Il PUC MID-TERM EXAMINATION, OCT/NOV.-2024
SUBJECT : MATHEMATICS (35)
‘Time : 3 Hours Max Marks : 80
Instructions =
1) The question paper has five parts namely A, B, C, D and E. Answer all the parts.
2) Part A has 15 Multiple choice questions, 5 Fill in the blanks of 1 mark each.
3) Use the graph sheet for question on linear programming problem in Part-E.
PART -A
I Answer ALL the multiple choice question: 1Sx1=15
1) The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is
A) Reflexive B) Symmetric C) Transitive) Equivalence relation
2) The modulus function f: R—>R given by f(x) = [xl is
A) one-one and onto B) one-one but not onto
C) onto but not one-one D) neither one-one nor onto
3) The principal value of cos"* (-%) is
a% B)™% 5% D) 2%
4) Match the following :
A B
a) Domain of sec"*x a (-%.%)
b) Domain of sin" x i)R-(-1,1)
©) Range of tan" x iti) (-1, 1]
A) a-(ii) b-(iii) c(i) B) a-(iii) b-() (ii) | C) a-(iil) b-(ii) -)._——_—D) a-(ii) b-(i) e-(ili)
5) Ifa matrix has 24 elements, then the total number of possible matrices of different order are
A)8 B)6 O4 D)2
x 2 |6
6) ithe x/= hg g/then x is equal to
A)6 B)+6 Cc) -6 DO
7) — The point of discontinuity of the function flx) = {, Vx ER, is
A)x=1 B)x=0 Ox=2 D)x
8) fy =log (logx), x > 1, then 9Y/, is
1 1 1 x
A) xlogx ®) logx ©) og(logx) —P) togx
9) Let Ibe an interval contained in the domain of a real valued function and then
Statement 1 ; fis said to be increasing on I, if x,
f{x,) < flx,) for all x,, x, €1
Statement 2 : fis said to be decreasing on I, if x, > x, in I=>{x,) > f(x,) for all x,, x,€1
A) Statement 1 is false statement 2 is true B) Statement 1 is true but statement 2 is false
) Both statement 1 and 2 are false D) Both statement 1 and 2 are true
10) The total revenue in Rs. received from the sale of x units of product is given
R(x) = 13x? + 26x + 15; then the marginal revenue when x = 7 is Rs.
A) 208 B) 108 ©) 308 D) 280
(PT.0,) 4)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
2.
The diesen codes of RSE LAT Ar
a -1 1 2 Mp piling xD tyise 1
SEE EEE OSES od KEM
The unit vector in the direction of the vector 21 +3} +k is
2i-3]+k _ 2i-3j-k a ~2i-3j-k ss 2i43j+k
via ) ha RT iia ) ia
The projection of the vector 4=2i+3}+2k on the vector b=i+2j+k is
XE Die. O% Ke
Ifa line makes angles 90°, 135°, 45¢ with X, ¥ and Z. axes respectively, then direction cosines
are
Oh Ketia.* Ke Ka 08 Ve Lago Hi 8
The angle between pair of lines given by 31+2}-4k) + 2(i+2]+2k) and
#=(si-2})+n(3i+2)+6k)then 9 is
ayeos'() — wyew'(2) og cos(32) pcos (%4)
Fill in the blanks by choosing the appropriate answer from those given in the bracket:
(4.9%. % % 3 12) Sx1=5
cosa sin a
sina cosa
Jsota-+a'= en te vate of oi
It value of tan“*(200s (2sin"(14))) i
The function {{x) = kx? if x<2 and {{x) = 3 if x > 2 is continuous at x = 2, then the value of
kis
The rate of change of area of a circle with respect to its radius at r= 6 ems is
ira
The value of i-(}xk) +}-(Kx 0 with respect to x.
dy
Ix = a(cos0+@sin®), y=a(sind-0cos0) then find
Find the intervals in which the function f, given by f{x) = x2- 4x +6 is
2) increasing
b) decreasing
ita j
dicular.
Find the cosine of the angle between the vectors j-2}+3k and 3}
PART -D
Answer any FOUR questions : Sx4=20
State whether the function f: R->R defined by f(x) = 1 +x? is one-one, onto or bijective. Justify
your answer.
Let f: N->Y be a function defined as f(x) = 4x + 3, where
y={yeN: y= 4x + 3, for some xeN}. Show that fis invertible and hence find the inverse
off,
+3)—5k then show that the vectors
0 67 o11 i
IfA=|-6 0 8| B=|1 0 2| C=|-2]. Calculate AC, BC and (A+B) C, verify
7 -8 0 120 3
that (A + B)C = AC + BC.
(TO) 42)
43)
44)
45)
47)
BC
123 41-5
IfA=| 5 7 9] and B=| 1 2 0 |then verify that (A-By = A’-B'.
211 none sy
Solve the following system of equations by matrix method :
2x+3y+32=5, x-2y+z=-4, 3x-y—2z = 3.
Ify=Ac™ + Be, show that 89 (m+n) +(mn)y =0
ix
Ify = (tan x)’ show that (x°+1)*y, + 2x (x #1) y, =
PARTE
Answer the following questions : (6+ 4=10)
Maximize Z = 3x + 2y subject to constraints;
x+2y S10, 3x+ySi5, x20, y20 by graphical method,
OR
Solve the following problem graphically Minimize and Maximize z = 5x + 10y subject to
x+2y<120, x+y260, x-2y20 x20 y20 ©
3 5a
ural’ slew that A?—SA + 71 = 0 where I is 2x2 identity matrix and O is 2x2 zero
matrix. Using this equation, find A“
OR
Find the values of k if
kx +1 if xm
fix) =
is continuous at x =
@
cosx if x>m
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