Maths Model Question Paper AP Andhra Pradesh : Intermediate I year www.bieap.gov.in

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Document Described : Maths Question Paper, Andhra Pradesh Question Paper

MODEL QUESTION PAPER
MATHEMATICS PAPER I (A)
(Algebra, VecrorAlgebra and Trigonometry)
(English Version)
Time : 3 Hrs. Max. Marks. 75
Note : Question paper consists of ‘Three’ Sections A, B and C.

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SECTION - A :
I. Very short answer questions 10 x 2 = 20 Marks
(Attempt all questions)
(each question carries ‘Two’ marks)
01. Find the domain of the real valued functions f(x) = N9-x2
02 In DABC, D is the mid point of BC. Express AB + AC in terms of AD
03. Find the vector equation of the line through the points 2 i + j + 3 k and -4 i + 3j - k
04. If a = i +2j + 3k and b = 3i - j + 2 k,then find the angle between
(2a + b) and (a +2b)
05. Sketch the graph of sin x in (0, 2p)
06. Find the value of cos245°-sin215°
07. Show that cos h (3x) = 4 cos h3 X - 3 cos hx.
08. If c2=a2+b2, write the value of 4 s(s-a) (s-b) (s-c) in terms of a and b.
10. Expand cos 4q in powers of cosq

SECTION - B :
II. Short answer questions. Attempt five questions 5 x 4 = 20 marks
11. f : A u B,g : B u C;
f = {(I, a), (2, c), (4, d), (3, d)}
and g-1 = {(2,a), (4, b), (1, c), (3, d)}
then compute (gof)-1 and f-1 og-1 .
12. Find the cube root of 37-30 N3.
14. By vector method, prove that the diagonals of a parallelogram bisect
each other.
15. Find the area:of the triangle formed with the points A(1, 2, 3), B (2, 3,
1) and C (3, 1, 2) by vector method.
16. Find the solution set of the equation 1 + sin2q =3 sinq cosq
17. Show that

SECTION - C :
Ill. Long answer questions : (Attempt ‘FIVE’ questions) 5 x 7 = 35 marks
18. If f : A u B and g : B u C are bijections,
then prove that gof : A u C is also bijection.
19. Using the principle of Mathematical induction show that
12 + (12 + 22) + (12 + 22 + 32) + .... upto n terms
= n (n +1)2 (n + 2)12
20. For any vector a, b; and c,
prove that (a x b) x c = (a .c) b - (b . c ) a
21. If A + B + C = 180°, then show that
sin 2A - sin 2B + sin2C = 4 cos A sin B cos C

MODEL QUESTION PAPER
MATHEMATICS PAPER - I (B)
(Calculus and Co-ordinate Gemetry)
English Version
Time : 3 Hours Max. Marks. 75
Note : Question paper consists of three sections A, B and C.
Section - A : (Very short answer type questions)
Attempt all questions : 10x2=20 marks
Each question carries two marks. ,
01. Write the condition that the equation ax+by+c=0
represents a non-vertical straight line. Also write its slope.
02. Transform the equation 4x-3y+ 12=0 into slope-intercept form and
intercept form of a straight line.
03. Find the ratio in which the point C (6,-17,-4) divides the line segment
joining the points A(2,3,4) and B(3,-2,2)
04. Evaluate
05. Evaluate
07. Find the derivative of log10x w.r.t x
08. IfZ = eax sinby then find Zny.
09. If y = x2 + 3x + 6, x = 10, Dx = 0.01, then find Dy and dy.

Section - B : (Short answer type questions)
Attempt any five questions. Each question carries Four marks
5x4=20 marks
11. Find the equation of locus of a point, the sum of whose distances
from (0, 2) and (0, -2) is 6 units
12. Show that the axes are to be rotated through an angle of Tan-1 so as to remove the xy term from the equation axr + 2hxy + byr = 0 If a f b and through the angle , if a = b
13. Show that the origin is within the triangle whose angular points are
(2,1), (3, -2) and (-4, 1)
14. Show that the line joining the points A (+6, -7, 0) and BC (16, -19, -4)
intersects the line joining the points P(0,3,-6) and Q (2,-5, 10) at the
point (1,-1,2)
15. Find the derivative of tan 2x from the first principles
16. A point P is moving with uniform velocity ‘V’ along a straight line AB. q
is a point on the perpendicular to AB at A and at a distance ‘l’ from it. Show that the angular velocity of P about q is
17. State and prove the Eulers theorem on homogeneous functions.

SECTION - C : 5 x 7 = 35 marks
18. Find the orthocentre of the triangle whose vertices are (5,-2), (-1,2)
and (1,4)
20. Find the angle between the lines joining the origin to the points of
intersection of the curve x2 + 2xy + y2 + 2x + 2y - 5 = 0 and the line 3 x -y + 1 = 0
21. If a ray makes angle a, b, g, and d with the four diagonals of a cube,
show that cos2a + cos2 b cos2g + cos2d =
22. If x logy = log x then prove that

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