TNSCERT XII Standard Mathematics Model Question Paper 2019 : Educational Research and Training Tamilnadu

Organisation : State Council of Educational Research and Training Tamilnadu
Exam : Higher Secondary Second Year
Document Type : XII Standard – Model Question Paper Download
Category or Subject : Mathematics
Website : http://www.tnscert.org/webapp2/xiimodelquestionspaper.aspx

TNSCERT XII Standard Mathematics Model Question Paper

** The Government of Tamil Nadu has taken a policy decision on reducing the maximum marks for Higher Secondary Board Examination from 1200 to 600 in order to reduce the examination stress of students besides reducing the number of papers for Language subjects from two to one.

Related : TNSCERT XII Standard English Model Question Paper 2019 : www.pdfquestion.in/33971.html

Note :
** These are only model questions. Teachers and students need to focus only on the Pattern of the questions.

Mathematics

Duration: 2.30 Hrs.
Marks : 90

Part – I

All questions are compulsory 20 × 1 = 20
Choose the correct answer
1. Let A be a square matrix all of whose entries are integers. Then which one of the following is true ?
a) If det (A) = +1, then A–1 exists but all its entries are not necessarily integers
b) If det (A) ? +1, then A–1 exists and all its entries are non integers
c) If det (A) = +1, then A–1 exists and all its entries are integers
d) If det (A) = +1, then A–1 need not exist

2. If abc are vectors such that abc0753,abc0753,then angle between vectorsabc and abc is
a) 600
b) 300
c) 450
d) 900

3. Let A and B denote the statements
A : Cosa + Cosb + Cosg = 0
B : Sina + Sinb + Sing = 0. If Cos (b – g) + Cos (g – a) + Cos (a – b) = -32 then
a) A is true and B is false
b) A is false and B is true
c) both A and B are true
d) both A and B are false

4. The conjugate of i13 + i14 + i15 + i16 is
a) 1
b) –1
c) 0
d) –i

5. The eccentricity of an ellipse with its centre at the origin is 12. If one of the directrices is x = 4, then the equation of the ellipse is
a) 3×2 + 4y2 = 1
b) 3×2 + 4y2 = 12
c) 4×2 + 3y2 = 12
d) 4×2 + 3y2 = 1

Download Model Question Paper :
Model – 1 :
https://www.pdfquestion.in/uploads/pdf2019/33980-Mat1.pdf
Model – 2 :
https://www.pdfquestion.in/uploads/pdf2019/33980-Mat2.pdf
Model – 3 :
https://www.pdfquestion.in/uploads/pdf2019/33980-Mat3.pdf

8. One of the foci of the rectangular hyperbola xy = 18 is
a) (6, 6)
b) (3, 3)
c) (4, 4)
d) (5, 5)

10. If y = 6x – x3 and x increases at the rate of 5 units per second, the rate of change of slope when x = 3 is
a) – 90 units/sec
b) 90 units/sec
c) 180 units/sec
d) –180 units/sec

12. The point on the curve x = at2, y = 2at, at which the tangent is at 450 to the x axis is
a) (2a, a)
b) (a, –2a)
c) (2a, 22a)
d) (a, 2a)

13. The area bounded by the parabola x2 = 4 – y and the lines y = 0 and y = 3 is
a) 143sq.units
b) 283 sq. units
c) 43 sq. units
d) 563 sq.units

17. The order of an element a of a group is 10. (ie) 0(a) = 10 Then the order of (a2)–1 is
a) 10
b) 5
c) 2
d) 1

18. The value of [3] + 11 ([5] + 11 [6]) is
a) [0]
b) [1]
c) [2]
d) [3]

19. When two dice are thrown the probability of getting one five is
a)2536
b)536
c)136
d)518

Part – II

Answer any Seven questions. Question 30 is Compulsory : 7 × 2 = 14
21. Consider the system of linear equation x1 + 2×2 + x3 = 3, 2×1 + 3×2 + x3 = 3, 3×1 + 5×2 + 2×3 = 1 find the solution if exists.
22. For any vector auru, prove that the value of aiajaka×()+×()+×()=22222.
23. If the cube roots of unity are 1, w, w2 then find the roots of the equation (x – 1)3 + 8 = 0.
24. Find the condition that y = mx + c may be a tangent to the conics parabola y2 = 4ax.
25. Prove that the function f(x) = x2 – x + 1 is neither increasing nor decreasing in [0, 1].
26. Find wt, if w = x2y – 10y3z3 + 43x – 7 tan (4y) where x = t, y = t2, z = t3

Part – III

Answer any Seven questions. Question No.40 is compulsory. 7 × 3 = 21
31. Solve by matrix inversion method x + y = 3, 2x + 3y = 8
32. What is the radius of the circle in which the sphere x2 + y2 + z2 + 2x – 2y – 4z – 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0.
33. Find the real and imaginary parts of the complex number Ziii=–3212019
34. The tangent at any point of the rectangular hyperbola xy = c2 makes intercepts a, b and the normal at the point makes intercepts p, q on the axes. Prove that ap + bq = 0.
35. Find the point of inflection to the curve y = sin2x where-<<22x.
36. Compute the area of the figure enclosed by the curves x2 = y, y = x + 2 and x axis.
37. Solve x2dy + y (x + y) dx = 0
38. Find the order of each element of the group (z12, +12).
39. In a binomial distribution the arithmetic mean and variance are respectively 4 and 3. If the random variable X denotes the number of successes in the corresponding experiment then find P(x = 2) / P (x =3) .
40. Verify Euler’s theorem for f(x, y) = fxxy()=+122

Part – IV

Answer all the questions  :7 × 5 = 35
41. a) Examine the consistency of the following system of equations. If it is consistent then solve using rank method.
4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1
or
b) Find the vector and cartesian equations to the plane through the point (–1, 3, 2) and perpendicular to the plane x + 2y + 2z = 5 and 3x + y + 2z = 8.

43. a) Find directrix, latus rectum of the ellipse 6×2 + 9y2 + 12x – 36y – 12 = 0 also draw the diagram.
or
b) The path of a ship can be described by a hyperbolic model centered at the origin, relative to two stations on the shore 168 miles apart that are located at the foci. If the ship is 40 miles south of the centre of the hyperbola, find the equation of the hyperbola.

44. a) Find the values of x, y whose product xy = 64 and such that 4x + 27y3 is maximum.
or
b) Prove that the sum of the intercepts on the co-ordinate axes of any tangent to the curve x = a Cos4 q , y = a Sin4 q, 02 is equal to a.

45. b) The plane region bounded by the curve ycosx=, 02 and the lines x = 0, y = 0 is rotated about x axis. Find the volume of the solid.

46. a) Derive the formula for the volume of a right circular cone with radius ‘r’ and height ‘h’. using integration.
or
b) A Bank pays interest by continuous compounding that is by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accures at 8% per year compounded continuously. Calculate the percentage increase in such an account over one year.