MATHEMATICS Padasalai’s Centum Coching Team –Special Question Paper

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Padasalai’s Centum Coching Team –Special Question Paper
MATHEMATICS
X – STD
MARKS: 100
SECTION – I (Marks: 15)
Note: (i) Answer all the 15 questions. (ii) Choose the correct answer in each question.
Each of the questions contains 4 options with just one correct option. (iii) Each question
carries one mark.
15 x 1 = 15
1. A = {5, 6, 7} B = {1, 2, 3, 4, 5} and f: A B is defined by f(x) = x – 2 then the range
of f is _____ (a) {1, 4, 5} (b) {1, 2, 3, 4, 5} (c) {2, 3, 4} (d) {3, 4, 5}
2. If 1 + 2 + 3+ …. + n = k then 13 + 23 + 33 + ….. + n3 is
(a) K2 (b) k3 (c) k (k + 1) (d) (k + 1) 3
3. If the product of the first 4 consecutive terms of a G.P is 256 and if the common ratio
is 4 and the first term is positive, then its 3rd term is
(a) 8 (b) 1 / 16 (c) 1 / 32 (d) 16
4. The system of equations x – 4y = 8, 3x – 12y = 24.
(a) has infinitely many solutions (b) has no solution (c) has a unique solution
(d) may or may not have a solution
5. Let b = a + c. Then the equation ax2 + bx + c = 0 has equal roots, if
(a) a = c (b) a = - c (c) a = 2c (d) a = - 2c
2
6. If ( 5  1 ) −1 = ( 20 ) then the value of x is
3
(a) 7 (b) – 7 (c) 1 / 7 (d) 0
7. If a straight line y = 2x + k passes through the point (1, 2) then the value of k is
(a) 0 (b) 4 (c) 5 (d) - 3
8. The angle of inclination of a straight line parallel to x axis is
(a) 0o (b) 60o (c) 45o (d) 90o
9. The sides of 2 similar triangles are in the ratio 2: 3, then their areas are in the ratio
(a) 9: 4 (b) 4: 9 (c) 2: 3 (d) 3: 2
10. ΔABC is a right angled triangle where B = 90 and BD
AC. If BD = 8 cm AD = 4
cm then CD is _____ (a) 24 cm (b) 16 cm (c) 32 cm (d) 8 cm
11. (1 + cot2 θ) )( 1 – cos θ) ( 1 + cos θ) = _____
(a) tan2 θ – sec2 θ (b) sin2θ – cos2 θ (c) sec2 θ – tan2 θ (d) cos2 θ – sin2 θ
12. A man is 28.5 m away from a tower. His eye level above the ground is 1.5 m. The
angle of elevation of the tower from his eyes is 45o. Then the height of the tower is
(a) 30 m (b) 27. 5 m (c) 28. 5 m (d) 27 m
13. If the radius of a sphere is half of the radius of another sphere, then their respective
volumes are in the ratio
(a) 1: 8 (b) 2: 1 (c) 1: 2 (d) 8: 1
14. Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of
variation is
(a) 42 (b) 25 (c) 28 (d) 48
15. The probability that a non – leap year will have 53 Sundays and 53 Mondays is
(a) 1 / 7 (b) 2 / 7 (c) 3 / 7 (d) 0
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SECTION – II (Marks : 20)
Note: (i) Answer any 10 questions in all. (ii) Question No. 30 is compulsory. Select any 9
questions from the first 14 questions. (iii) Each question carries 2 marks.
10 x 2 = 20
16. Let U = {4, 8, 12, 16, 20, 24, 28} A = {8, 16, 24} B = {4, 16, 20, 28} Find (AUB) l
and (A∩B)l
17. A = { -2, -1, 1, 2} and f = {(x, 1/x) : x ∈ A} Write down the range of f. is f a function
from A to A?
18. Prove that (x – 1) is a factor of x3 – 6x2 + 11 x – 6
19. Simplify x + 8
x–2 2–x
2
10
−1
20. Find a and b if a
+ b
=
3
5
1
2 −5
3 5
21. Prove that
are multiplicative inverse to each other.
1 2 −1 3
22. Find the slope and y intercepts of the equation 4x – 2y + 1 = 0
23. If AB and CD are two chords of a circle which intersect each other internally at P and
CP = 4 cm, AP = 8 cm, PB = 2 cm then find PD.
24. Prove that (sin6 θ + cos6 θ ) = 1 – 3 sin2 θ cos2 θ
25. A ladder leaning against a vertical wall, makes an angle of 60o with the ground. The
foot of the ladder is 3.5 m away from the wall. Find the length of the ladder.
26. If the curved surface area of a solid hemisphere is 2772 sq.cm, then find its total
surface area.
27. The volume of a solid right circular cone is 4928 cu. Cm.. if its height is 24 cm then
find the radius of the cone ( = 22 / 7)
28. If n = 10, x = 12 and Ʃx2 = 1530 then calculate the coefficient of variation
29. Find the probability that a non – leap year selected at random will have 53 Fridays.
30. (a) Find the sum of the geometric series 1 + 11 + 111+ …… to 20 terms. (OR)
(b) Prove that the straight lines x + 2y + 1 = 0 and 2x – y + 5 = 0 are perpendicular to
each other.
SECTION – III (Marks: 45)
Note: (i) Answer any 9 questions in all. (ii) Question No. 45 is compulsory. Select any 8
questions from the first 14 questions. (iii) Each questions carries 5 marks.
9 x 5 = 45
31. Using venn diagram verify A \ (B∩C) = (A \ B) U (A \ C)
32. A function f : [1, 6)  R is defined as follows
1+x
1≤ x < 2
f (x) = 2x – 1
2≤x<4
2
3x – 10
4≤x<6
Find the value of (i) f(5) (ii) f (3) (iii) f(1) (iv) f(2) – f(4) (v) 2 f(5) – 3 f(1)
33. If a, b, c are in G.P and a 1/x = b 1/y = c 1/z show that x, y, z are in A.P (where x, y, z ≠
0)
34. If S1, S2 and S3 are the sum of first n, 2n and 3n terms of a geometric series
respectively then prove that S1(S3 – S2) = (S2 – S1)2.
35. Factorize x3 – 3x2 – 10x + 24.
36. If ax4 – bx3 + 40 x2 + 24 x + 36 is perfect square then find the values of a and b.
37. Solve
3 2
4 5


=
8
13
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38. Find the area of the quadrilateral formed by the points (-4, -2) (-3, -5) (3, -2) and (2,
3)
39. Find the equation of the line whose gradient is 3 / 2 and which passes through p,
where p divides the line segment joining A (-2, 6) and B (3, -4) in the ratio 2: 3
internally.
40. State and prove Pythagoras theorem.
41. A girl standing on a lighthouse built on a cliff near the seashore, observes two boats
due East of the lighthouse. The angles of depression of the two boats are 30o and 60 o.
The distance between the boats is 300 m. Find the distance of the top of the lighthouse
from the sea level
42. A capsule is in the shape of a cylinder with 2 hemispheres stuck to each of its ends.
The length of entire capsule is 4 1/3 cm and the diameter of the capsule is 2/3 cm.
Now 63 such capsules are kept inside a cylindrical vessel. The remaining capacity of
the vessel is filled with 86 / 9 cu. Cm of liquid. Find the height of the vessel, if the
base area of the vessel is 20 sq.cm
43. Find the variance of the following distribution
C.I
3.5 – 4.5
4.5 – 5. 5
5. 5 – 6.5
6. 5 – 7. 5 7. 5 – 8. 5
f
9
14
22
11
17
44. Two dice are rolled simultaneously. Find the probability that the sum of the numbers
on the faces is neither divisible by 3 nor by 4.
45. (a) If  and  are the roots of the equation 2x2 – 3x - 5 = 0, form a quadratic equation
whose roots are  2   2 (OR)
(b) A cylindrical bucket of height 32 cm and radius 18 cm is filled with sand. The
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.
SECTION – IV (Marks: 20)
Note: (i) This section contains 2 questions, each with 2 alternatives. (ii) Answer both the
questions choosing either of the alternatives. (iii) Each questions carries 10 marks
2x 10 = 20
46. (a) Construct a triangle PQR such that PQ = 4 cm R = 25o and the altitude from R to
PQ is 4. 5 cm
(OR)
(b) Construct a cyclic quadrilateral PQRS such that PQ = 5.5 cm, QR = 4.5 cm QPR
= 45o and PS = 3 cm
47. (a) Solve graphic ally (2x + 1) (x – 3) = 0
(OR)
(b) A bank gives 10% S.I on deposits for senior citizens. Draw the graph for the
relation between the sum deposited and the interest earned for one year. Hence find
(i) the interest on the deposit of Rs.650
(ii) the amount to be deposited to earn an interest of Rs.45.
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வா .
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Mr. A. NIVAS, B.Sc., B.Ed., B.T.Asst., Velavan matric hr.sec.school, Palavanjipalayam, ­ 641 608 Tirupur. Cell No: 9942240841 If any doubt, Please contact our Padasalai’s Centum Coaching Team Co­ordinator:
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