Maths Sample Question Paper HSC / Plus Two / 12th Std / +2 : www.dge.tn.gov.in Directorate of Government Examination

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Document Described : Maths Question Paper, Tamil Nadu Question Paper

DEPARTMENT MODEL QUESTION - I
HIGHER SECONDARY – SECOND YEAR
MATHEMATICS
Time : 3 Hours Max. Marks : 200

SECTION – A : 40 x 1 = 40
(i) All questions are compulsory.
(ii) Each question carries 1 mark.
(iii) Choose the most suitable answer from the given four alternatives.

http://dge.tn.gov.in/schoolsyllabus/
http://dge.tn.gov.in/schoolsyllabus/...lass12MAEQ.pdf

(3) If the equation - 2x + y + z = l
x - 2y + z = m
x + y - 2z = n
such that l + m + n = 0, then the system has
(1) a non-zero unique solution (2) trivial solution
(3) Infinitely many solutions (4) No Solution
(12) If the point represented by the complex number iz is rotated about the origin through the angle in the counter clockwise direction then the complex number representing the new position is
(1) iz (2) - iz (3) - z (4) z
(16) The line 4x + 2y = c is a tangent to the parabola y2 = 16x then c is
(1) - 1 (2) - 2 (3) 4 (4) - 4
(17) The area of the triangle formed by the tangent at any point on the rectangular hyperbola xy = 72 and its asymptotes is
(1) 36 (2) 18 (3) 72 (4) 144
(18) The centre of the ellipse is (4, - 2) and one of the focus is (4, 2). The other focus is
(1) (4, 0) (2) (8, 0) (3) (4, - 6) (4) (8, - 6)
(38) The distribution function F(X) of a random variable X is
(1) a decreasing function (2) non decreasing function
(3) a constant function (4) increasing first and then decreasing
(39) In a Poisson distribution if P(X = 2) = P(X = 3) then the value of its parameter l is
(1) 6 (2) 2 (3) 3 (4) 0
(40) A property of cumulative distribution function F(x) is
(1) it is strictly increasing (2) 0 < F(x) < 1 , - ¥ < x < ¥
(3) F(- ) = - 1 (4) F() = 1

SECTION – B :
(i) Answer 10 questions.
(ii) Question 55 is compulsory and choose any 9 questions from the remaining
(iii) Each question carries 6 marks.
(41) Examine the consistency of the system of equations 10 ´ 6 = 60 2x - 3y + 7z = 5, 3x + y - 3z = 13, 2x + 19y - 47z = 32
(52) Show that (p Ù q)® (p Ú q) is a tautology.
(53) Suppose that the probability of suffering a side effect from a certain vaccine is 0.005. If 1000 persons are inoculated. Find approximately the probability that (i) atmost 1 person suffer. (ii) 4, 5 or 6 persons suffer. [e-5 = 0.0067]

SECTION – C :
(i) Answer 10 questions.
(ii) Question 70 is compulsory and choose any 9 questions from the remaining
(iii) Each question carries 10 marks.
(60) A comet is moving in a parabolic orbit around the sun which is at the focus of a parabola. When the comet is 80 million kms from the sun, the line segment from the sun to the comet makes an angle of radians with the axis of the orbit. find (i) the equation of the comet’ s orbit (ii) how close does the comet come
nearer to the sun? (Take the orbit as open rightward).
(61) Find the eccentricity, centre, foci, vertices of the ellipse 25x2 + 9y2 - 50x + 36y - 164 = 0
(62) A car A is travelling from west at 50 km/hr. towards East and car B is travelling towards north at 60 km/hr. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 kilometers and car B is 0.4 kilometers from the intersection?
(63) A poster is to have an area of 180 cm2 with 1 cm margins at the bottom and sides and a 2 cm margin at the
top. What dimensions will give the largest printed area?
(70) (a) The rate at which the population of a city increases at any time is proportional to the population at that time. If there were 1,30,000 people in the city in 1960 and 1,60,000 in 1990 what population may be anticipated in 2020.
(OR)
(b) A satellite is travelling around the earth in an elliptical orbit having the earth at a focus and of eccentricity 1/2 . The shortest distance that the satellite gets to the earth is 400 kms. Find the longest distance that the satellite gets from the earth.