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Padasalai.net Centum Question Paper

1. If 𝐴 = {(𝑥, 𝑦): 𝑦 = sin 𝑥 , 𝑥 ∈ 𝑅} and 𝐵 = {(𝑥, 𝑦): 𝑦 = cos 𝑥 , 𝑥 ∈ 𝑅} then 𝐴 ∩ 𝐵 contains

(1) no element (2) infinitely many elements

(3) only one element (4) cannot be determined

2. The domain of the function 𝑓 = {(1,3), (3,5), (2,6)} is

(1)1, 3 and 2 (2) {1,3,2} (3){3,5,6} (4) 3, 5 𝑎𝑛𝑑 6

3. The value of log31

81 is

(1)−2 (2)−8 (3)−4 (4) −9

4. For any 𝑥, 𝑦 ∈ ℝ, |𝑥 + 𝑦| ≤

(1) |𝑥| + |𝑦| (2) |𝑦| (3) |𝑥| |𝑦| (4) |𝑥|

5. If tan 400 = 𝜆, then tan 1400−tan 1300

1+tan 1400 tan 1300=

(1) 1−𝜆2

𝜆 (2)

1+𝜆2

𝜆 (3)

1+𝜆2

2𝜆 (4)

1−𝜆2

2𝜆

6. cos (3𝜋

2− 𝜃) =

(1) − cos 𝜃 (2) − sin 𝜃 (3) sin 𝜃 (4) cos 𝜃

7. The number of rectangles that a chess board has

(1) 81 (2) 99 (3) 1296 (4) 6561

8. Number of triangles formed by joining the vertices of an octagon is ……..

(1) 56 (2) 28 (3) 112 (4) 12

9. The value of 1 − 1

2(

2

3) +

1

3 (

2

3)

2−

1

4 (

2

3)

3+ …….. is

(1) log (5

3) (2)

3

2 log (

5

3) (3)

5

3 log (

5

3) (4)

2

3 log (

2

3)

10. The term containing 𝑥6 in the expansion of (2𝑥3 + 𝑥−1)10 is

(1)7 (2)8 (3)9 (4)10

11. A line perpendicular to the line 5𝑥 − 𝑦 = 0 forms a triangle with the coordinate axes. If the

area of the triangle is 5 sq.units, then its equation is

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(1) 𝑥 + 5𝑦 ± 5√2 = 0 (2) 𝑥 − 5𝑦 ± 5√2 = 0 (3) 5𝑥 + 𝑦 ± 5√2 = 0 (4) 5𝑥 − 𝑦 ± 5√2 = 0

12. The vertices of a triangle are (6,0), (0, 6) and (6, 6).The distance between its circumcentre

and centroid is

(1) 2√2 (2) 2 (3) √2 (4) 1

13. What must be the matrix X, if 2X +[1 23 4

] = [3 87 2

]?

(1) [1 32 −1

] (2) [1 −32 −1

] (3) [2 64 −2

] (4) [2 −64 −2

]

14. If A (𝑎𝑑𝑗 𝐴) = 81, for a 3 x 3 matrix, then det A is equal to

(1) 1 (2) 2 (3) 4 (4) 8

15. If |�⃗� + �⃗⃗�| = 60, |�⃗� − �⃗⃗�| = 40 and |�⃗⃗�| = 46, then |�⃗�| is

(1) 42 (2) 12 (3) 22 (4) 32

16. If �⃗� is a non-zero vector and 𝑚 is a non-zero scalar then 𝑚�⃗� is a unit vector if

(1) 𝑚 = ±1 (2) 𝑎 = |𝑚| (3) 𝑎 =1

|𝑚| (4) 𝑎 = 1

17. lim𝑥→0

8𝑥−4𝑥−2𝑥+1𝑥

𝑥2=

(1) 2 log 2 (2) 2(log 2)2 (3) log 2 (4) 3 log 2

18. The value of lim𝑥→1

𝑥2+4𝑥−5

𝑥−1

(1) 0 (2) 6 (3) 5 (4) −6

19. If 𝑦 = cos(sin 𝑥2), then 𝑑𝑦

𝑑𝑥 at 𝑥 = √

𝜋

2 is

(1) −2 (2) 2 (3)−2 √𝜋

2 (4)0

20. If 𝑓(𝑥) =𝑒4𝑥

1+2𝑒𝑥 than 𝑓′(0) is

(1) 9

10 (2)

10

9 (3) −10 (4)

4

3

21. Justify the truness of the statement: “An element of a set can never be a subset of itself”

22. Solve : 2|𝑥 + 1| − 𝑥 = 4𝑥 − 4

23. Find the value of sin 1500

24. Find the value of (𝑛+3)!

(𝑛+1)!



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25. Compute 1024

26. Find the equation of a straight line cutting an intercept of 5 from the negative direction of the

𝑦-axis and is inclined at an angle 1500 to 𝑥-axis

27. If 𝐴 is a square matrix and |𝐴| = 2, find the value of |𝐴𝐴𝑇|

28. If �⃗�, �⃗⃗� and 𝑐 are the sides of a triangle taken in order then �⃗� + �⃗⃗� + 𝑐 = 0⃗⃗

29. Compute lim𝑥→−2

(−3

2𝑥)

30. Differentiate the following with respect to 𝑥, 𝑦 = (𝑥 −1

𝑥)

2

31. Show that the relation 𝑥𝑦 = −2 is a function for a suitable domain. Find the domain and the

range of the function.

32. Find the logarithm of 1728 to the base 2√3

33. In a school, each section of class XI has exactly 40 students. If there are 4 sections, in how

many ways can a set of students representatives be selected from each section.

34. If 𝑡𝑘 is the 𝑘th term of a GP, then show that 𝑡𝑛−𝑘 , 𝑡𝑛, 𝑡𝑛+𝑘 also form a G.P for any positive integer 𝑘

35. Find the equation of the line passing through (−3,5) and perpendicular to the line through the

points (2,5) and (−3,6)

36. If two rows (columns) of a matrix are identical, then its determinant is zero.

37. Let 𝐴 and 𝐵 be two points with position vectors 2�⃗� + 4�⃗⃗� and 2�⃗� − 8�⃗⃗� . Find the position

vectors of the points which divide the line segment joining 𝐴 and 𝐵 in the ratio 1:3 internally

and externally.

38. Evaluate lim𝑥→0

(1 + sin 𝑥)2 𝑐𝑜𝑠𝑒𝑐 𝑥

39. Find the derivative of the sin function, sin 𝑥

40. Prove cos(𝛼 − 𝛽) = cos 𝛼 cos 𝛽 + sin 𝛼 sin 𝛽

41. a) A simple cipher takes a number and codes it, using the function 𝑓(𝑥) = 3𝑥 − 4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line 𝑦 = 𝑥 (by drawing the lines)

(OR)

41. b). Let Z denote the set of all integers Define R on Z as follows 𝑅 = {(𝑛, 𝑚) ∈ 𝑅 if 𝑛 ≡ 𝑚(𝑚𝑜𝑑 9)}

Verify whether it is an equivalence relation.



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42. a) Resolve the following rational expressions into partial fractions 1

𝑥2−𝑎2

(OR)

42. b) Prove that cos 𝐴 cos 2𝐴 cos 22 𝐴 cos 23 𝐴 … cos 2𝑛−1 𝐴 =sin 2𝑛𝐴

2𝑛 sin 𝐴

43.a) In a ∆𝐴𝐵𝐶, if sin 𝐴

sin 𝐶=

sin(𝐴−𝐵)

sin (𝐵−𝐶) , Prove that 𝑎2, 𝑏2, 𝑐2 are in Arithmetic Progression.

(OR)

43 b) Prove that (2𝑛)!

𝑛!= 2𝑛(1.3.5 … (2𝑛 − 1))

44 a) Prove that √𝑥3 + 73

− √𝑥3 + 43

is approximately equal to 1

𝑥2 when 𝑥 is large

(OR)

44.b) The sum of the distance of a moving point from the points (4,0) and (−4,0) is always 10 units.

Find the equation of the locus of the moving point.

45. a) Find the equation of the straight line passing through point (2,2) and the sum of the intercept

is 9.

(OR)

45. b) Without expanding the determinants, show that |𝐵| = 2|𝐴|, where𝐵 =

[𝑏 + 𝑐 𝑐 + 𝑎 𝑎 + 𝑏𝑐 + 𝑎 𝑎 + 𝑏 𝑏 + 𝑐𝑎 + 𝑏 𝑏 + 𝑐 𝑐 + 𝑎

] and 𝐴 = [𝑎 𝑏 𝑐𝑏 𝑐 𝑎𝑐 𝑎 𝑏

]

46 a) Show that the points 𝐴(1,1,1), 𝐵(1,2,3)and 𝐶(2, −1,1) are vertices of an isosceles triangle

(OR)

46.b) Prove that lim𝑥→𝑎

𝑥𝑛−𝑎𝑛

𝑥−𝑎= 𝑛𝑎𝑛−1

47. a) State and prove Chain Rule or composite function rule or function of a function rule

(OR)

47. b) Find the cosine and sine angle between the vectors �⃗� = 2𝑖̂ + 𝑗̂ + 3�̂� and �⃗⃗� = 4𝑖̂ − 2𝑗̂ + 2�̂�

Prepared by

K. Dinesh, M.Sc., M.Phil., P.G.D.C.A., (Ph.D)

Way to success teachers team,

General body member, SMART Teachers Association

P.G. Asst. in Mathematics, UDVHSS, Trichy (Ex.)

Personal Address

K. Dinesh, 69, Anna nagar west, Pettavaithalai, Srirangam taluk, Trichy-Dt-639 112

Cell: 7418865975




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