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S.B. Roll No. ______________
APPLIED MATHEMATICS-I
1st Exam/2455/0251/5402/Common/Dec-2013
Time: 3 hours Max. Marks: 75
Section-A
Q1. Choose the correct answer 1x5=5
1. 5th term of the series ¼ - ½ +1 …………… is
a. 4 b. 2 c. -2 d -4
(x 1) 2 (y2)2
om
2. The equation - =1 represents a(an)
25 16
a. Circle b. parabola c. ellipse d. Hyperbola
C
3. Cos2430 + Cos2470 is equal to
a. 0 b. ½ c. 1 d. 2
u.
4. The value of i4+2i6-3i8+7i10 is
ur
a. 11 b. -10 c. -11 d. 10
n n
5. The total number of terms in (1-x) (1+x) is
G
a. 2n b. 2n+1 c. n d. n+1
Q2. State whether the following statements are true or false 1x5=5
dy
1. The mid point of A(-3,2) and (5,4) is (1,-3)
2. X2+y2-2x +4y-10=0 is a circle with centre at (1,2)
3.
tu
If cos + sec =2 then cos = sec = 1
4. The angle -14250 lies in 1st quadrant
tS
(3x 2)(4x 3)
5. The fraction is a proper fraction
es
(x 1)(x 2)(x 3)
Q3. Fill in the blanks. 1 X 5=5
.B
i. The interior angle of a regular hexagon is __________ radians
ii. The value of Cos 700Cos100 + Sin700Sin100 is ______________
w
iii. The area of a triangle whose vertices are (4,4), (3-16) and (3,-2) is ___________
iv. The characteristic of the logarithm of 9.514 is ___________
w
v. The expansion of (2+x)-2 is valid for ____________
w
Section-B
Attempt any six questions 6 X 5=30
1
1. Resolve 3 into partial fractions
x +1
2. Prove that 3 Cos230 – Sin230 = 2Cos530
3. Find the third vertex of a triangle whose two vertices are (-1,4); (5,2) and centroid is at the point
(0,-3)
4. Find the equation of the line that is perpendicular to 3x + 2y-8=0 and passes through the mid-
point of the joining (5,-2) and (2,2)
5. Find the term independent of x in the expansion of 1
12
FG IJ
6. If n Pr = 1680 and n Cr = 70, find n and r..
2x 3
x H K
7. Find x from the equation. Sec(900 + A) + x SinA tanA(900+A) = Cos(900+A)
tanA Co t A
8. Prove that + -1+ seC A C o seC A
1 CotA 1-tan A
1
9. If a3+ b3 = 0 and a + b 0, show that log (a+b) = 2
[log a + log b + log 3]
Cont.........
S.B. Roll No. ______________
APPLIED MATHEMATICS-I
1st Exam/2455/0251/5402/Common/Dec-2013
Time: 3 hours Max. Marks: 75
Section-A
Q1. Choose the correct answer 1x5=5
1. 5th term of the series ¼ - ½ +1 …………… is
a. 4 b. 2 c. -2 d -4
(x 1) 2 (y2)2
om
2. The equation - =1 represents a(an)
25 16
a. Circle b. parabola c. ellipse d. Hyperbola
C
3. Cos2430 + Cos2470 is equal to
a. 0 b. ½ c. 1 d. 2
u.
4. The value of i4+2i6-3i8+7i10 is
ur
a. 11 b. -10 c. -11 d. 10
n n
5. The total number of terms in (1-x) (1+x) is
G
a. 2n b. 2n+1 c. n d. n+1
Q2. State whether the following statements are true or false 1x5=5
dy
1. The mid point of A(-3,2) and (5,4) is (1,-3)
2. X2+y2-2x +4y-10=0 is a circle with centre at (1,2)
3.
tu
If cos + sec =2 then cos = sec = 1
4. The angle -14250 lies in 1st quadrant
tS
(3x 2)(4x 3)
5. The fraction is a proper fraction
es
(x 1)(x 2)(x 3)
Q3. Fill in the blanks. 1 X 5=5
.B
i. The interior angle of a regular hexagon is __________ radians
ii. The value of Cos 700Cos100 + Sin700Sin100 is ______________
w
iii. The area of a triangle whose vertices are (4,4), (3-16) and (3,-2) is ___________
iv. The characteristic of the logarithm of 9.514 is ___________
w
v. The expansion of (2+x)-2 is valid for ____________
w
Section-B
Attempt any six questions 6 X 5=30
1
1. Resolve 3 into partial fractions
x +1
2. Prove that 3 Cos230 – Sin230 = 2Cos530
3. Find the third vertex of a triangle whose two vertices are (-1,4); (5,2) and centroid is at the point
(0,-3)
4. Find the equation of the line that is perpendicular to 3x + 2y-8=0 and passes through the mid-
point of the joining (5,-2) and (2,2)
5. Find the term independent of x in the expansion of 1
12
FG IJ
6. If n Pr = 1680 and n Cr = 70, find n and r..
2x 3
x H K
7. Find x from the equation. Sec(900 + A) + x SinA tanA(900+A) = Cos(900+A)
tanA Co t A
8. Prove that + -1+ seC A C o seC A
1 CotA 1-tan A
1
9. If a3+ b3 = 0 and a + b 0, show that log (a+b) = 2
[log a + log b + log 3]
Cont.........
