CAREER POINT RAJSTHAN BOARD OF SENIOR SECONDARY EXAMINATION MATHEMATICS. xf.kr

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1 CAREER POINT MOCK TEST PAPER RAJSTHAN BOARD OF SENI SECONDARY EXAMINATION ukekad Roll No. No. of Questions No. of Pinted Pages - 8 MATHEMATICS f.k le; : ¼?k.Vsa iw.kkzaad : 8 GENERAL INSTRUCTIONS TO THE EXAMINEES : ijh{kkffkz;ksa ds fy, lkeku; funzs'k % 1. Candidate must wite his / he Roll No. fist on the question pape compulsoily. ijh{kkfkhz lozizfke vius iz'u i=k ij ukekad vfuok;z% fy[ksaa. All the questions ae compulsoy. lhkh iz'u gy djus vfuok;z gsaa. Wite the answe to each question in the given answe-book only. izr;sd iz'u dk mùkj nh bz mùkj&iqfldk esa gh fy[ksaa 4. Fo questions having moe than one pat, the answes to those pats ae to be witten togethe in continuity. ftu iz'uksa esa vkufjd [k.m gsa] mu lhkh ds mùkj,d lkfk gh fy[kasa CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 1

2 5. If thee is any eo / diffeence / contadiction in Hindi & English vesions of the question pape, the question of Hindi vesion should be teated valid. iz'u i=k ds fgunh o vazsth :ikuj esa fdlh izdkj dh fojks/kkhkkl gksus ij fgunh Hkk"kk ds iz'u dks gh lgh ekusaa 6. Section Q. Nos. Maks pe questions A B 11 5 C 6 5 [k.m iz'u la[;k vad izr;sd iz'u v c 11 5 l Thee ae intenal choices in Q. Nos. 11 to 1,, 6 and 9. iz'u la[;k 11 ls 1 vksj, 6, 9 eas vkufjd fodyi gsaa 8. Thee is no oveall choice. Howeve Intenal choice has been povided in 4 questions of thee maks each and questions of five maks each. You have to attempt only one of the altenatives in all such questions. iw.kz iz'u&i=k esa fodyi ugha gs] fqj Hkh hu vadksa okys 4 iz'uksa esa Fkk ik p vadksa okys iz'uksa esa vkafjd fodyi gsa],sls lhkh iz'uksa esa ls vkidksa,d gh fodyi djuk gsa CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page #

3 [k.m & v SECTION A 1 Q.1 Find the pincipal value of tan 1 sec ( ). tan 1 sec 1 ( ) dk eq[; eku Kk dhft,a Q. Find the value of + y fom the following equation : = 7 y fueu lehdj.k ls + y dk eku Kk dhft, : = y Q. Let A be a squae mati of ode. Wite the value of A, whee A = 4. ekuk A Øe dk oz esfvªdl gs] ks A dk eku fyf[k,] tgk A = 4 Q.4 Given e (tan + 1) sec d = e f() + c. fn;k gs] e (tan + 1) sec d = e f() + c. Q.5 Wite the value of ( î ĵ).kˆ + î. ĵ ( î ĵ).kˆ + î.ĵ dk eku fyf[k,a Q.6 Find the distance of the plane 4y + 1z = fom the oigin. ley 4y + 1z = dh ewy fcunq ls nwjh Kk dhft,a Q.7 Evaluate ( 1 ) d ( 1 ) d dk eku Kk dhft,a Q.8 Find a b, if a = î + ĵ+ kˆ and b = î + 5ĵ kˆ. ;fn a = î + ĵ+ kˆ vksj b = î + 5ĵ kˆ ] ks a b Kk dhft,a CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page #

4 Q.9 Show the feasible egion unde the following constaints : + 4y 4,, y fueu O;ojks/kksa + 4y 4,, y dk lqla {ks=k n'kkzb;sa Q.1 Two cads ae dawn at andom and without eplacement fom a pack of 5 playing cads. Find the pobability that both the cads ae black. 5 iùkksa dh,d ìh esa ls ;kn`pn;k fcuk izflfkkfi fd;s ;s nks iùks fudkys,a nksuksa iùkksa ds dkys ja dk gksus dh izkf;dk Kk dhft,a [k.m & c SECTION B Q.11 If = sin 1 t a, y = cos 1 t a, show that dy y =. d Diffeentiate tan 1 ;fn = sin 1 t a, y = cos 1 t a 1 with espect to. gs] ks iznf'kz dhft, dy y =. d tan 1 1 dk ds lkis{k vodyu dhft,a Q.1 Evaluate : 1 d π sin Evaluate : d cos 1 π d dk eku Kk dhft,a sin d dk eku Kk dhft,a cos CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 4

5 cos sin Q.1 If F () = sin cos, then pove that F (). F (y) = F ( + y). 1 1 By using elementay opeations, find the invese of the mati A = cos sin ;fn F () = sin cos gs] ks fl) dhft, fd F (). F (y) = F ( + y). 1 1 izkjafhkd :ikuj.k ds iz;ks }kjk vko;wg A = 5 1 dk O;qRØe Kk dhft,a 1 Q.14 Solve the following diffeential equation : (1 + )dy + y d = cot d ;. fueu vody lehdj.k dks gy dhft, : (1 + )dy + y d = cot d ;. Q.15 Find the aea of the egion enclosed by the paabola = y, the line y = + and the -ais. ijoy; = y, js[kk y = +,oa -v{k ls f?kjs {ks=k dk {ks=kqy Kk dhft,a Q.16 Given two independent events A and B such that P(A) =., P(B) =.6. Find (i) P(A and B), (ii) P(A and not B). A vksj B nks Loa=k?kVuk, nh bz gas] tgk P(A) =., P(B) =.6 ks (i) P(A vksj B), (ii) P(A vksj B ugha) dk eku Kk dhft,a Q.17 Find the value of k so that the function is continuous at the point = 5. k + 1, f () = 5, if 5 if > 5 k dk eku Kk dhft, kfd iznùk Qyu = 5 ij l~ gks] f () = k + 1, ;fn 5, ;fn 5 > 5 CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 5

6 Q.18 Evaluate d 7 6. d 7 6 Kk dhft,a Q.19 An edge of a vaiable cube is inceasing at the ate of cm/second. How fast is the volume of the cube inceasing when the edge is 1 cm long?,d ifjozu'khy?ku dk fdukjk lseh@lsd.m dh nj ls c<+ jgk gsa?ku dk vk;u fdl nj ls c<+ jgk gs tcfd fdukjk 1 lseh yeck gs\ Q. Find the equations of the tangent and nomal to the paabola y = 4a at the point (at, at). ijoy; y = 4a ds fcunq (at, at) ij Li'kZ js[kk vksj vfhkyec ds lehdj.k Kk dhft,a π/ sin Q.1 Evaluate : d. cos π/ sin d dk eku Kk dhft,a cos y Q. Find the aea of the egion bounded by the ellipse + = y nh?kzo`ùk + = 1 ls f?kjs {ks=k dk {ks=kqy Kk dhft,a 16 9 Q. Minimize Z = + 5y subject to the constaints + y + y, y An aeoplane can cay a maimum of passenges. A pofit of Rs. 4 is made on each fist class ticket and a pofit of Rs. 6 is made on each economy class ticket. The ailine eseves at least seats fo fist class. Howeve, at least 4 times as many passenges pefe to tavel by economy class than by the fist class. Fomulate the linea pogamming poblem to maimize the pofit of the ailine. CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 6

7 fueufyf[k O;ojks/kksa ds vuz Z = + 5y dk U;wuehdj.k dhft, % + y + y, y,d gokbz tgkt vf/kde ;kf=k;ksa dks ;k=kk djk ldk gsa izr;sd izfke Js.kh ds fvdv ij 4 :- vksj llh Js.kh ds fvdv ij 6 :- dk ykhk dek;k tk ldk gsa,;jykbu de ls de lhvsa izfke Js.kh ds fy, vkjf{k djh gsa Fkkfi izfke Js.kh dh vis{kk de ls de 4 qus ;k=kh llh Js.kh ds fvdv ls ;k=kk djus dks ojh;k nss gsaa,;jykbu ds vf/kde ykhk ds fy, jsf[kd izkszkeu lel;k dk fu:i.k dhft,a Q.4 If a fai coin is tossed 1 times, find the pobability of eactly fou heads. ;fn,d fu"i{kikh fldds dks 1 ckj mnkyk ;k ks Bhd pkj fpùk vkus dh izkf;dk Kk dhft,a Q.5 If a = î + ĵ + kˆ, b = î + ĵ + kˆ and c = î + ĵ ae such that a + λb is pependicula to c, then find the value of λ. ;fn a = î + ĵ + kˆ, b = î + ĵ + kˆ vksj c = î + ĵ bl izdkj gsa fd a + λb, c ij yec gs] ks λ dk eku Kk dhft,a [k.m & l SECTION C Q.6 Pove that y y p py = (1 + pyz) ( y) (y z) (z ). z z pz Solve the following system of equations by mati method : y + z = 8 + y z = 1 4 y + z = 4 p fl) dhft, fd y y py = (1 + pyz) ( y) (y z) (z ). z z pz fueufyf[k lehdj.k fudk; y + z = 8 + y z = 1 4 y + z = 4 dks vko;wg fof/k ls gy dhft,a CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 7

8 1 sin Q.7 Evaluate : d 1 sin 1 1 d dk eku Kk dhft, : Q.8 Find the equation of the plane though the intesection of the planes y + z 4 = and + y + z = and the point (,, 1). ml ley dk lehdj.k Kk dhft, tks leyksa y + z 4 = vksj + y + z = ds izfpnsnu Fkk fcunq (,, 1) ls gksdj tkk gsa dy y Q.9 Solve the diffeential equation y + sin =. d Solve the diffeential equation yd ( + y ) dy =. dy y vody lehdj.k y + sin = dks gy dhft,a d vody lehdj.k yd ( + y ) dy = dks gy dhft,a Q. Evaluate : 1 d d dk eku Kk dhft,a CP Towe, Road No.1, IPIA, Kota (Raj.), Ph: Page # 8

xf.kr MATHEMATICS Ñi;k tk p dj ysa fd bl iz'u&i= esa eqfnzr iz'u 20 gsaa Please make sure that the printed question paper are contains 20 questions.

xf.kr MATHEMATICS Ñi;k tk p dj ysa fd bl iz'u&i= esa eqfnzr iz'u 20 gsaa Please make sure that the printed question paper are contains 20 questions. CLASS : th (Sr. Secondary) Code No. 6 Series : SS-M/08 Roll No. SET : C f.kr MATHEMATICS [ Hindi and English Medium ] ACADEMIC/OPEN (Only for Fresh/Re-appear Candidates) Time allowed : hours ] [ Maimum