# Log_Ph-1-2-3_QE_S&P (PQRS & J-Batch) WA.pdf

STUDY INNOVATIONSEducator à Study Innovations

Question bank on Vector, 3D and Complex Number & Misc. Subjective Problem Select the correct alternative : (Only one is correct) Q.1 If a = 11 , b = 23 , a  b = 30 , then a + b is : (A) 10 (B) 20 (C) 30 (D) 40 Q.2 The position vector of a point P moving in space is given by OP = R = (3cos t)ˆi + (4 cos t) ˆj + (5sin t)kˆ . The time 't' when the point P crosses the plane 4x – 3y + 2z = 5 is  (A) 2  sec (B) 6  sec (C) 3  sec (D) 4 sec Q.3 Indicate the correct order sequence in respect of the following : I. The lines x  4 – 3 = y + 6 1 y + 6 = 1 and x 1 1 = y 2 – 2 z 3 = 2 are orthogonal. II. The planes 3x – 2y – 4z = 3 and the plane x – y – z = 3 are orthogonal. III. The function f (x) = ln(e–2 + ex) is monotonic increasing  x  R. IV. If g is the inverse of the function, f (x) = ln(e–2 + ex) then g(x) = ln(ex – e–2). (A) FTFF (B) TFTT (C) FFTT (D) FTTT z1 Q.4* If is purely imaginary then 2 is equal to : (A) 1 (B) 2 (C) 3 (D) 0 Q.5 In a regular tetrahedron, the centres of the four faces are the vertices of a smaller tetrahedron. The ratio of the volume of the smaller tetrahedron to that of the larger is m , where m and n are relatively prime n positive integers. The value of (m + n) is (A) 3 (B) 4 (C) 27 (D) 28 Q.6 If a , b, c are non-coplanar unit vectors such that    = 1  + c) then the angle between a & b is a x(bx c) (b (A) 3 /4 (B) /4 (C) /2 (D)  Q.7 The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where A  (3, –2, 1); B  (3, 1, 5); C  (4, 0, 3) and D  (1, 0, 0) is 2 (A) 5 (B) (C) 2 (D) Q.8* Let z be a complex number, then the region represented by the inequality z + 2< z + 4 is given by : (A) Re (z) >  3 (B) Im (z) <  3 (C) Re (z) <  3 & Im (z) >  3 (D) Re (z) <  4 & Im (z) >  4 Q.9 The volume of the parallelpiped whose edges are represented by the vectors a = 2 i  3j + 4 k , b = 3i  j + 2 k , c = i + 2 j  k is : (A) 7 (B) 5 (C) 4 (D) none Q.10 Let u,v,w be the vectors such that u + v + w = 0 , if u = 3 , v = 4 & w = 5 then the value of u .v + v .w + w .u is : (A) 47 (B) 25 (C) 0 (D) 25 Q.11 Let a = ˆi  ˆj , b = ˆj  kˆ , c = kˆ  ˆi . If d is a unit vector such that a .d = 0 = [b, c,d] then d (A)  1 (ˆi+ˆj2kˆ ) (B)  1 (ˆi+ˆjkˆ ) (C)  1 (ˆi+ˆj +kˆ ) (D) ± kˆ Q.12* If z be a complex number for which z + 1 z = 2 , then the greatest value of z is : (A) + 1 (B) + 1 (C) 2 1 (D) none Q.13 If the non  zero vectors a & b r  a = b is : are perpendicular to each other, then the solution of the equation ,   1     1   (A) r = xa + a . a (C) r = x a  b (a  b) (B) r = x b    b . b (D) r = x b  a (a  b) where x is any scalar. Q.14 The lines x  2 = y  3 = z  4 and x 1 = y  4 = z  5 are coplanar if 1 1

## Recommandé

Vector & 3D complex & Misc(12th).pdf par
Vector & 3D complex & Misc(12th).pdfSTUDY INNOVATIONS
7 vues22 diapositives
Vector-03-Exercise- 1 par
Vector-03-Exercise- 1STUDY INNOVATIONS
11 vues20 diapositives
QE Determinant & Matrices (13th)WA.pdf par
QE Determinant & Matrices (13th)WA.pdfSTUDY INNOVATIONS
18 vues12 diapositives
Straight line and circle WA.pdf par
Straight line and circle WA.pdfSTUDY INNOVATIONS
28 vues16 diapositives
Vector Dpp (1-10) 12th ) WA.pdf par
Vector Dpp (1-10) 12th ) WA.pdfSTUDY INNOVATIONS
212 vues19 diapositives
Vector-02-Exercise par
Vector-02-ExerciseSTUDY INNOVATIONS
7 vues7 diapositives

## Similaire à Log_Ph-1-2-3_QE_S&P (PQRS & J-Batch) WA.pdf

Ph-1,2,3 & Seq & Prog13th.pdf par
Ph-1,2,3 & Seq & Prog13th.pdfSTUDY INNOVATIONS
8 vues16 diapositives
3-D-02-Exercise-1 par
3-D-02-Exercise-1STUDY INNOVATIONS
6 vues7 diapositives
Quantitative aptitude question par
Quantitative aptitude questionlovely professional university
1K vues7 diapositives
Vector-04-Exercise-II par
Vector-04-Exercise-IISTUDY INNOVATIONS
26 vues28 diapositives
Straight Lines-03-Exercise par
Straight Lines-03-ExerciseSTUDY INNOVATIONS
35 vues21 diapositives
Quiz (1-11) WA PQRS.pdf par
Quiz (1-11) WA PQRS.pdfSTUDY INNOVATIONS
9 vues7 diapositives

## Plus de STUDY INNOVATIONS

Physics-31.Rotational Mechanics par
Physics-31.Rotational MechanicsSTUDY INNOVATIONS
2 vues14 diapositives
Physics-30.24-Physics-Solids and Semiconductors par
Physics-30.24-Physics-Solids and SemiconductorsSTUDY INNOVATIONS
2 vues40 diapositives
Physics-28..22-Electron & Photon par
Physics-28..22-Electron & PhotonSTUDY INNOVATIONS
2 vues30 diapositives
Physics-27.21-Electromagnetic waves par
Physics-27.21-Electromagnetic wavesSTUDY INNOVATIONS
2 vues17 diapositives
Physics-26.20-Wave Optics par
Physics-26.20-Wave OpticsSTUDY INNOVATIONS
2 vues27 diapositives
Physics-25.19 -Ray Optics par
Physics-25.19 -Ray OpticsSTUDY INNOVATIONS
2 vues46 diapositives

### Plus de STUDY INNOVATIONS(20)

Physics-24.18-Electromagnetic induction & Alternating current par STUDY INNOVATIONS
Physics-24.18-Electromagnetic induction & Alternating current
Physics-22.15-THERMAL & CHEMICAL EFFECTS OF CURRENT & THERMOELECTRICITY par STUDY INNOVATIONS
Physics-22.15-THERMAL & CHEMICAL EFFECTS OF CURRENT & THERMOELECTRICITY
Physics-11.3-Description of motion in two and three dimensions par STUDY INNOVATIONS
Physics-11.3-Description of motion in two and three dimensions

## Dernier

Guess Papers ADC 1, Karachi University par
Guess Papers ADC 1, Karachi UniversityKhalid Aziz
99 vues17 diapositives
INT-244 Topic 6b Confucianism par
INT-244 Topic 6b ConfucianismS Meyer
45 vues77 diapositives
EILO EXCURSION PROGRAMME 2023 par
EILO EXCURSION PROGRAMME 2023info33492
202 vues40 diapositives
Jibachha publishing Textbook.docx par
Jibachha publishing Textbook.docxDrJibachhaSahVetphys
54 vues14 diapositives
Thanksgiving!.pdf par
Thanksgiving!.pdfEnglishCEIPdeSigeiro
500 vues17 diapositives
Payment Integration using Braintree Connector | MuleSoft Mysore Meetup #37 par
Payment Integration using Braintree Connector | MuleSoft Mysore Meetup #37MysoreMuleSoftMeetup
50 vues17 diapositives

### Dernier(20)

Guess Papers ADC 1, Karachi University par Khalid Aziz
Guess Papers ADC 1, Karachi University
Khalid Aziz99 vues
INT-244 Topic 6b Confucianism par S Meyer
INT-244 Topic 6b Confucianism
S Meyer45 vues
EILO EXCURSION PROGRAMME 2023 par info33492
EILO EXCURSION PROGRAMME 2023
info33492202 vues
Payment Integration using Braintree Connector | MuleSoft Mysore Meetup #37 par MysoreMuleSoftMeetup
Payment Integration using Braintree Connector | MuleSoft Mysore Meetup #37
Creative Restart 2023: Atila Martins - Craft: A Necessity, Not a Choice par Taste
Creative Restart 2023: Atila Martins - Craft: A Necessity, Not a Choice
Taste45 vues
11.30.23A Poverty and Inequality in America.pptx par mary850239
11.30.23A Poverty and Inequality in America.pptx
mary850239130 vues
Monthly Information Session for MV Asterix (November) par Esquimalt MFRC
Monthly Information Session for MV Asterix (November)
Esquimalt MFRC107 vues
The Accursed House by Émile Gaboriau par DivyaSheta
The Accursed House by Émile Gaboriau
DivyaSheta251 vues
NodeJS and ExpressJS.pdf par ArthyR3
NodeJS and ExpressJS.pdf
ArthyR348 vues

### Log_Ph-1-2-3_QE_S&P (PQRS & J-Batch) WA.pdf

• 1. Question bank on Vector, 3D and Complex Number & Misc. Subjective Problem Select the correct alternative : (Only one is correct) Q.1 If  a = 11 1 ,  b = 23 ,   a b  = 30 , then   a b  is : (A) 10 (B) 20 (C) 30 (D) 40 Q.2 ThepositionvectorofapointPmovinginspaceisgivenby k̂ ) t sin 5 ( ĵ ) t cos 4 ( î ) t cos 3 ( R OP      . The time 't' when the point P crosses the plane 4x – 3y + 2z = 5 is (A) 2  sec (B) 6  sec (C) 3  sec (D) 4  sec Q.3 Indicate the correct order sequence in respect of the following : I. The lines 3 4 x   = 1 6 y   = 1 6 y   and 1 1 x   = 2 2 y   = 2 3 z  are orthogonal. II. The planes 3x – 2y – 4z = 3 and the plane x – y – z = 3 are orthogonal. III. The function f (x) = ln(e–2 + ex) is monotonic increasing  x R. IV. If g is the inverse of the function, f (x) = ln(e–2 + ex) then g(x) = ln(ex – e–2). (A) FTFF (B)TFTT (C) FFTT (D)FTTT Q.4* If 2 1 z z is purelyimaginarythen 2 1 2 1 z z z z   is equal to : (A) 1 (B) 2 (C) 3 (D) 0 Q.5 In a regulartetrahedron, the centres ofthe four faces are thevertices of a smallertetrahedron. The ratio of the volume ofthe smaller tetrahedron to that of the larger is n m ,where m and n arerelativelyprime positive integers. The value of (m + n)is (A) 3 (B) 4 (C) 27 (D) 28 Q.6 If    a b c , , arenon-coplanarunitvectorssuchthat      a x bxc b c ( ) ( )   1 2 thentheanglebetween b & a   is (A) 3 /4 (B) /4 (C) /2 (D)  Q.7 The sineof angle formed bythe lateral faceADC and plane of thebaseABC of thetetrahedronABCD where A  (3, –2, 1); B  (3, 1, 5); C  (4, 0, 3) and D  (1, 0, 0) is (A) 2 29 (B) 5 29 (C) 3 3 29 (D) 2 29 Q.8* Let z be a complex number, then the region represented by the inequality z + 2< z + 4is given by : (A) Re (z) >  3 (B) Im(z) < 3 (C) Re (z) <  3 & Im (z) >  3 (D) Re (z) <  4 & Im (z) >  4 Q.9 The volume of the parallelpiped whose edges are represented by the vectors  a i j k    2 3 4    ,  b i j k    3 2    ,  c i j k       2 is : (A) 7 (B) 5 (C) 4 (D) none
• 2. Q.10 Let w , v , u    bethevectors suchthat 0 w v u       ,if 5 w & 4 v , 3 u       then the value of u . w w . v v . u         is : (A) 47 (B) 25 (C) 0 (D) 25 Q.11 Let  a = j ˆ î  ,  b= k̂ j ˆ  ,  c= î k̂  . If  d is a unit vector such that      a d b c d . [ , , ]   0 then  d (A) ) k̂ 2 j ˆ î ( 6 1    (B) ) k̂ j ˆ î ( 3 1    (C) ) k̂ j ˆ î ( 3 1    (D) ± k̂ Q.12* If z be a complex number for which z z   1 2 , then the greatest value of z is : (A) 2 1  (B) 3 1  (C) 2 2 1  (D) none Q.13 If the non  zero vectors   a b & are perpendicular to each other, then the solution of the equation ,    r a b   is : (A)         r xa a a a b    1 . (B)         r xb b b a b    1 . (C)    r xa b   (D)    r xb a   where x is anyscalar. Q.14 Thelines k 4 z 1 3 y 1 2 x       and 1 5 z 2 4 y k 1 x      arecoplanar if (A) k = 1 or – 1 (B) k = 0 or – 3 (C) k = 3 or – 3 (D) k = 0 or – 1 Q.15 Whichoneof thefollowingstatementis INCORRECT ? (A) If   n a . = 0 ,   n b . = 0 &   n c . = 0 for some non zero vector  n , then     a b c = 0 (B) there exist a vector having direction angles  = 30º &  = 45º (C) locus of point for which x = 3 & y = 4 is a line parallel to the z - axis whose distance from the z-axis is 5 (D)InaregulartetrahedronOABCwhere'O'istheorigin,thevector OA OB OC      isperpendicular to the planeABC. Q.16* Given that the equation, z2 +(p+ iq)z+ r+ is = 0 has a real root where p, q, r, s  R.Then which one is correct (A) pqr = r2 + p2s (B) prs = q2 + r2p (C) qrs = p2 + s2q (D) pqs = s2 + q2r Q.17 The distance ofthe point (3, 4, 5) from x-axis is (A) 3 (B) 5 (C) 34 (D) 41 Q.18 Givennonzerovectors C and B , A    ,thenwhich oneofthefollowingis false? (A)Avector orthogonal to C and B A     is ± C ) B A (      (B)Avector orthogonal to B A    and B A    is ± B A    (C)Volume of the parallelopiped determined by C and B , A    is | C · B A |     (D)Vector projection of B onto A   is | B | B · A   
• 3. Q.19 Given three vectors    a b c , , such that they are nonzero, noncoplanar vectors, then which of the followingarenoncoplanar. (A)       a b b c c a    , , (B)       a b b c c a    , , (C)       a b b c c a    , , (D)       a b b c c a    , , Q.20* The sum i + 2i2 + 3i3 + ........ + 2002i2002, where i = 1  is equal to (A) – 999 + 1002i (B) – 1002 + 999i (C) – 1001 + 1000i (D) – 1002 + 1001i Q.21 Locus of the point P, for which OP  represents a vector with direction cosine cos  = 1 2 ( 'O' is the origin) is : (A)Acircle parallel to yz plane withcentre on the xaxis (B) a coneconcentric with positive xaxis havingvertex at the originand the slant height equal to the magnitudeofthevector (C)a rayemanatingfrom the origin and making an angleof60ºwith xaxis (D) a disc parallel to yz plane withcentre on xaxis & radius equal to| | OP  sin 60º Q.22 Alinewithdirectionratios(2,1,2)intersectsthelines ) k̂ j ˆ î ( j ˆ r        and ) k̂ ĵ î 2 ( î r        at A and B, then l (AB) is equal to (A) 3 (B) 3 (C) 2 2 (D) 2 Q.23 The vertices of a triangle areA(1, 1, 2), B(4, 3, 1) & C(2, 3, 5).The vector representing the internal bisector of theangleAis : (A)    i j k   2 (B) 2 2    i j k   (C) 2 2    i j k   (D) 2 2    i j k   Q.24* Lowest degree ofa polynomial with rational coefficients if one of its rootis, i  2 is (A) 2 (B) 4 (C) 6 (D) 8 Q.25 Aplane vector has components 3 & 4 w.r.t. the rectangular cartesian system. This system is rotated through an angle  4 in anticlockwisesense.Then w.r.t. thenew system the vectorhascomponents : (A) 4, 3 (B) 7 2 1 2 , (C) 1 2 7 2 , (D) none Q.26 Let  a = xi + 12j  k ;  b = 2i + 2xj + k &  c = i + k . If the ordered set      b c a is left handed , then: (A) x  (2, ) (B) x  (,  3) (C) x  ( 3, 2) (D) x  { 3, 2} Q.27 If k̂ j ˆ î cos    , k̂ j ˆ cos î    & k̂ cos j ˆ î    (      2 n ) are coplanar then the value of            2 ec cos 2 ec cos 2 ec cos 2 2 2 equal to (A) 1 (B)  (C) 3 (D) none of these Q.28* The straight line (1 + 2i)z + (2i – 1) z = 10i on the complex plane, has intercept onthe imaginaryaxis equal to (A) 5 (B) 2 5 (C) – 2 5 (D) – 5
• 4. Q.29 The perpendicular distance of an angular point of a cube of edge 'a' from the diagonal which does not pass thatangularpoint, is (A) a 3 (B) a 2 (C) a 2 3 (D) a 3 2 Q.30 Which one of the following does not hold for the vector V  =      a x b x a ? (A) perpendicular to  a (B) perpendicular to  b (C) coplanar with  a &  b (D) perpendicular to  a x  b . Q.31* Let z1,z2 &z3 bethecomplex numbersrepresentingthevertices ofatriangleABC respectively.If P is a point representing the complex number z0 satisfying; a(z1 z0) + b(z2 z0) + c(z3 z0) = 0, then w.r.t. the triangleABC, the point Pis its : (A) centroid (B) orthocentre (C) circumcentre (D) incentre Q.32 Given the position vectors of the vertices of a triangleABC, ) a ( A  ; ) b ( B ; ) c ( C .Avector r  is parallel to the altitude drawn from the vertexA, making an obtuse angle with the positiveY-axis. If | r |  = 34 2 ; k̂ 3 j ˆ î 2 a     ; k̂ 4 j ˆ 2 î b     ; k̂ 2 j ˆ î 3 c     , then r  is (A) k̂ 6 j ˆ 8 î 6    (B) k̂ 6 j ˆ 8 î 6   (C) k̂ 6 j ˆ 8 î 6    (D) k̂ 6 j ˆ 8 î 6   Q.33* The complex number, z = 5 + i has anargument which is nearlyequal to : (A) /32 (B) /16 (C) /12 (D) /8 Q.34 If k̂ j ˆ î a     , k̂ j ˆ î b     , k̂ j ˆ 2 î c     , then the value of c . c b . c a . c c . b b . b a . b c . a b . a a . a                   equal to (A) 2 (B) 4 (C) 16 (D) 64 Q.35* If the equation x2 + ax + b = 0 where a, b  R has a non real root whose cube is 343 then (7a + b) has the value (A) 98 (B) – 49 (C) – 98 (D) 49 Direction for Q.36 to Q.40. Let k̂ 3 j ˆ 2 î A     and k̂ 5 j ˆ 4 î 3 B     Q.36 The value of the scalar 2 2 ) B · A ( | B A |       is equal to (A) 8 (B) 10 7 (C) 7 10 (D) 64 Q.37 Equation of a line passing through the point with position vector j ˆ 3 î 2  and orthogonal to the plane containingthevectors A  and B  ,is (A) k̂ j ˆ ) 3 2 ( î ) 2 ( r          (B) k̂ j ˆ ) 3 2 ( î ) 2 ( r          (C) k̂ j ˆ ) 3 2 ( î r         (D) none
• 5. Q.38 Equation of a plane containing the point with position vector ) k̂ j ˆ î (   and parallel to the vectors A  and B  , is (A) x + 2y + z = 0 (B) x – 2y – z – 2 = 0 (C) x – 2y + z – 4 = 0 (D) 2x + y + z – 1 = 0 Q.39 Volume of the tetrahedron whose 3 coterminous edges are the vectors A  , B  and k̂ 4 j ˆ î 2 C     is (A) 1 (B) 4/3 (C) 8/3 (D) 8 Q.40 Vector component of A  perpendicular to thevector B  is given by (A) 2 B ) B A ( B       (B) 2 B ) B A ( A       (C) 2 A ) B A ( B       (D) 2 A ) B A ( A       Select the correct alternatives : (More than one are correct) Q.41 If a, b, c are different real numbers and a i b j ck      ; bi c j a k      & ci a j bk      are position vectors of threenon-collinear pointsA, B &C then: (A) centroid oftriangleABC is   a b c i j k     3    (B)   i j k   is equallyinclinedto the threevectors (C)perpendicular from the originto theplane of triangleABC meet at centroid (D)triangleABCis an equilateraltriangle. Q.42 The vectors    a b c , , are of thesame length & pairwise form equal angles. If  a i j     &  b j k     , the pv's of  c can be : (A) (1, 0, 1) (B)         4 3 1 3 4 3 , , (C) 1 3 4 3 1 3 , ,        (D)         1 3 4 3 1 3 , , Q.43* Which of the following locii of z on the complex plane represents a pair of straight lines? (A) Re z2 = 0 (B) Im z2 = 0 (C) z + z = 0 (D) z1= zi Q.44 If    a b c , , &  d are linearlyindependent set of vectors &K a K b K c K d 1 2 3 4        = 0 then : (A) K1 + K2 + K3 + K4 = 0 (B) K1 + K3 = K2 + K4 = 0 (C) K1 + K4 = K2 + K3 = 0 (D) none of these Q.45 If    a b c , , &  d are the pv's of the pointsA, B, C & D respectivelyin three dimensional space & satisfy the relation3 2 2     a b c d    =0, then : (A)A, B, C & D are coplanar (B) the line joiningthe points B& D divides the line joining the pointA& C in the ratio 2 : 1. (C) theline joiningthe pointsA& C divides the line joiningthepoints B & D in the ratio 1: 1 (D) the four vectors    a b c , , &  d arelinearlydependent. Q.46* If z3  i z2  2 i z  2 = 0 then z can be equal to : (A) 1  i (B) i (C) 1 + i (D)  1  i
• 6. Q.47 If  a &  b are two non collinear unit vectors &  a ,  b , x  a  y  b form a triangle, then : (A) x =  1 ; y = 1 &   a +  b  = 2 cos   a b            2 (B) x =  1 ; y = 1 & cos   a b        +   a +  b  cos      a a b ,          =  1 (C)   a +  b  =  2 cot   a b            2 cos   a b            2 & x =  1 , y = 1 (D) none Q.48 The lines with vector equations are ;  r1 =         3 6 4 3 2    ~  i j i j k  and  r2 =         2 7 4    ~  i j i j k  are such that : (A) theyare coplanar (B) theydo not intersect (C) theyare skew (D) the angle between them is tan1 (3/7) Q.49* Given a, b,x, yR thenwhich of the followingstatement(s) hold good? (A) (a + ib) (x + iy)–1 = a – ib  x2 + y2 = 1 (B) (1–ix) (1 + ix)–1 = a – ib  a2 + b2 = 1 (C) (a + ib) (a – ib)–1 = x – iy  |x + iy| = 1 (D) (y – ix) (a + ib)–1 = y + ix |a – ib| = 1 Q.50 The acute angle that the vector 2 2    i j k   makes with the plane contained by the two vectors 2 3    i j k   and    i j k   2 is given by: (A) cos–1 1 3       (B) sin–1 1 3       (C) tan–1   2 (D) cot–1   2 Q.51 ThevolumeofarighttriangularprismABCA1B1C1 isequalto3.Ifthepositionvectorsoftheverticesof the baseABC areA(1, 0, 1) ; B(2,0, 0) and C(0, 1, 0) the position vectors of the vertexA1 can be: (A) (2, 2, 2) (B) (0, 2, 0) (C) (0,  2, 2) (D) (0,  2, 0) Q.52* If xr = CiS  2r       for 1  r  n r, n  N then : (A) Limit n   Re xr r n         1 =  1 (B) Limit n   Re xr r n         1 = 0 (C) Limit n   Im xr r n         1 = 1 (D) Limit n   Im xr r n         1 = 0
• 7. Q.53 If a line has a vector equation,    r i j i j     2 6 3      then which of the following statements holds good ? (A)the lineis parallel to 2 6   i j  (B) the line passes through thepoint 3 3   i j  (C) the line passes through the point   i j  9 (D)thelineis parallel to xyplane Q.54 If    a b c , , are non-zero, non-collinear vectors such that a vector  p = a b cos     2      a b c and a vector  q = a c cos           a c b then  p +  q is (A) parallel to  a (B) perpendicular to  a (C) coplanarwith   b c & (D) coplanar with a  and c  Q.55* The greatest valueof the modulus ofof the complex number 'z' satisfyingtheequality z z  1 = 1 is (A)   1 5 2 (B) 3 5 2  (C) 3 5 2  (D) 5 1 2  SUBJECTIVE: Q.1 Let j ˆ î 3 a    and ĵ 2 3 î 2 1 b    and b ) 3 q ( a x 2       , b q a p y       . If y x    , then express p as a function of q, say p = f (q), (p  0 & q  0) and find the intervals of monotonicity of f (q). Q.2 Using onlythe limit theorems 1 x x n Lim 1 x   l = 1 and x 1 e Lim x 0 x   = 1. Evaluate 1 x x n x x Lim x 1 x     l . Q.3 The three vectors  a i j k    4 2    ;  b i j k    2   and  c i k   2  are all drawn from the point with p.v. j ˆ î . Findthe equationof theplanecontainingtheir endpoint in scalar dot product form. Q.4 (cos cos ) 2 1 2 1 2 2 n n x x dx     z   where n N  Q.5 Let points P, Q & R have position vectors, 1 r  = 3i  2j  k; 2 r  = i + 3j + 4k & 3 r  = 2i+j2k respectively, relative toan origin O. Find the distance of Pfrom the plane OQR. Q.6 Evaluate:     3 1 dx ) 3 x )( 2 x )( 1 x ( Q.7 Given that vectors    A B C , , form a triangle such that    A B C   , find a,b,c,d such that the area of the triangle is5 6 where  A = ai + bj + ck;  B= di + 3j + 4k &  C =3i + j  2k.
• 8. Q.8                       1 n 0 k n 1 k n k n dx x n 1 k n k x n Lim Q.9 Find the distance of the point P(i + j + k) from the plane L which passes through the three points A(2i + j + k), B(i +2j + k), C(i+ j + 2k).Also find thepvofthefoot of the perpendicularfrom Pon the plane L. Q.10 Evaluate: (a)   dx x cos x sin x cos x sin 3 4 4 , x         2 , 0 ; (b)   dx x cos x sin x cos x sin 3 4 4 Q.11 Findtheequationofthestraightlinewhichpassesthroughthepointwithpositionvector a  ,meetstheline c t b r      and is parallel to the plane 1 n . r    . Q.12 Integrate:   x sin x cos dx 3 3 . Q.13 Findtheequationofthelinepassingthroughthepoint(1, 4,3)whichis perpendiculartobothofthelines 2 1 x  = 1 3 y  = 4 2 z  and 3 2 x  = 2 4 y  = 2 1 z   Also find all points on this linethe square of whose distance from (1, 4,3) is 357. Q.14 1 n n 2 2 n 2 n 1 n n Lim               Q.15 If z-axis be vertical, find the equation of the line of greatest slope through the point (2, –1, 0) on the plane 2x + 3y – 4z = 1. Q.16 Let I =    2 0 dx x sin b x cos a x cos and J =    2 0 dx x sin b x cos a x sin , where a > 0 and b > 0. Compute the values of Iand J.
• 9. ANSWER KEY Select the correct alternative : (Only one is correct) Q.1 B Q.2 B Q.3 C Q.4 A Q.5 D Q.6 A Q.7 B Q.8 A Q.9 A Q.10 B Q.11 A Q.12 A Q.13 A Q.14 B Q.15 B Q.16 D Q.17 D Q.18 D Q.19 A Q.20 D Q.21 B Q.22 A Q.23 D Q.24 B Q.25 B Q.26 C Q.27 B Q.28 A Q.29 D Q.30 B Q.31 D Q.32 A Q.33 B Q.34 C Q.35 A Q.36 C Q.37 A Q.38 C Q.39 B Q.40 A Select the correct alternatives : (More than one are correct) Q.41 A,B,C,D Q.42 A,D Q.43 A,B Q.44 A,B,C Q.45 A,C,D Q.46 B,C,D Q.47 A,B Q.48 B,C,D Q . 49 A,B,C,D Q.50 B,D Q.51 A,D Q . 52 A,D Q.53 B,C,D Q.54 B,C Q.55 B,D SUBJECTIVE: Q.1 p = ,decreasing in q  (–1, 1), q  0 Q.2 – 2 Q.3 = 3 Q.4 Q.5 3 units Q.6 1/2 Q.7 (8, 4, 2, 11) or (8, 4, 2, 5) Q.8 Q.9 Q.10 (a) C – where t = cot 2 x; (b) + C, where t = tan 2 x Q.11 Q.12 2 [tan –1 (sin x + cos x) + ln + C Q.13 , ; (–9, 20, 4) ; (11, –12, 2) Q.14 e –1 Q.15 Q.16 ,
Langue couranteEnglish
Español
Portugues
Français
Deutsche
© 2023 SlideShare de Scribd