
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

CBSE Class XII 2014 : MATHEMATICS

11 pages, 68 questions, 36 questions with responses, 77 total responses,

	cbse12	+Fave Message
	Profile Timeline Uploads Q & A

Home > cbse12 > F Also featured on: azhar1996 kky_eck and 7 more

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

H$moS> Z . Series OSR Code No. amob Z . 65/1 narjmWu H$moS >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Roll No. Candidates must write the Code on the title page of the answer-book. H $n`m Om M H$a b| {H$ Bg Z-n _o _w{ V n > 11 h & Z-n _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Z ~a H$mo N>m C ma -nwp VH$m Ho$ _wI-n > na {bI| & H $n`m Om M H$a b| {H$ Bg Z-n _| >29 Z h & H $n`m Z H$m C ma {bIZm ew $ H$aZo go nhbo, Z H$m H $_m H$ Ad ` {bI| & Bg Z-n H$mo n T>Zo Ho$ {bE 15 {_ZQ >H$m g_` {X`m J`m h & Z-n H$m {dVaU nydm _| 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>m Ho$db Z-n H$mo n T>|Jo Am a Bg Ad{Y Ho$ Xm amZ do C ma-nwp VH$m na H$moB C ma Zht {bI|Jo & Please check that this question paper contains 11 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 29 questions. Please write down the Serial Number of the question before attempting it. 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. J{UV MATHEMATICS {ZYm [aV g_` : 3 K Q>o A{YH$V_ A H$ : 100 Time allowed : 3 hours 65/1 Maximum Marks : 100 1 P.T.O. gm_m ` {ZX}e : (i) g^r Z A{Zdm` h & (ii) Bg Z n _| 29 Z h Omo VrZ I S>m| _| {d^m{OV h : A, ~ VWm g & I S> A _| 10 Z h {OZ_| go `oH$ EH$ A H$ H$m h & I S> ~ _| 12 Z h {OZ_| go `oH$ Mma A H$ H$m h & I S> g _| 7 Z h {OZ_| go `oH$ N> A H$ H$m h & (iii) I S> A _| g^r Zm| Ho$ C ma EH$ e X, EH$ dm ` AWdm Z H$s Amd `H$Vm AZwgma {XE Om gH$Vo h & (iv) nyU Z n _| {dH$ n Zht h & {\$a ^r Mma A H$m| dmbo 4 Zm| _| VWm N> A H$m| dmbo 2 Zm| _| Am V[aH$ {dH$ n h & Eogo g^r Zm| _| go AmnH$mo EH$ hr {dH$ n hb H$aZm h & (v) H $bHw$boQ>a Ho$ `moJ H$s AZw_{V Zht h & `{X Amd `H$ hmo Vmo Amn bKwJUH$s` gma{U`m _m J gH$Vo h & General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, Section B comprises of 12 questions of four marks each and Section C comprises of 7 questions of six marks each. (iii) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question. (iv) There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions. (v) 65/1 Use of calculators is not permitted. You may ask for logarithmic tables, if required. 2 I S> A SECTION A Z g `m 1 go 10 VH$ `oH$ Z 1 A H$ H$m h & Question numbers 1 to 10 carry 1 mark each. 1. `{X N na R = {(x, y) : x + 2y = 8} EH$ g ~ Y h , Vmo R H$m n[aga {b{IE & If R = {(x, y) : x + 2y = 8} is a relation on N, write the range of R. 2. `{X tan 1 x + tan 1 y = If tan 1 x + tan 1 y = 3. , xy < 1 4 h , Vmo x + y + xy H$m _mZ {b{IE & , xy < 1, then write the value of x + y + xy. 4 `{X A EH$ Eogm dJ Am `yh h {H$ Ohm I EH$ V g_H$ Am `yh h & A2 = A h , Vmo 7A (I + A)3 H$m _mZ {b{IE, If A is a square matrix such that A2 = A, then write the value of 7A (I + A)3, where I is an identity matrix. 4. `{X x y 2x y z w x y If 2x y 3x 5. `{X 1 0 z 1 = 0 w 7 8 2 4 6 7 8 4 2 4 h , Vmo x+y H$m _mZ kmV H$s{OE & 4 , find the value of x + y. 5 h , Vmo x H$m _mZ kmV H$s{OE & 7 If 4 5 7 3x 65/1 = , find the value of x. 6 4 3 P.T.O. x 6. `{X f (x ) t sin t dt h , Vmo f (x) H$m _mZ kmV H$s{OE & 0 x If f (x) t sin t dt , then write the value of f (x). 0 7. _mZ kmV H$s{OE 4 2 x 2 x 1 : dx Evaluate : 4 2 8. x 2 x 1 dx p H$m dh _mZ kmV H$s{OE {OgHo$ {bE g{Xe g_m Va h & ^ ^ ^ 3i + 2 j + 9k Find the value of p for which the vectors ^ ^ ^ i 2p j + 3 k are parallel. 9. ^ ^ ^ ^ ^ ^ a = 2i + j + 3k, b = i + 2 j + k a . ( b c ) kmV H$s{OE & 10. ( b c ), if ^ ^ j + 2k. ^ ^ ^ i 2p j + 3 k ^ ^ ^ 3 i + 2 j + 9k and ^ ^ ^ c = 3i + j + 2k h , Vmo ^ ^ ^ ^ ^ ^ a = 2i + j + 3k, b = i + 2 j + k and `{X Find a . ^ c =3i + VWm `{X EH$ aoIm Ho$ H$mVu` g_rH$aU VWm 3 x y 4 2z 6 5 7 4 h , Vmo Cg aoIm H$m g{Xe g_rH$aU {b{IE & If the cartesian equations of a line are vector equation for the line. 65/1 4 3 x y 4 2z 6 , write the 5 7 4 I S> ~ SECTION B Z g `m 11 go 22 VH$ `oH$ Z 4 A H$ H$m h & Question numbers 11 to 22 carry 4 marks each. `{X \$bZ f : R R, f(x) = x2 + 2 X m h , Vmo 11. fog VWm gof VWm x , x 1 x 1 gof ( 3) kmV H$s{OE g : R R, g(x) = kmV H$s{OE Am a AV fog (2) VWm mam & If the function f : R R be given by f(x) = x2 + 2 and g : R R be x given by g(x) = , x 1, find fog and gof and hence find fog (2) x 1 and gof ( 3). 12. {g H$s{OE {H$ 1 x tan 1 1 x 1 x 1 cos 1 x, = 4 2 1 x 1 x 1 2 AWdm `{X x 2 1 tan 1 x 4 + tan x 2 x 4 = 4 h , Vmo x H$m _mZ kmV H$s{OE & Prove that 1 x tan 1 1 x 1 x 1 1 cos 1 x, x 1 = 4 2 2 1 x OR x 2 1 If tan 1 x 4 + tan 13. x 2 x 4 = 4 , find the value of x. gma{UH$m| Ho$ JwUY_m] H$m `moJ H$aHo$, {g H$s{OE {H$ x y x 5x 4 y 4x 2x 10x 8y 65/1 x 8x 3x x3 5 P.T.O. Using properties of determinants, prove that x y 4x 2x 10x 8y `{X x 5x 4 y 14. x 8x 3x x = ae (sin cos ) x3 y = ae (sin + cos ) VWm h , Vmo = 4 na dy dx H$m _mZ kmV H$s{OE & Find the value of dy at = , if x = ae (sin cos ) and dx 4 y = ae (sin + cos ). 15. `{X y = P eax + Q ebx d 2y dx 2 (a + b) h , Vmo Xem BE {H$ dy + aby = 0. dx If y = P eax + Q ebx, show that d 2y dx 16. x Ho$ 2 (a + b) dy + aby = 0. dx dh _mZ kmV H$s{OE {OgHo$ {bE y = [x (x 2)]2 EH$ dY _mZ \$bZ h & AWdm dH $ x2 a2 y2 b2 1 Ho$ {~ X ( 2 a, b) na ne aoIm VWm A{^b ~ Ho$ g_rH$aU kmV H$s{OE & Find the value(s) of x for which y = [x (x 2)]2 is an increasing function. OR Find the equations of the tangent and normal to the curve at the point ( 2 a, b). 65/1 6 x2 a2 y2 b2 1 17. _mZ kmV H$s{OE : 0 4 x sin x 1 cos 2 x dx AWdm _mZ kmV H$s{OE : x 2 dx x 2 5x 6 Evaluate : 0 4 x sin x 1 cos 2 x dx OR Evaluate : 18. x 2 x 2 5x 6 AdH$b g_rH$aU O~ x = 1 h , Vmo dx dy = 1 + x + y + xy dx y = 0 h & H$m {d{e > hb kmV H$s{OE, {X`m J`m h {H$ Find the particular solution of the differential dy = 1 + x + y + xy, given that y = 0 when x = 1. dx 19. AdH$b g_rH$aU (1 + x2) 1 dy + y = e tan x dx Solve the differential equation (1 + x2) 65/1 7 equation H$mo hb H$s{OE & 1 dy + y = e tan x . dx P.T.O. 20. A, B, C VWm D, {OZHo$ p W{V ^ ^ ^ ^ ^ ^ ^ ^ j k , 3 i + 9 j + 4 k VWm 4 ( i + j + k ) h , Xem BE {H$ Mma {~ X g{Xe H $_e g_Vbr` h & ^ ^ ^ 4i + 5j + k, AWdm ^ ^ ^ H$m a = i + j + k ^ ^ ^ c = i + 2 j + 3 k Ho$ `moJ\$b g{Xe JwUZ\$b 1 Ho$ ~am~a h & g{Xem| ^ ^ ^ b = 2i + 4 j 5k VWm H$s {Xem _| EH$ _m H$ g{Xe Ho$ gmW A{Xe H$m _mZ kmV H$s{OE Am a AV b + c H$s {Xem _| EH$ _m H$ g{Xe kmV H$s{OE & Show that the four points A, B, C and D with position vectors ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 4 i + 5 j + k , j k , 3 i + 9 j + 4 k and 4 ( i + j + k ) respectively are coplanar. OR ^ ^ ^ The scalar product of the vector a = i + j + k with a unit vector along ^ ^ ^ ^ ^ ^ the sum of vectors b = 2 i + 4 j 5 k and c = i + 2 j + 3 k is equal to one. Find the value of and hence find the unit vector along b + c . 21. EH$ aoIm {~ X (2, 1, 3) go hmoH$a OmVr h VWm aoImAm| ^ ^ ^ ^ ^ ^ r = ( i + j k ) + (2 i 2 j + k ) VWm ^ ^ ^ ^ ^ ^ r = (2 i j 3 k ) + ( i + 2 j + 2 k ) na b ~dV h & CgH$m g_rH$aU, g{Xe VWm H$mVu` $n _| kmV H$s{OE & A line passes through (2, 1, 3) and is perpendicular to the lines ^ ^ ^ ^ ^ ^ r = ( i + j k ) + (2 i 2 j + k ) and ^ ^ ^ ^ ^ ^ r = (2 i j 3 k ) + ( i + 2 j + 2 k ). Obtain its equation in vector and cartesian form. 22. EH$ `moJ Ho$ g\$b hmoZo H$m g `moJ CgHo$ Ag\$b hmoZo go VrZ JwZm h & m{`H$Vm kmV H$s{OE {H$ AJbo nm M narjUm| _| go H$_-go-H$_ 3 g\$b hm|Jo & An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes. 65/1 8 I S> g SECTION C Z g `m 23 go 29 VH$ `oH$ Z Ho$ 6 A H$ h & Question numbers 23 to 29 carry 6 marks each. 23. Xmo {d mb` A VWm B AnZo MwZo h E {d m{W `m| H$mo {Z H$nQ>Vm, g `dm{XVm VWm ghm`H$Vm Ho$ _y `m| na nwa H$ma XoZm MmhVo h & {d mb` A AnZo H $_e 3, 2 VWm 1 {d m{W `m| H$mo BZ VrZ _y `m| Ho$ {bE `oH$ H$mo H $_e < x, < y VWm < z XoZm MmhVm h O~{H$ BZ nwa H$mam| H$m Hw$b _y ` < 1,600 h & {d mb` B AnZo H $_e 4, 1 VWm 3 {d m{W `m| H$mo BZ _y `m| Ho$ {bE Hw$b < 2,300 nwa H$ma d $n XoZm MmhVm h (VWm nhbo {d mb` O go hr VrZ _y `m| na dhr nwa H$ma am{e XoZm MmhVm h ) & `{X BZ VrZm| _y `m| na {XE JE EH$-EH$ nwa H$ma H$s Hw$b am{e < 900 h , Vmo Am `yhm| H$m `moJ H$aHo$ `oH$ _y ` Ho$ {bE Xr JB nwa H$ma am{e kmV H$s{OE & Cn`w $ VrZ _y `m| Ho$ A{V[a $ EH$ A ` _y ` gwPmBE, Omo nwa H$ma XoZo Ho$ {bE em{_b H$aZm Mm{hE & Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award < x each, < y each and < z each for the three respective values to 3, 2 and 1 students respectively with a total award money of < 1,600. School B wants to spend < 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is < 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award. 24. Xem BE {H$ EH$ r { `m Ho$ Jmobo Ho$ A VJ V A{YH$V_ Am`VZ dmbo b ~-d mr` e Hw$ H$s D $MmB 8 27 4r 3 h & `h ^r Xem BE {H$ Bg e Hw$ H$m A{YH$V_ Am`VZ Jmobo Ho$ Am`VZ H$m hmoVm h & Show that the altitude of the right circular cone of maximum volume that 4r can be inscribed in a sphere of radius r is . Also show that the 3 8 maximum volume of the cone is of the volume of the sphere. 27 65/1 9 P.T.O. 25. _mZ kmV H$s{OE : 1 4 cos x sin4 x dx Evaluate : 26. 1 cos 4 x sin4 x dx g_mH$bZ H$m `moJ H$aHo$ EH$ Eogo { H$moUr` jo H$m jo \$b kmV H$s{OE Omo erfm] ( 1, 2), (1, 5) VWm (3, 4) mam {Kam h & Using integration, find the area of the region bounded by the triangle whose vertices are ( 1, 2), (1, 5) and (3, 4). 27. g_Vbm| x + y + z = 1 VWm 2x + 3y + 4z = 5 H$s {V N>oXZ aoIm H$mo A V{d > H$aZo dmbo VWm g_Vb x y + z = 0 Ho$ b ~dV g_Vb H$m g_rH$aU kmV H$s{OE & Cn`w $ kmV {H$E JE g_Vb H$s _yb-{~ X go X ar ^r kmV H$s{OE & AWdm aoIm ^ ^ ^ ^ r = 2 i 4 j + 2 k + (3 i ^ ^ r . (i 2j + ^ k) = 0 + 4^ j ^ + 2k) VWm g_Vb Ho$ {V N>oXZ {~ X H$s {~ X (2, 12, 5) go X ar kmV H$s{OE & Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x y + z = 0. Also find the distance of the plane obtained above, from the origin. OR Find the distance of the point (2, 12, 5) from the point of intersection of ^ ^ ^ ^ ^ ^ the line r = 2 i 4 j + 2 k + (3 i + 4 j + 2 k ) and the plane ^ ^ ^ r . ( i 2 j + k ) = 0. 65/1 10 28. EH$ {Z_m UH$Vm H $nZr H$jm XII Ho$ {bE J{UV _| ghm`H$ {ejU gm_J r Ho$ Xmo Z_yZo A VWm B ~ZmVr h & Z_yZo A H$m `oH$ ZJ ~ZmZo Ho$ {bE 9 l_ K Q>o Am a 1 l_ K Q>m nm {be H$aZo _| bJmVr h , O~{H$ Z_yZo B Ho$ `oH$ ZJ ~ZmZo _| 12 l_ K Q>o VWm nm {be H$aZo _| 3 l_ K Q>o bJmVr h & ~ZmZo VWm nm {be H$aZo Ho$ {bE {V g mh Cnb Y A{YH$V_ l_ K Q>o H $_e 180 VWm 30 h & H $nZr Z_yZo A Ho$ `oH$ ZJ na < 80 VWm Z_yZo B Ho$ `oH$ ZJ na < 120 H$_mVr h & Z_yZo A VWm Z_yZo B Ho$ {H$VZo-{H$VZo ZJm| H$m {Z_m U {V g mh {H$`m OmE {H$ A{YH$V_ bm^ hmo ? Bg Z H$mo a {IH$ moJ m_Z g_ `m ~ZmH$a J m\$ mam hb H$s{OE & {V g mh A{YH$V_ bm^ `m h ? A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of < 80 on each piece of type A and < 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit ? Make it as an LPP and solve graphically. What is the maximum profit per week ? 29. VrZ {g o$ h & EH$ {g o$ Ho$ XmoZm| Amoa {MV hr h , X gam {g $m A{^ZV h {Og_| {MV 75% ~ma H$Q> hmoVm h VWm Vrgam {g $m ^r A{^ZV h {Og_| nQ>> 40% ~ma H$Q> hmoVm h & VrZ {g $m| _| go `m N>`m EH$ {g $m MwZH$a CN>mbm J`m & `{X {g o$ na {MV H$Q> hmo, Vmo `m m{`H$Vm h {H$ dh XmoZm| Amoa {MV dmbm {g $m h ? AWdm W_ N>:$ YZ nyUm H$m| _| go Xmo g `mE `m N>`m ({~Zm {V WmnZ) MwZr JB & _mZm X XmoZm| g `mAm| _| go ~ S>r g `m ` $ H$aVm h & `m p N>H$ Ma X H$m m{`H$Vm ~ Q>Z kmV H$s{OE VWm Bg ~ Q>Z H$m _m ` ^r kmV H$s{OE & There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin ? OR Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution. 65/1 11 P.T.O.

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)

Deepak Nair
(20)

Rupal Gupta
(12)

Karthik Shivkumar
(11)

luckykaul
(7)

Formatting page ...

Additional Info : CBSE Class XII Board Solved Question Paper 2014 Mathematics
Tags : CBSE Board 2015, Specimen Question Paper 2014 Mathematics, social science, social studies, hcg, history, civics, solved sample mock guess question paper, cbse class XII syllabus, cbse class 12 previous years model papers., cbse, cbse papers, cbse sample papers, cbse books, portal for cbse india, cbse question bank, central board of secondary education, cbse question papers with answers, prelims preliminary exams, pre board exam papers, cbse model test papers, solved board question papers of cbse last year, previous years solved question papers, free online cbse solved question paper, cbse syllabus, india cbse board sample questions papers, last 10 years cbse papers, cbse question papers 2017, cbse guess sample questions papers, cbse important questions, specimen / mock papers 2018.

cbse12 chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: