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.

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1 CLASS : th (Sr. Secondary) Code No. 0 Series : SS-M/07 Roll No. SET : A f.kr MATHEMATICS [ Hindi and English Medium ] ACADEMIC/OPEN (Only for Fresh Candidates) (Evening Session) Time allowed : hours ] [ Maimum Marks : 80 Ñi;k tk p dj ysa fd bl iz'u&i= esa eqfnzr iz'u 0 gsaa GRAPH Please make sure that the printed question paper are contains 0 questions. iz'u&i= esa nkfgus gkfk dh vksj fn;s ;s dksm uecj rfkk lsv dks Nk= mùkj&iqflrdk ds eq[;&i`"b ij fy[ksaa The Code No. and Set on the right side of the question paper should be written by the candidate on the front page of the answer-book. Ñi;k iz'u dk mùkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ksaa Before beginning to answer a question, its Serial Number must be written. mùkj&iqflrdk ds chp esa [kkyh iuuk@iuus u NksMsa+A Don t leave blank page/pages in your answer-book. mùkj&iqflrdk ds vfrfjdr dksbz vu; 'khv ugha feysha vr% vko';drkuqlkj gh fy[ksa vksj fy[kk mùkj u dkvsaa Ecept answer-book, no etra sheet will be given. Write to the point and do not strike the written answer. ijh{kkfkhz viuk jksy ua0 iz'u&i= ij vo'; fy[ksaa Candidates must write their Roll Number on the question paper. d`i;k iz'uksa dk mùkj nsus ls iwoz ;g lqfuf'pr dj ysa fd iz'u&i= iw.kz o lgh gs] ijh{kk ds mijkur bl lecu/k esa dksbz Hkh nkok Lohdkj ugha fd;k tk;ska 0/ (Set : A) P. T. O.

2 0/ (Set : A) ( ) 0/ (Set : A) Before answering the question, ensure that you have been supplied the correct and complete question paper, no claim in this regard, will be entertained after eamination. lkeku; funsz'k % (i) bl iz'u-i= esa 0 iz'u gsa] tks fd pkj [k.mksa % v] c] l vksj n esa ck Vs, gsa % [k.m ^v* % bl [k.m esa,d ç'u gs tks cgqfodyih; çdkj ds 6 (i-vi) Hkkksa esa gsa izr;sd Hkk vad dk gsa [k.m ^c* % bl [k.m esa ls rd dqy nl ç'u gsaa çr;sd ç'u vadksa dk gsa [k.m ^l* % bl [k.m esa ls 6 rd dqy ik p ç'u gsaa çr;sd ç'u 4 vadksa dk gsa [k.m ^n* % bl [k.m esa 7 ls 0 rd dqy pkj ç'u gsaa çr;sd ç'u 6 vadksa dk gsa (ii) lhkh ç'u vfuok;z gsaa (iii) [k.m ^n* ds dqn ç'uksa esa vkarfjd fodyi fn;s ;s gsa] muesa ls,d gh iz'u dks pquuk gsa (iv) fn;s ;s zkq-isij dks viuh mùkj-iqflrdk ds lkfk vo'; urfkh djsaa (v) zkq-isij ij viuh mùkj-iqflrdk dk Øekad vo'; fy[ksaa (vi) dsyd;qysvj ds ç;ks dh vuqefr ugha gsa General Instructions : (i) This question paper consists of 0 questions which are divided into four Sections : A, B, C and D : Section 'A' : This Section consists of one question which is divided into 6 (i-vi) parts of multiple choice type. Each part carry mark. Section 'B' : This Section consists of ten questions from to. Each question carries marks. Section 'C' : This Section consists of five questions from to 6. Each question carries 4 marks. Section 'D' : This Section consists of four questions from 7 to 0. Each question carries 6 marks. (ii) All questions are compulsory. (iii) Section 'D' contains some questions where internal choice have been provided. Choose one of them.

3 ( ) 0/ (Set : A) (iv) You must attach the given graph-paper along with your answer-book. (v) You must write your Answer-book Serial No. on the graph-paper. (vi) Use of Calculator is not permitted. [k.m v SECTION A. (i) eku yhft, fd f : R R, f() = 4 }kjk ifjhkkf"kr gs] lgh mùkj dk p;u dhft, % f,dsdh vkpnknd gs f cgq,d vkpnknd gs f,dsdh gs] fdurq vkpnknd ugha gs (D) f u rks,dsdh gs] vksj u gh vkpnknd gs Let f : R R be defined as f() = 4, choose the correct answer : f is one-one onto f is many-one onto f is one-one but not onto (D) f is neither one-one nor onto dk eku gs % (ii) tan ( ) sec ( ) (D) tan ( ) sec ( ) is equal to : (D) 0/ (Set : A) P. T. O.

4 (iii) ;fn vko;wg + 7 y = y ( 4 ) 0/ (Set : A) gks] rks vksj y ds eku gsa % =, y = 7 =, y = =, y = 7 (D) =, y = + 7 y If the matrices =, then the values of y an are : =, y = 7 =, y = =, y = 7 (D) =, y = (iv) ;fn A, dksfv dk O;qRØe.kh; oz vko;wg gs] rks adj A dk eku gs % (v) A A A (D) A Let A be a non-singular square matri of order. Then adj A is : A A A (D) A ;fn Qyu f ;fn (, = ij larr gks] rks k dk eku gs % ;fn > k +, ) = cos, (D) buesa ls dksbz ugha k +, if If the function f ( ) = is continuous at =, cos, if > then the value of k is : 0/ (Set : A)

5 ( ) 0/ (Set : A) (D) None of these (vi) o`ùk ds {ks=qy ds ifjorzu dh nj] bldh f=t;k r ds lkis{k r = ij gs % 0 8 (D) The rate of change of the area of a circle with respect to its radius r at r = is : 0 8 (D) (vii) oø y = + ij og fcunq gs] ftl ij Li'kZ js[kk y = gs % (, 0) (, 7) (0, ) (D) (, 9) The point on the curve y = + at which the tangent is y =, is : (, 0) (, 7) (0, ) (D) (, 9) (viii) 6 + d tan + c tan + c sin + c (D) buesa ls dksbz ugha 6 + d is equal to : tan + c (i) sin 0 dk eku gs % tan 0/ (Set : A) P. T. O. + c sin + c (D) None of these d dk eku gs %

6 (D) 0 sin d is equal to : (D) ( 6 ) 0/ (Set : A) () fueufyf[kr lehdj.kksa esa ls fdl lehdj.k dk O;kid gy y = c e + ce gs % + = 0 d y = 0 d = 0 d (D) + y = 0 d Which of the following differential equation has y the general solution? + = 0 d y = 0 d = 0 d (D) + y = 0 d = c e + c (i) vody lehdj.k e dy + ( ye + ) d = 0dk O;kid gy gs % e as ye + = c e = c + e y + y = c (D) ye y = c + 0/ (Set : A)

7 ( 7 ) 0/ (Set : A) The general solution of the differential equation e dy + ( ye + ) d = 0 is : (ii) lfn'k ye + = c e = c + e y + y = c (D) ye y = c a = iˆ + ˆj + kˆ dk lfn'k + b = i ˆ + ˆj + kˆ ij iz{ksi gs % 6 6 (D) 6 The projection of vector a = iˆ + ˆj + kˆ on b = i ˆ + ˆj + kˆ is : 6 6 (iii) js[kkvksa (D) 6 + y z + = = 4 rfkk + y 4 = dks.k gs % 8 cos cos 8 (D) cos cos 7 8 Angle between the pair of lines + y 4 = = z is : = z ds ;qxe ds chp dk + y z + = = 4 and 0/ (Set : A) P. T. O.

8 8 cos cos 8 (D) ( 8 ) 0/ (Set : A) cos cos (iv) ;fn iklksa dk,d tksm+k mnkyk tkrk gs] rks izr;sd ikls ij le vhkkt; la[;k izkir djus dh izkf;drk gs % (D) The probability of obtaining an even prime number on each die, when a pair of dice is rolled is : 6 0 (D) (v) ;fn,d U;k ; fldds dks 0 ckj mnkyk ;k gks] rks Bhd N% fpr izkir djus dh izkf;drk gs % (D) buesa ls dksbz ugha If a fair coin is tossed ten times, the probability of getting eactly si heads is : (D) None of these 0/ (Set : A)

9 (vi) ;fn P =, P = 0 gks] rks P(A/B) gs % ( 9 ) 0/ (Set : A) 0 (D) ifjhkkf"kr ugha If P =, P = 0, then P(A/B) is : 0 (D) Not defined [k.m c SECTION B. ;fn Qyu f : R R, f() = 4 + }kjk iznùk gks] rks fn[kkb, fd f O;qRØe.kh; gs vksj f dk izfrykse Kkr dhft,a Let f : R R, given by f() = 4 +. Show that f is invertible and find the inverse of f.. fln~/k dhft, % Prove that : 6 sin sin = tan = tan 4. vko;wg A = ds fy, lr;kfir dhft, fd A + A',d lefer vko;wg gsa / (Set : A) P. T. O.

10 . ( 0 ) 0/ (Set : A) For the matri A =, verify that A + A' is a symmetric matri sin α cos α sin α 0 sinβ cos α sinβ 0 dk eku Kkr dhft,a Evaluate : 0 sin α cos α sin α 0 sinβ cos α sinβ 0 dk eku fudkfy,a d Find + + d 7. eku Kkr dhft, sin 4 cos d Evaluate : sin cos 4 d 8. y-v{k dks ewy fcunq ij Li'kZ djus okys o`ùkksa ds dqy dk vody lehdj.k Kkr dhft,a Find the differential equation of the family of circles touching the y-ais at the origin. 9. ;fn y = A sin + B cos gks] rks fln~/k dhft, fd + y = 0 d d y gsa If y = Asin + B cos, then prove that +y = 0. d 0. sin dk e cos ds lkis{k vodyu Kkr dhft,a Differentiate sin w.r.t. e cos. 0/ (Set : A)

11 ( ) 0/ (Set : A).,d vufhkur (unbiased) ikls dks nks ckj mnkyk ;ka eku ysa A?kVuk ^igyh mnky ij fo"ke la[;k izkir gksuk* vksj B?kVuk ^f}rh; mnky ij fo"ke la[;k izkir gksuk* n'kkzrs gsaa?kvukvksa A vksj B ds Lokra ; dk ijh{k.k dhft,a An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B be the event 'odd number on the second throw'. Check the independence of the events A and B. [k.m l SECTION C. fn[kkb, fd sin + cos + tan = gsa Show that sin + cos 4 + tan 6 6 =. log. ) (log + dk ds lkis{k vodyu dhft,a 4 Differentiate log (log ) + w.r.t.. 4. og vurjky Kkr dhft, ftlesa f ( ) = sin + cos, 0 }kjk iznùk Qyu f fujurj o/kzeku ;k fujurj Ðkleku gsa 4 Find the interval in which the function f given by f ( ) = sin + cos, 0 is strictly increasing or strictly decreasing..,d fu'kkusckt ds y{;-hksnu dh izkf;drk gsa og de ls de fdruh ckj ksyh pyk, fd 4 y{; dks de ls de,d ckj Hksnus dh izkf;drk 0.99 ls vf/kd gks \ 4 The probability of a shooter hitting a target is 4. How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99? 0/ (Set : A) P. T. O.

12 ( ) 0/ (Set : A) 6. lfn'k i ˆ + ˆj + kˆ dk lfn'kksa iˆ + 4ˆj kˆ vksj λ i ˆ + ˆj + kˆ ds ;ksqy dh fn'kk esa] ek=d lfn'k ds lkfk vfn'k q.kuqy,d ds cjkcj gs] rks λ dk eku Kkr dhft,a 4 The scalar product of the vector i ˆ + ˆj + kˆ with a unit vector along the sum of vectors iˆ + 4ˆj kˆ and λ i ˆ + ˆj + kˆ is equal to one, find the value of λ. 0/ (Set : A) [k.m n SECTION D 7. fueu lehdj.k fudk;ksa dks vko;wg fof/k }kjk gy dhft, % 6 y + z + 4y z y + z = 7 = = Solve the system of equations by matri method : y + z + 4y z y + z = 7 = = 8. -v{k ds Åij rfkk o`ùk + y = 8,oe~ ijoy; y = 4 ds e/;orhz {ks= dk {ks=qy Kkr dhft,a 6 Find the area lying above -ais and included between the circle + y = 8 and the parabola y = 4. vfkok OR js[kk y = +, -v{k,oe~ dksfv;ksa = rfkk = ls f?kjs {ks= dk {ks=qy Kkr dhft,a

13 ( ) 0/ (Set : A) Find the area of the region bounded by the line y = + and the ordinates = and =. ˆ ˆ ˆ) 9. leryksa r.( i + j + k = 6 vksj r.( i + j + 4kˆ) = ds izfrpnsnu rfkk fcunq (,, ) ls tkus okys lery dk lfn'k lehdj.k Kkr dhft,a 6 ˆ ˆ Find the vector equation of the plane passing through the intersection of the planes r.( iˆ + ˆj + kˆ) = 6 and r.( ˆ i + ˆj + 4kˆ) = and the point (,, ). vfkok OR js[kkvksa r = ( iˆ + ˆj + kˆ) + λ(ˆ i ˆj + kˆ ) rfkk r ( ˆ i ˆj kˆ ) U;wure nwjh Kkr dhft,a = µ ( ˆ i + ˆj + kˆ ) + ds chp Find the shortest distance between the lines : r = ( iˆ + ˆj + kˆ) + λ(ˆ i ˆj + kˆ) and r = ( ˆ i ˆj kˆ ) + µ ( ˆ i + ˆj + kˆ ). 0. vkys[kh; fof/k }kjk fueu jsf[kd-lehdj.kksa dks gy dhft, % 6 fueu O;ojks/kksa ds vurzr + y 60 + y 0 y 0, y 0 z + 9y = dk U;wure vksj vf/kdre eku Kkr dhft,a Solve the following linear programming graphically : 0/ (Set : A) P. T. O.

14 Minimize and maimize + y 60 ( 4 ) 0/ (Set : A) z = + 9y subject to the constraints + y 0 y 0, y 0 0/ (Set : A)

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