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Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
fuEufyf[kr O;atdksa dks vkaf'kd fHkUukas esa O;Dr dhft,&
03½ ��� ����� 04½
��������� � 05½ �������
06½ ����� � 07½ � ������ 08½
������ 09½
������������� 10½ ����������� 11½
��������������
12½ ����������� 13½
������ ��� 14½ ��������� ���
15½ ���������� ���
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 002- Determinants (lkjf.kdlkjf.kdlkjf.kdlkjf.kd½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 003- Matrix (vkO;wgvkO;wgvkO;wgvkO;wg½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
¼v½ x + y + z = 6, x + 2y + 3z =14, x + 4y +9z = 36
¼c½ x + y + z = 5, 2x + y – z = 2, 2x – y + z = 2
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 004- Iverse Trigonometric Functions (izfrykse f=dks.kferh; Qyuizfrykse f=dks.kferh; Qyuizfrykse f=dks.kferh; Qyuizfrykse f=dks.kferh; Qyu½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
15½ fl) dhft, fd &¼v½ 2tan�� ab����� tan ∅ d = cos�� I� OPQ ∅��� OPQ ∅K ¼c½ tan�� e√������ f = � tan�� +
Practice Paper- 12- Maths- 005- Product of Vectors (lfn’lfn’lfn’lfn’kksa dk xq.kuQykksa dk xq.kuQykksa dk xq.kuQykksa dk xq.kuQy½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
15½ lfn’k fof/k ls fl) dhft, fd ¼dksbZ ,d½& ¼v½ cos(A - B) = cosA cosB + sinA sinB ¼c½ sin (α + β) = sin α cos β + cos α sin β ¼l½ ac cosB – bc cosA = a2 – b2 ¼n½ c2 = a2 + b2 – 2 ab cosC
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 006- Plane (lllleryeryeryery½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 007- Straight Line & Sphere (ljy js[kkljy js[kkljy js[kkljy js[kk vkSj xksykvkSj xksykvkSj xksykvkSj xksyk½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 008- Vector Form of Plane, Straight Line & Sphere
(lery] lery] lery] lery] ljy js[kk vkSj xksykljy js[kk vkSj xksykljy js[kk vkSj xksykljy js[kk vkSj xksyk dk lfn”dk lfn”dk lfn”dk lfn”k #ik #ik #ik #i½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each.
01½ ml lery dk lehdj.k Kkr djks tks ewy fcanq ls 7 bdkbZ nwjh ij gS rFkk lfn’k 4� + 2� − 3j� ij yac gSA
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 009- Differentiation (vodyuvodyuvodyuvodyu½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No. 11 to 15 are long answer type questions, carrying 5 marks each. (iv) solve any one in each of the questions.
fuEufyf[kr Qyuksa dk x ds lkis{k vodyu dhft,& (izR;sd esa dksbZ ,d)
01½ (i) ����� QRS �� (ii) ��. %&'+ (iii) ���� �OPQ � (iv) sin x2
02½ (i) cos x xos2x cos3x (ii) e log tanx (iii) e - logx (iv) tan�� b��8����8��� 03½ (i) �√OP� � (ii) %&'%&'%&'+ (iii) sin2 x2 (iv) %&'b���?G����?G��
04½ (i) logb�OPQ ����OPQ �� (ii) sin xo (iii) 2tan� (iv) sec�� ����� + sin�� �����
05½ (i) ���[�����[� (ii)
QRS ��OPQ � (iiii) √tan + (iv) %&'��sec +�
06½ ¼v½ ;fn ( = �√�� gks] rks x = 16 ij �(�� dk eku Kkr dhft,A
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 010-Applicatins of Differentiation (vodyu dvodyu dvodyu dvodyu ds vuqiz;ksxs vuqiz;ksxs vuqiz;ksxs vuqiz;ksx½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each.(iv)Solve any one in each of the questions 6 to 15.
01½ ,d d.k ,d ljy js[kk esa xfreku gSA d.k ds }kjk t lsd.M ess r; dh xbZ nwjh s ( ehVj esa ) laca/k
� = -�� + ��� ds }kjk nh tkrh gSA fl) dhft, fd le; t ij d.k dk Roj.k blds }kjk t le; esa r; dh
xbZ nwjh ds cjkcj gSA
02½ ,d d.k fu;r LFkku O ls 10 eh- nwjh ij Lkw= � = 1 + 16� − 2� ls xfreku gSA ;fn og O ls tkus okyh
js[kk esa xfreku gks] rks O ls mldh nwjh Kkr dhft, tc og foijhr fn”kk esa ykSVuk izkjaHk djsxkA
03½ ,d d.k fuEukafdr fu;e ls ljy js[kk esa xfreku gS& s = 5e–t cost tc t = π/2 gks] rks bldk osx o Roj.k
Practice Paper- 12- Maths- 011 - Indefinite Integration (vfuf’vfuf’vfuf’vfuf’pr lekdyupr lekdyupr lekdyupr lekdyu½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each.
(iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each.(iv)Solve any one in each of the questions 1 to 15.
fuEu dk x ds lkis{k lekdyu dhft,& ¼izR;sd esa ls dksbZ ,d½
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X Practice Paper- 12- Maths- 012 - Definite Integration (fuf’fuf’fuf’fuf’pr lekdyupr lekdyupr lekdyupr lekdyu½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each.
(iii) Qu. No.11to14 are long answer type questions, carrying 5 marks each.(iv)Solve any one in each of the questions 1 to 14.
01½ ¼i½ 2��+��� ¼ii ½ ����?G �L� ¼iii ½ √1 + sin + �+L ~� ¼iv½ + log + �+ � ¼v½ + tan�� + �+���
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 013 – App. Of Definite Integral (fuf”fuf”fuf”fuf”pr lekdypr lekdypr lekdypr lekdy ds vuqiz;ksxds vuqiz;ksxds vuqiz;ksxds vuqiz;ksx½½½½
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each.
(ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
14½ ml f=Hkqt dk {ks=Qy lekdyu }kjk Kkr dhft, ftldh Hkqtk,W y = 2x + 1, y = 3x + 1 rFkk x = 4 gSaA 15½ js[kk y = x rFkk odz y2 = 16x ds chp ds {ks= dk {ks=Qy Kkr dhft,A
vFkok
odz y2 = x vkSj x2 = y ds chp dk {ks=Qy Kkr dhft,A
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 014 – Differntial Equations (vody lehdj.kvody lehdj.kvody lehdj.kvody lehdj.k½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Coaching classes for- IIT, AIPMT, PET, PAT, PMT, PPT, XII, XI, X
Practice Paper- 12- Maths- 015 – Correlation & Regression (lg&llg&llg&llg&laca/k ,oa lekJ;.kaca/k ,oa lekJ;.kaca/k ,oa lekJ;.kaca/k ,oa lekJ;.k½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Practice Paper- 12- Maths- 016 –Probability (izkf;drkizkf;drkizkf;drkizkf;drk½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to15 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Practice Paper- 12- Maths- 017 – Statics (fLFkfrfLFkfrfLFkfrfLFkfr foKkufoKkufoKkufoKku½½½½ Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to14 are long answer type questions, carrying 5 marks each.
-&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 01½ ,d fcanq ij fdz;k dj jgs cy P vkSj Q dk ifjekeh cy R gSA ;fn P = 8, Q = 15 vkSj R = 17 gks] rks P vkSj Q ds e/; dks.k Kkr dhft,A 02½ ,d d.k ij fdz;k djrs gq, rhu cy larqyu esa gSaA igys nks ds chp dk dks.k 900 gS vkSj nwljs rFkk rhljs ds chp dk dks.k 1200 gSA cyksa dk vuqikr Kkr dhft,A 03½ cy 20N ds ?kVd cy Kkr dhft, tks mlls foijhr fn”kkvksa esa 300 vkSj 600 ds dks.k cukrs gSA 04½ ,d gh lery ij fdz;k”khy rhu cy F1, F2 vkSj F3 larqyu esa gSA ;fn F1 cy F2 vkSj F3 ls dze”k% 1200 vkSj 900 ds dks.k cukrs gS] rks cyksa ds ifj.kkeksa es vuqikr Kkr dhft,A 05½ nks cyksa P vkSj Q dk ifj.kkeh R cy P ds lkFk ledks.k cukrs gS rks fl) dhft, fd R2 + P2 = Q2 06½ nks cyksa P vkSj Q dk ifj.kkeh P dh fn”kk ls ledks.k cukrs gq, dk;Z djrk gSA fl) dhft, fd cyksa ds
chp dk dks.k cos�� I�¶· K gksxkA 07½ 12 N vkSj 14 N ds nks cy ,d nwljs ls 450 ds dks.k ij fdz;k”khy gSa] cyksa dk ifj.kkeh rFkk ifj.kkeh dh fn'kk Kkr dhft,A
08½ dks.k θ ij fdz;k dj jgs nks cy P vkSj Q dk ifj.kkeh cy �2� + 1��¸ + ¹ ds cjkcj gSA tc cy xU 2~ − Dy dks.k ij fdz;k djrs gSa] rks ifj.kkeh cy �2� − 1�√¸2 + ¹2 ds cjkcj gksrk gS] fl) djks fd
tan D = � − 1� + 1 09½ tc nks cjkcj cy 2θ dks.k ij fdz;k djrs gS rks ifj.kkeh cy 2R gS vkSj tc 2φ dks.k ij fdz;k djrs gSa rks mudk ifj.kkeh cy R gSA fl) dhft, fd cos θ = 2 cos φ
10½ fdlh cy F dks nks Hkkxksa ess fo;ksftr fd;k x;k gSA muesa ls ,d fo;ksftr Hkkx cy F ij yac vkSj ifjek.k esa mlds cjkcj gks] rks nwljs fo;ksftr Hkkx dh fn”kk rFkk ifjek.k Kkr dhft,A
vFkok 70 fdyksxzke dk ,d fi.M dze”k% 6 ehVj vkSj 8 ehVj yach nks Mksfj;ksa }kjk ,d {kSfrt js[kk }kjk ,d {kSfrt js[kk esa 10 ehVj dh nwjh ij nks fcanqvksa ls yVdk gqvk gSA Mksfj;ksa esa ruko Kkr dhft,A
11½ nks P vkSj Q dk ifj.kkeh R gS rFkk muds chp dk dks.k α gSA ;fn P dks nqxquk dj fn;k tk;s rks ifj.kkeh
vFkok ,d fcanq ij fdz;k dj jgs rhu cy P, Q, R larqyu esa gSaA P vkSj Q ds chp dk dks.k P vkSj R ds chp ds dks.k ls nqxquk gSA fl) dhft, fd R2 = Q (Q – P)
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to14 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
01½ 60 ehVj ÅWph ehukj ds f”k[kj ls ,d fi.M 20 eh@ls- ds osx ls Åij dh vksj Qsadk tkrk gSA ;fn g = 10 m/s2 gks] rks tehu ij fdl le; fxjsxk\ 02½ ,d fi.M dks ÅWph ehukj ls i`Foh rd fxjus esa 2 lsd.M dk le; yxrk gSA ehukj dh ÅWPkkbZ Kkr dhft,A ( g = 10m/s2)
03½ nks iRFkj nks fofHkUu ÅWpkb;ksa ls fxjk, tkrs gSaA ;fn budh ÅWpkb;ksa esa vuqikr h1 : h2 gks rks fl) dhft, fd iRFkjksa ds tehu rd igWqpus esa fy;s x;s le; dk vuqikr √h1 :√ h2 gSA 04½ ,d fdzdsV f[kykM+h xsan dks 100 ehVj dh nwjh ij Qsad ldrk gSA ogh f[kykM+h mlh xsan dks fdruh ÅWpkbZ rd Qsad ldrk gSA 05½ nks d.k {kSfrt ls 300 rFkk 600 dk dks.k cukrh gqbZ fn”kkvksa esa izf{kIr fd, x,A ;fn os ,dleku ÅWpkb;ksa rd igqWprs gksa rks fn[kkb, fd muds iz{ksi oxs √3 % 1 ds vuqikr esa gSaA 06½ ,d euq"; ,d unh dks ikj dj] nwljs fdukjs ds Bhd lEeq[k fcanq ij igqWpuk pkgrk gSA ;fn og viuh uko dks /kkjk ds osx ls √2 xqus osx ls pykrk gS] rks Kkr dhft, fd mls uko dks /kkjk ds lkFk fdruk dks.k cukrs gq, j[kuk pkfg,\ 07½ ;fn x, x,y, z ,d xfreku d.k }kjk dze”k% poas] qosa] rFkk rosa lsdaM esa r; dh xbZ nwfj;kW gksa] rks fl) dhft, fd x(q – r) + y(r – p) + z(p – q) = 0 08½ ,d Vªsu tks ijLij 4 fdeh dh nwjh ij fLFkr nks LV”kuksa ij #drh gS] ,d LVs”ku ls nwljs rd dh ;k=k esa 4 feuV dk le; ysrh gSA ;g ekurs gq, fd Vªsu igys Roj.k x ls vkSj fQj eanu y ls ( nksuksa ,dleku ) xfr djrh gS] fl) dhft, fd �� + �* = 2 09½ ,d d.k 300 ds mRFkku ij 49 eh@ls- ds osx ls izf{kIr fd;k tkrk gSA Kkr dhft,& (i) mÏ;u dky (ii) {kSfrt ijkl (iii) egRre ÅWpkbZA (iv) egRre ÅWpkbZ rd igqpus esa yxk le;A 10½ fl) dhft, fd] ;fn {kSfrt ijkl R ij ,d xksyh dk mÏ;u dky T lsdaM gks] rks {kSfrt ls mldh fn”kk
dk >qdko tan�� I�»� ¼ K gksxkA 11½ ,d d.k osx u ls bl izdkj Qsadk tkrk gS fd mldh {kSfrt ijkl mldh egRre ÅWpkbZ dh nqxquh gSA
fl) dhft, fd ijkl �½��� gSA
12½ /kjkry ls ,d xsan bl izdkj Qsadh tkrh gS fd og x ehVj nwj fLFkr ,d nhokj dks Bhd ikj dj tkrh gS rFkk og nhokj ds ikn ls y ehVj dh nwjh ij fxjrh gSA ;fn iz{ksi dks.k 450 gks rks fl) dhft, fd nhokj
dh ÅWPkkbZ �*�* ehVj gSA
13½ nks fi.M ,d gh fcanq ls {kSfrt ls º� rFkk º dks.k cukrh fn’kkvksa esa izf{kIr fd, tkrs gSa vkSj {kSfrt /kjkry ds ,d gh fcanq ij vk?kkr djrs gSaA ;fn t1 rFkk t2 muds mÏ;u dky gksa] rks fl) dhft, fd & �� − � �� + � = sin�º� − º �sin�º� + º � 14½ ,d d.k 24 eh@ls- ds izkajfHkd osx ls pyuk izkjaHk djrk gSA ;fn og ,d ljy js[kk esa 2 eh@ls2 ds ,dleku Roj.k ls pyrk gS] rks Kkr dhft,& (i) 5 lsd.M ckn d.k dk osx (ii) 4 lsd.M ds d.k }kjk pyh nwjh (iii) d.k dk osx tc og 81 ehVj dh nwjh r; dj pqdk gksA (iv) 7 osa lsd.M es d.k }kjk pyh nwjh
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to14 are long answer type questions, carrying 5 marks each. -&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 01½ cwyh; chtxf.kr ls lacaf/kr }Srrk dk fl)kar fyf[k,A
Note- (i) Qu. No. 1 to 5 are very short answer type questions, carrying 2 marks each. (ii) Qu. No. 6 to 10 are short answer type questions, carrying 4 marks each. (iii) Qu. No.11to14 are long answer type questions, carrying 5 marks each.