Applied mathematics-1
Previous year question paper with solutions for Applied mathematics-1 May-2018
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Question paper 1
SECTION-A
Q1. Choose the correct answer.
(i) The modulus of 1 + Ý…√3 is a) √2 b) -1 c) 2 d) 0
Answer:
z = 1 +
|z| =
Option C
(ii) The value of 3π/12 radians in degree is
a) 60° b) 45° c) 90° d) 120°
Answer:
π radian = 1800
Option B
(iii) Characteristic of log 0.07426 is
a) 1 b) 2 c) 0 d) 1
Answer:
log0.07426 = -2.6001 (Find with the help of log table)
option B
(iv) If Sin (A-B) = ½ and Cos (A+B) = ½ then value of A and B will be
a) A=15° , B=45° b) A=45°, B=15° c) A=45°, B=45° d) A=30°, B=60°
Answer:
We know that
Option B
(v) The centroid of a triangle with two vertices (3,4) (-1,-9) is (2, -4) then third vertex is a) (-4 , -7) b) (4, -7) c) (4,7) d) (-4,7)
Answer:
Vertices of triangle are (3,4),(-1,-9) and let third vertices is (x,y).
Its centroid is (2,-4)
Formula of centroid
=
Option B
Q2. State True or False.
a. The series of the R.H.S of the expansion (1 + x)n extends to infinity
Answer:
False
b. If k, k+1, k+3 are in G.P, then k=2
Answer:
k, k+1,k+3, ------
k = 2
2,3,5,….. is not in G.P.
False
c. Value of tan 120° is √3
Answer:
False
d. Sec(270 ÌŠ + θ) = Cosecθ
Answer:
True
e. The point (3,4); (7,7); (x,4) are collinear, if x=3
Answer:
(3,4),(7,7) and (x,4) are collinear if x=3
A (3,4), B (7,7), C(3,4)
By distance formula
True
Q3. Fill in the blanks.
i. Radius is a -------- angle.
Answer:
constant
ii. The revolving line is always ---------
Answer:
rotate about fixed point.
iii. If CosA = ½ then Cos3A =
Answer:
cos3A = -1
iv. The conic is parabola if ---------
Answer:
e = 1
v. Equation of line perpendicular to line ax+by+c=0 is -------
Answer:
-bx+ay+c = 0
SECTION-B
Q4. Attempt any six questions.
a. In how many ways, 3 boys and 3 girls are seated at round table, so that no two girls sit together.
Answer:
3 boys can be seated at a round table in
i.e. 
WaysWhen 3 boys have occupied their seats in any one of these
Ways, then 3 girls can occupy any 3 out of 3 seats between boys so that no two girls are sitting together. This can be done in 
waysHence required number of ways
= 12 Ans
b. Find the co-ordinates of the incentre of the triangle whose vertices are (-36,7), (20,7) and (0,-8)
Answer:
Formula of the center of the triangle is
, where a,b,c are the length of the sides of triangle.To find a,b and c by distance formula
e
Put all values in formula
c. Resolve \((3x+7) \over (x+3)(x^2 + 1)\) into partial fractions
Answer:
Resolve
into partial fractions.
= 
= 
Comparing coefficients of x, x2 and constant terms
----- 1
----- 2
----- 3From 2
This is put in 1
------ 4Subtract 4 from 3
As
From 3
= 
Ansd. A (10, 4); B (-4, 9); C (-2,-1) are the vertices of a triangle ABC, find the equation of the median through A.
Answer:
D is mid point of BC
To find the co-ordinate of D is
We write the equation of line AB by using Two-point form,
e. Prove that Cos α + Cos(α+2π/3) + Cos(α+4π/3) = 0
Answer:
Prove that
L.H.S.
f. If l\({log x \over y-z} = {logy \over z-x} = {log z \over x-y} \) then show that x2y2z2 = 1
Answer:
If
then Show that 
Sol :
And
Take
Taking log on both sides
Using 1 and 2
Hence it is proved that
g. Prove that \(sinA Sin3A Sin5A Sin7A\over CosA Cos 3A Cos 5A cos 7A\) = tan4A
Answer:
Prove that
Sol. L.H.S.
By using C,D formulae from trignomentary
h. Prove that \( { cot\theta + Coses\theta - 1\over cot\theta + Coses\theta + 1} = {1+Cos \theta \over sin \theta}\)
Answer:
Prove that
Sol:
L.H.S.
i. How many terms of the series 3+8+13+18+ ------ must be taken so that their sum is 1010?
Answer:
3+8+13+18+ ……………
This is A.P
Formula
