Question paper contains three sections A, B & C. Each part is compulsory.

2 SECTON A has
20MCQs, attempt any 16 out of 20.
3 SECTION B has 20MCQs, attempt any 16 out of 20
4SECTION Chas 10MCQs, attempt any 8 out of 10.
There is no negative marking.
6 All questions carry
equal marks.
SECTION A

1The function f:[0, n] >R defined by flx) =

cosx is
(a) one one function
(b) onto function
(c) many - one function

(d) none of these

On the set of natural numbersN, the relation Rdefined by aRb iff LCM of a and b is 4. Then the
relation R is
(a) reflexive but not symmetric
(b) reflexive and transitive
(c) symmetric only
(d) neither reflexive nor
symmetric
3 The domain of function f(x) =
cos (3x2 1) -

(a)-v2.]
(d)-V3,3
4 Thevalue of cos (tan tan
(a)- 1
(b)0
()
d)
5
x = then the matrix Xis
(b) ]

6 Find the minor of the

element of second row and third column in the
2-3 5 following det
6
0 4
5
 (a) 13
(b) 4 ) 5 (d) 0

7 If f(x) =
x2+4x -5 and A
(G thern f(A) is equal to
b)
()
(d
8 If A =
( and 143| =
64, then the value of xis
(a) t2
(b) +4
(c) t8
(d) +3

9 I fA=(200 and B (49

(a)-7000
10
=
then 14B
b) 3000
() 460
(d) 2000

10 For any 2 2 matrix A, if

x
A(adj A) ( =
then the value of JA| is
(a) 10
(b)2 20
()100
(d) 0

11 Let A = |
108-68
-2 3
is the inverse of A, then the value of kis
1
(a)-2
(b) 2
(c)5
(d)-1
0
zifr *
12 If fx)= is continuous at x =
0, then the value of k is
= 0
(a) 1
b)2
()2
(d)
13 If Sx)= 3 - 1Sxsl

, then f(x) is:

4-x 1Sxs4
(a) Continuous as
well as differentiable atx =1
(b) Continuous but not differentiable at x 1
(c) Differentiable but not continuous at x =1
(d) None of the above

14 Ifx sint cos 2t and y =

costsin 2t, thenat t =
* is
dx
(a)-2
(b) 2

(d)
15 If y tan-1 (o**in). thenis:
LcoB Y-sin x dx
(a) 1 -1 (c) % (d) -1/2
16 If y =
4x- 5 is a
tangent to the curve y =
px3 +q at (2,3), then the values of p and
are q respectively
(a) -2,-7
(b)-2,7
(c) 2,-7
(d) 2,7
17 The value of that the
a, so sum of the squares of the roots
assume the least value, is of the equation x'-(a-2)x-a+1=0
(a) 2 b) 0 (c) (d) None of these

18 The function f(x) =

x* 2x is strictly increasing in the interval
-

(a) (-2,-1)
(b) (1,2)
(c) (0,1)
(d)(-1.0)
19 The feasible region satisfied by the constraints x
y20,5x +y25,x +6y 2 6 is bounded by +ys5,x s 4,ys 4,x 2 0,
(a) 4 straight lines
(b) 5 straight lines
(c) 6 straight lines
(d) 7 straight lines
20 The x coordinate of the point on the curve
1S f(x) vx(7x -6) where the
=

tangent is parallel to x axis

 (a)-
(b)
(c)
(d)
SECTION B
21 Let f:
[0, o) [0,2] is defined by f() =then f is 2x

(a) one-one but not onto

(b) onto but not one-one
(c) one-one and onto
(d) neither one-one nor onto
22
Let A R-{3},B
= =
R- {1} and a function f: A
> B defined by f(x)
(a) Injective but not
=
*Then the function 1 is
surjective
(b) bijective
(c) surjective but not injective
(d) neither injective nor surjective
23 Consider the
non-empty set consisting of children in a family and a relation R defined as a relation
R defined as aRb if a is a brother of b. Thern R is
(a) symmetric but not transitive
(b) neither symmetric nor transitive
(c) symmetric and transitive
(d) transitive but not symmetric
24
The value of sin cos
(a)
(b)-
(c)
(d)0
25 The value of sec2 (tan"1 2)is
(a) 1
(b).
5
(d) 3

26
The value of tancos(s
(a) 3
2

(b)
(c)
(d)
 is a matrix satisfying AA' = 9l3, then the values of a and b respectively are
27 If A

(a) 1,2
(b)-1,2
(c)-2,-1
(d)-2,1

28 If A =
9 . -G ).c-(iand D-(t5 ")suchthat(2A-39C=D.then the
value of x is
(a)-6
(b) 3
(c) -4
(d) 6

29 If A = ( and B = and A +8) - 42 + B, then x +yequals to

(a) 2
(b))5
(c)4
(d) 3
a11 a12 a13
30 If matrix A . and its inverse A-l = 2 1 22 2 3 then the value of azg is
la31 a32 a33
(a)20
(b)
(c)-
(d)
0 01
31 If A = then
o adja | equals to
lo 0 a
(a) a
(b) a5
) a27

(d) a
32 I -1 then the value of x is
(a) 3
(b) 6
(c) t6
(d) +3
33 Ify
cos ()- sin* (G then
is
(a) 3/1
(b) 3/1-y?
(c) 9y
(d)-9y
34 If f(x) =
(logcot x tan x)(logtanx cot x) +tan" then f' (2) equals to
(a)
(b)
(c) 1
(d)-1

35 The maximum value of x*,x>0 is

(a) e 1 (d) None

36 The function f(x) = 2x3 -

3x2 12x+ 4 has

(a) 2 points of local maxima
(b) 2 points of local minima
c) neither maxima nor minima
(d) 1 point of local maxima &1 point of local minima
37 The the curve y = e at the
tangent to point (0,1) meets x axis at
(a) (1,0)
(b) (-.0
(c) (2,0)
(d) (3,0)
38 The interval in which the function f(x) =
2x3 +9x2 +12x-1
(a) -1, o) decreasing is
(b) -co,-2]
(c)-1,1]
(d)[-2,-1
39 The maximum value
of P =
x+3y such that 2x +y s 20,x +2y s 20,x
(a) 0 2 0&y 20 is
(b) 50
(c) 30
(d) none of these
40 For the
following feasible region, the linear constraints are

(0,6)

o 4.0) (11,0)

(a) x20,y 2 0,3x

+2y2 12, x + 3y 2 11
b) x 20,y 2 0,3x + 2y s
12, 3y x+ 2 11
 (c) x20,y2 0,3x + 2y s 12, x + 3y s 11
(d) None of these

SECTION C
41 Corner points of the feasible region determined by the system of linear constraints are
(O,10), (5,5), (15,15) and (0,20). Let Z = px+qy where p, q> 0. Condition on p and q so that the
maximum of Z occurs at both the points (15,15) and (0,20) is
(a) P = 2q
(b)p
(c) q = 3p
(d) p = q

42 Maximize Z =
3x +5y subject to the constraintsx20,y2 0,3x +y 21, x +4ys 24,x +ys9 is
(a) 20 at (1,0)
(b) 30 at (0,6)
(c) 37 at (4.5)
(d) 33 at (6,3)
43 The
equation of normal to the curve
3x-y =
8which is parallel to the line x +3y = 8 is
(a) 3x-y =8
(b) 3x +y +8 0
(c)x+3y =0
(d)x +3yt8 =0
44 If the curve
ky + x2 = 7 andx =
y cut orthogonally at (1,1), then the value of k is
(a) 6
(b) -6
(c)0
(d) 1

45 The solution set of

equation |1 5=0is:
22x 5x2
(a) {0,1)
(b) {1,2)
(c)(1,5)
(d) {2,-1)

CASESTUDY
An architect
designs a building fur multi- national company. The floor consists
a
of
region with semicircular ends having a perimeter of 200m as shown below.
a
rectangular

A v/2
 Based on the above information answer the following:
46 If x& y represents the length and hread th of the rectangular region, then the relation between the
variables is:
(a) x + t y = 100

(b) 2x +Ty = 200

()TX+y = 50
(d) x +y = 100
47 The area of the rectangular region A expressed as a function of x is
(a)(100x x2)
h)(100x-x2)
()(100-)
(d) Ty2+ (100x - x*)

48 Maximum value of area Ais

(a) m2
(b)
206 m
(c) 5000 2
(d) 2
49 The CEO of multi-national company is interested in maximizing the area of the whole floor
including the semi- circular ends. For this to happen the value of x should be
(a) Om
(b) 30m
(c) S0m
(d) 80m
50 The extra area generated if the area of the whole floor is maximized is:
(a) 50002
(b).

7000
(c)m
(d) No change. Both the areas

1. (a) one - one function 2. () Symmetric only 3. (d) -t 2 4. (c) 1 125. (b) [1-220]6. (a) - 5 7. (d) [ 8
480]8.(b)249.(a) -7000 10. (a) 1011.(c) 5 12.(6) 2 13.(a)-3 14.(c) 1 2 15.(d) -2 x2 16.(c) p =2, q-
7 17.(a) 1 e 18.(b) (1, 2) 19.(b) 5 straightlines 20.(c) 27
SECTIONB
21.(a) one - one but not onto 22.(b) bijective 23.(d) Transitive but not symmetric 24.(b) -T 10 25.(c) 5

26.(b) 3-152 27.(c) - 2, -1 28.(a) - 6 29.(b) 5 30.(b) 25 31.(a) a6 32.(c) t6 33.(d) - 9y 34.(a) 1 235.(b) 12
36.(d) 1 point of local maxima &1 point of local minima 37.(b) (-1 2,0) 38.(d) [-2, -1]39.(c) 30 40.(c)
x20, y2 0, 3x + 2ys 12, x + 3ys 11

SECTION C
41.(c) q= 3p 42.(c) 37 at (4, 5) 43.(d) x +3y t8 -044.(a) 6 45.(b) {1, 2} 46.(b) 2x + ry 200 47.(a) 2 n
(100x-x 2) 48.(c) 5000 m2 49.(a) O m 50, (d) No change. Both areas are equal.