Find the director cosine of the straight line whose direction ratio are -1, 3, 4. / QQQ) tl i-3j+2k cT^fT 4/+y—/t c^ ^l^^T WcT <^1uTtJ vrft Find a unit vector perpendicular to both i-3y' +2A: and 4 i+j-k. A A A AAA Q(9) ^FT Find the value of 3iU(jxk) + 2hn(ixj). A A AA A A Q(8) y=log(sinax) eft — If y=log(sinax), find —. dx Q(7) y=2x -4x+7 ' Find the point on the curve y=2x-4x+7, where the tangent is parallel to x-axis. Q(6) cos 65 sin 25 sin 65 cos 25 cos 65 sin 25 sin 65 cos 25 Evaluate - t, eft (A+B)2 4>T ^H ^RT 1 0 1 2 -1 2 3 0 A = Q(5) . Find (A+B)2. 1 0 1 2 and B = -1 2 3 0 If ,4 = Q(4) ^ J J Construct a 3X3 matrix whose (i, j) element is given by aij = Q(3) - cos"1 (cos—) 4 5TRT Evaluate : cos ' (cos—) 4 Q(2) - a*b = 2Da";a,b^z\ (2*5)+ (5*2) *, z+ A binary composition * is defined in z* by a*b = 2Dab;a,b-e-z*\ Find (2*5) + (5*2). Where z+ is the set of positive integers. TEiTquestion paper consists of 29 questions divided into three sections- A, B and C. Section- A comprises 10 questions of 1 Marks each. Section- B comprises 12 questions of 4 marks each and Section- C comprises 7 questions of 6 marks each. Section- A l)C\t> =^- JO • |^w,^M
Transcript
Find the director cosine of the straight line whose direction ratio are -1, 3, 4. /QQQ)tli-3j+2k cT^fT 4/+y—/t c^^l^^T WcT <^1uTtJ vrft
Find a unit vector perpendicular to both i-3y'+2A: and 4 i+j-k.A A AAAAQ(9)^FT
Find the value of 3iU(jxk) + 2hn(ixj).A A AA A AQ(8)
y=log(sinax) eft —
If y=log(sinax), find —.dx
Q(7)y=2x -4x+7
'Find the point on the curve y=2x-4x+7, where the tangent is parallel to x-axis.
Q(6)
cos 65 sin 25
sin 65 cos 25
cos 65 sin 25
sin 65 cos 25Evaluate -
t, eft (A+B)2 4>T ^H ^RT1 01 2
-1 2
3 0A =
Q(5)
. Find (A+B)2.1 01 2
and B =-1 2
3 0If ,4 =Q(4)
^ JJ
Construct a 3X3 matrix whose (i, j) element is given by aij =Q(3)
- cos"1 (cos—)45TRT
Evaluate : cos '(cos—)4
Q(2)
- a*b = 2Da";a,b^z\ (2*5)+ (5*2)*, z+
A binary composition * is defined in z* by a*b = 2Dab;a,b-e-z*\ Find (2*5) +
(5*2). Where z+ is the set of positive integers.
TEiTquestion paper consists of 29 questions divided into three sections- A, B and C. Section- Acomprises 10 questions of 1 Marks each. Section- B comprises 12 questions of 4 marks each
and Section- C comprises 7 questions of 6 marks each.
Section- A l)C\t> =^- JO •
|^w,^M
dx.1 + COS XJ
r xsm-xEvaluate :Q(18)x4+9
+3^^^
x-2 _ ^-6 _ z-3~2~~ 3 ~~A~
Evaluate : f—rQ(17)(b) f^RcR ^WHH tl(a)
Find the interval on which the function /(x) = 2x3 -15x2 + 36x +11;x e R is(a) increasing (b) decreasing
The volume of a sphere is increasing at the rate of 16 cm /sec. Find the rate of ^
increase in its radius when the length of its radius is 2 cm.Q(16)
y = (sinx)-T
If ^ = (sin xf + xsin r , then find ^.Q(15)
X=0sinx
4at x=0.sin x\
Examine the continuity of the function : f(x) =Q(14)
= (l + a2+62)3
2a6-26l-a2+62 2a
-2a l-a2-62
4= (l + a2+b2)2 . 1^3
+ a2-62 2a6-26
2a6 l-a2+62 2a
26-2a l-a2-62
Prove that:Q(13)
= -x+2; x ef(x) = 4x-l c^TT g(x)
(i)//W(ii)/"(iii) g/(j)(iv) ^
4Let f(x) = 4x-l and g(x) = -x+2; x <= R Find the following(i) /"/(*)(ii) fg(x)(iii) g/(x)(iv) gg(x)
Solve : tan"12jc+tan"13x = —.
Section-B
Q(12)
Q(H)
Solve: (>/+!)—+^ = 0.)Q (26)
x=4 ?1^ y2=4x
Using integration, find the area of the region bounded by x=4 and y -4x.0(25)f(x)=3x3-9x2+17\\, 3]
+17 in theFind the maximum and minimum values of the function f(x)=3x -9xintei-val [1,3].
Q(24)^^T0
-1
-2
-5
0-1
L
323
A=
.
0-1
-2
-5
0-1
^cT
323
Find the inverse of A =Q(23)^ 4^-^^Section- C
P(A)=—,P(B) ^ — ^ P(A\JB)=— eft P(A/B)
=^- fmdP(A/B).= -,P(B) = -i andQ(22)1, -2, 3u\ Wt
tl(1, 0, 4)
Find the equation of the plane passing through the point (1,0, 4) andperpendicular to the straight line whose direction ratio are 1, -2, 3.
ORw11
Show that the lines — = —— = -— and -— = —— = -— intersect and final their12 32 3 4
point of intersection.
Q(21)
ABC m c^^ #f ^ 11W^ % A(2,-l,3),B(l,0,-2)cT^C(l,l,
(i) AB (ii) BC (iii) AB (iv)
Let A(2,-l,3), B(l,0,-2) and C(l,l,l) be the verticles of a triangle ABC. Find the
following - (i) AB (ii) BC (iii) AB (iv) BCAQ(20)
gRT W^^FTjjc2<ft
Evaluate jx2dx as a limit of sum.
1 + COS XURT
0.(19)
nm<u kZ = 3x + 5y-2x+y<4
x+y>3x-2y<2x, y>0 ^
fkr
cSolve graphically the following LPP :Maximize Z = 3x + 5ysubject to -2x+y<4
x+y>3x-2y<2
and x, y>0
Q(29)
E2 cT2TTE3UlcT
1 eflcT, 5f cfSTT E tjcj^ eM ffeT
(iv)P(E/E2) (v)P(E/E3)(i)P(Ei)
^tef 116 ^TTeT, 4A, B, C ^fA, B, C
Three urns A, B, C contain 6 red and 4 white; 2 red and 6 white and 1 red and 5white balls respectively. Let Ej, E2 and E3 be events of choosing the urns A, Band C respectively and E be the event of drawing a red ball. Now find thefollowing —(i)P(E,) (ii)P(E3) (iii)P(E/Ei) (iv)P(E/E2) (v)P(E/E3) (vi)P(Ei/E)
Q(28)c^fTg3TT ^Hdd
r =A D
lines- r = (/+ 2 j-4*) + A(2i+ 3y+ 6k)and r = (3/+ 3 j-5k) + n{-2i+3j + $k).A ?
Find the vector and Cartesian equations of the plane containing the two straightOR
Lt:r = 3i-J+k+A(i-J+4k)
_,A AAA A AL2: r = 2 i+ j- 4 k+ fi{i+ j- k)
L2 : r = 2 i+ j- 4 k+ ju(i+j- k)
AA A A
Find the shortest distance between the straight lines-Li:r = 3'i-J+k+X(i-j+4k) /\^//^^
