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Type of Announcement : 12 Th board Mock test for Mathematics
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Mock test for Mathematics
Tamil Nadu Pre-board Class XII

Section A
Note :
(i) All questions are compulsory.
(ii) Each question carries one mark.
(iii) Choose the most suitable answer from the given four alternatives.

1. The centre of the ellipse is (4, -2) and one of the focus is (4, 2). The other focus is
(A) (4,0)
(B) (8,0)
(C) (4,-6)
(D) (8,-6)
2. The function f (x) = x2-x+1 in [0, 1] is
(A) an increasing function
(B) a monotonic function
(C) a decreasing function
(D) neither decreasing nor increasing
3. The length of the curve 4y2= x3 between x = 0 and x = 1 is
(A) 61 27 (B) 64 27 (C) 125 64 (D) 61 64
4. The value of [3]+11 ([5]+11 [6]) is
(A) [0]
(B) [1]
(C) [2]
(D) [3]
4. Which of the following is a statement?
(A) Give me a cup of tea
(B) Wish you all success
(C) How beautiful you are!
(D) The set of rational numbers is finite
5. In a Poisson distribution if P (X = 2) = P(X = 3) then the value of its parameter ? is
(A) 6
(B) 2
(C) 3
(D) 0
6. If the line 4x+2y=C is a tangent to parabola y2 = 16x then ‘C’ is
(A) -1
(B) -2
(C) 4
(D) -4

Section B
Note :
(i) Answer any ten questions.
(ii) Question 55 is compulsory and choose any 9 questions from the remaining.
(iii) Each question carries six marks.

1. Solve :
x + y+ 2z = 0
3x + 2y + z = 0
2x + y+ z = 0
2. Find the Vector and Cartesian equation of the sphere on the join of the points A and B having position vectors 2i + 6j + 7k and 2i + 4j + 3k respectively as a diameter.
3. The head light of a motor vehicle is a parabolic reflector of diameter 12cm and depth 4 cm. Find the position of bulb on the axis of the reflector for effective functioning of the head light.
4. Determine where the curve y=x3-3x+1 is concave upward, and where it is concave downward. Also find the inflection points.
5. (a) Show that e-x is strictly decreasing in R.
(b) Find the Maclaurin’s series for cos x.
6. Solve the differential equation: (D2 – 4D + 1)y=x2.
7. Prove that , for any proposition p, q, the compound proposition (p ->q)<->(~ q ->~p) is a tautology.

Section C
Note :
(i) Answer any ten questions.
(ii) Question 7 is compulsory and choose any 9 questions from the remaining.
(iii) Each question carries ten marks.

1. Verify whether the given system of equations is consistent, by Rank method. If it is consistent, solve them. 2x + 5y + 7z = 52, x + y + z = 9, 2x + y + z = 0
2. Find the vector and Cartesian equation of the plane passing through the points with position vectors 3i+ 4j+2k, 2i+2j+k and 7i +k.
3. 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 3? 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).
4. Find the eccentricity, centre, foci and vertices of the following hyperbola and draw the diagram: 12x2 – 4y2 – 24x + 32y – 127 = 0
5. A car A is traveling from west at 50 km/hr. and car B is traveling 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?
6. Show that the volume of the largest right circular cone that can be inscribed in a sphere of radius a is 8/27 (volume of the sphere)
7. The rate at which the population of a city increases at any time is proportional to the population at the 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
8. A satellite is traveling around the earth in an elliptical orbit having the earth at a focus and of eccentricity 12. The shortest distance that the satellite gets to the earth is 400 kms. Find the longest distance that the satellite gets from the earth.

See more questions download here : upes.ac.in/pdf/TN_XII_PreBoard_2012_Math_Question.pdf
If you want answer key for maths question paper : upes.ac.in/pdf/TN_XII_PreBoard_2012_Math_Answersheet.pdf