Applied mathematics-1
Previous year question paper with solutions for Applied mathematics-1 May-2017
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Question paper 1
SECTION A
Q. 1) Choose the correct answer
(i) 5th term of series 3, 8, 13, 18 _ _ _ _ _ _ _ _ _ _
a) 21 b) 22 c) 23 d) 24
Answer:
(ii) The total number of terms in (x + a)8
a) 7 b) 8 c) 9 d) 10
Answer:
(iii) value of cos 900
a) 0 b) 1 c) -1 d) none of these
Answer:
(iv) modulus of 1 + i √3 is equal to
a) 2 b) 1 c) 10 d) 2
Answer:
(v) The radius of the circle x2 + y2 − 4x + 6y − 25 = 0
a) √37 b) √38 c) 38 d) 37
Answer:
Q. 2) State true or false
(i) The midpoint of A(-3,2) and B(5,4) is (1, -3)
Answer:
(ii) angle 13250 lies in I ୱ୲ quadrant
Answer:
(iii) sec (900 − Q) = cosecQ
Answer:
iv) Two lines are parallel if their slopes are equal
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(v) a, b, c are in A.P. if ܾ = \(a-c \over 2\)
Answer:
Q. 3) Fill in the blanks
(i) The value sin 450 cos 300 – cos450 sin 300 is _________________
Answer:
(ii) The area of triangle whose vertices are (4,4),(3,-16) and (3,-2) is _ _ _ _ _ _ _ _ _
Answer:
(iii) If the end points of the diameter of circle are (2,3) and (6,5) then the centre of circle is _ _ _ _ _ _
Answer:
(iv) value of cos \(\pi \over 2\) + ݅ sin \(\pi \over 2\) =_ _ _ _ _ _ _ _
Answer:
(v) value of 8!/6!
Answer:
SECTION B
Q. 4) Attempt any 6 Questions
(i) Which term of the series 3 + 7 + 11 + 15 + _ _ _ _ _ _ _ _ _ _ is 47 ?
Answer:
(ii) Sum the series 3 + 33 + 333 + _ _ _ _ _ _ _ _ _ _ _ _ _ _ to n terms.
Answer:
(iii) Find the 4th term in the expansion of \(({ x \over a} + {a \over x} )\)10
Answer:
(iv) if sin (A + B) = 1 , cos(A − B) = √3/2 then find A and B
Answer:
(v) Prove that \({cos 17 + sin 17 \over cos 17 - sin 17 } = tan 62\)
Answer:
(vi) Find the co-ordinates of a point which divides the line joining the points (1,3) and (6,-3) Internally in the ratio 2 : 1
Answer:
(vii) Find the equation of the straight line passing through (2,5) and perpendicular to 5x +2y +8 = 0
Answer:
(viii) Find the | distance of the point (3,4) from the line 12x + 5y + 7 = 0
Answer:
(ix) Show \(3 log {3 \over 4} + 2 log {2 \over 5} - 2log {3\over 10} = log 3\)
Answer:
SECTION C
Q. 5) Attempt any 3 Questions
(i) Resolve \(x^2 \over (x-1)(x-2)(x-3)\) into partial fraction
Answer:
(ii) (a) Find the equation of the circle whose centre is the point (2, 3) and which passes Through the point (5, 7) (b) Find the equation of the circle passing through the points (0, 0) , (1, 0) , (0,1)
Answer:
(iv) (a) Prove that \(\sqrt 3 cos 23^0 - sin 23^0 \over 2 \) = cos 530
(b) Prove that sin1500 cos 1200 +cos 3300 sin 6600 = −1
Answer:
(v) (a) if the three vertices of a rectangle are the points (2, -2) , (8,4) , (5,7) find the Co-ordinate of the fourth vertex.
(b) Find the equation of line joining two points (1, 2) and (2, 3)
Answer: