3 4)
3
11. If the ratio of the height of a tower and the length of its shadow is 3 : 1, then the angle of elevation
of the sun has measure
1) 90° 2) 60° 3) 45° 4) 30°
10th Std - Mathematics 20
12. A spherical ball of radius r1 units is melted to mark 8 new identical balls each of radius r2 units.
Then r1 : r2 is
1) 1 : 4 2) 4 : 1 3) 1 : 2 4) 2 : 1
13. A fair die is thrown once. The probability of getting a prime (or) composite number is
5 1
1) 1 2) 0 3) 4)
6 6
14. Which of the following is not a measure of dispersion?
1) Range 2) Standard deviation
3) Arithmetic mean 4) Variance

PART - II
Note: Answer any 10 questions. Question No. 28 is compulsory. 10×2=20

15. Let f be a function from R to R defined by f(x) = 3x – 5. Find the values of a and b given that (a, 4) and
(1, b) belong to f.
16. If R = {(x, –2), (–5, y)} represents the identity function, find the value of x and y?
17. Find the common difference of an A.P. in which t18 – t14 = 32.
18. Find the number of integer solutions 3x ≡ 1 (mod 15)
19. Find the sum of 1 + 3 + 5 + ….. + 55.
20. Solve 2x2 – 2 6 x + 3 = 0
24
21. If the difference between a number and its reciprocal is , find the number.
5
-13
22. If α and β are the roots of equation 7x2+ax+2 = 0 and if β – α = .
Find the values of α. 7
23. The line through the points (–2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and
(x, 24). Find the value of x.
24. From the top of a rock 50 3 m high, the angle of depression of a car on the ground is observed to be 30°.
Find the distance of the car from the rock.
25. A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume
is 3 3 : 4.
26. Find the standard deviation of first 21 natural numbers.
27. A and B are two candidates seeking admission to IIT. The probability that A getting selected is 0.5 and
the probability that both A and B getting selected is 0.3. Prove that the probability of B being selected is
atmost 0.8.
28. P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm, PB = 6 cm, AQ = 5 cm and
QC = 10 cm, show that BC = 3PQ.

PART - III
Note: Answer any 10 questions. Question No. 42 is compulsory. 10×5=50

29. Write the domain of the following functions: (i) f (x) =

(2 x + 1)
ii) g (x) = x - 2
x-9
30. If f : R ® R and g : R ® R are defined by f (x)= x5 and g (x) = x4 then check if f and g are one-one and
fog is one - one?
31. If the sum of the first p terms of an A.P is ap2 + bp. Find its common difference.
32. A man joined a company as Assistant Manager. The company gave him a starting salary of ` 60,000 and
agreed to increase his salary 5% annually. What will be his salary after 5 years?

A. SIVAMOORTHY, BT. Asst. GHS, Perumpakkam, Villupuram Dt.

 21 Model Question Papers
33. If the roots of the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are real and equal prove that either
a = 0 (or) a3 + b3 + c3 = 3abc.
34. Find the LCM of the following polynomical a2 + 4a – 12, a2 – 5a + 6 whose GCD is a – 2.
æ 1 2ö æ 0 3ö æ -1 5ö
35. If A = ç ÷ , B = ç ÷ ,C= ç , Prove that A(BC) = (AB) C.
è 3 4ø è -1 5ø è 1 3÷ø
36. The perpendicular PS on the base QR of a ∆ PQR intersects QR at S, such that QS = 3 SR.
Prove that 2PQ2 = 2PR2 + QR2
37. Find the equation of the median and altitude of ∆ABC through A where the vertices are
A(6, 2), B(–5, –1) and C(1, 9).
æ cos3 A - sin 3 A ö æ cos3 A + sin 3 A ö
38. Prove that ç – = 2 sinAcosA
è cos A - sin A ÷ø çè cos A + sin A ÷ø
39. If the slant height of the frustum cone is 10 cm and perimeters of its circular base are 18 cm and 28 cm
respectively. What is the curved surface area of a the frustum?
40. A right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice cream. The ice
cream is to be filled in cones of height 9 cm and base radius 3 cm, having a hemispherical cap. Find the
number of cones needed to empty the container.
41. The following table gives the values of mean and variance of heights and weights of the 10th standard
students of a school
Height Weight
Mean 155 cm 46.50 cm
Variance 72.25 cm 28.09 cm
Which is more varying than the other?
42. A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two
consecutive heads.

PART - IV
Note: Answer all the questions. 2×8=16

43. a) Draw the two tangents from a point which is 10cm away from the centre of a circle of radius 5cm.
Also, measure the lengths of the tangents.
(OR)
3
b) Construct a triangle similar to a given triangle PQR with its sides equal to of the corresponding
3 5
sides of the triangle PQR (scale factor < 1)
5

44. a) Draw the graph of y = x2 – 5x – 6 and hence solve x2 – 5x – 14 = 0

(OR)
b) The following table shows the data about the number of pipes and the time taken to till the same tank.
No. of pipes (x) 2 3 6 9
Time Taken (in min) (y) 45 30 15 10
Draw the graph for the above data and hence
(i) find the time taken to fill the tank when five pipes are used
(ii) Find the number of pipes when the time is 9 minutes.

***