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Revised & Latest NCERT Exemplar (Latest Edition) Problems with Solutions An exceptionally useful Question Bank for School Examinations as well as Engineering & Medical Entrance Examinations

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izLrkouk lEiw.kZ ns'k esa le:i f'k{kk O;oLFkk ykxw djus ds Øe esa] vusd jkT;&cksMks± us jk"Vªh; 'kSf{kd vuqla/kku rFkk izf'k{k.k ifj"kn~ (NCERT) ds lg;ksx ls le:i (,d leku) ikB~;Øe dks ykxw fd;k gSA ek/;fed rFkk mPprj ek/;fed d{kkvksa ds fo|kfFkZ;ksa ds fy, xgu v/;;u rFkk fo"k; ds Li"V Kku dks lqfuf'pr djus ds fy,] n fMikVZesaV vkWQ ,twds'ku bu lkbal ,.M eSFkesfVDl (DESM) rFkk ,u-lh-bZ-vkj-Vh- (NCERT) us d{kk VI ls XII rd foKku rFkk xf.kr fo"k;ksa esa ,XtsEIyj izkWCyEl rS;kj fd;k gSA ,XtsEIyj izkWCyEl esa fofHkUu izdkj ds rFkk fofHkUu dfBukbZ ds Lrjksa ds iz'uksa dks ladfyr fd;k x;k gS tks ijh{kk dh mRre rS;kjh es lgk;d gksrs gSaA ;s iqLrdsa u dsoy cksMZ ijh{kkvksa dh rS;kjh dj jgs fo|kfFkZ;ksa dh leL;kvksa dks /;ku esa j[kdj rS;kj dh xbZ gaS vfirq IITJEE, NEET, AIIMS vkfn dh izos'k ijh{kkvksa dh rS;kjh esa Hkh lgk;d fl¼ gksaxhA vksloky cqDl us vkids fy, NCERT ,XtsEIyj ikB~;iqLrdksa ds uohure vad ds izR;sd iz'u dk gy rS;kj fd;k gSA gekjk fo'okl gS fd vksloky NCERT ,XtsEIyj lkWY;w'ku fo|kfFkZ;ksa dks fdlh Hkh ijh{kk esa ljyrk vkSj fo'okl ds lkFk lQyrk fnykus esa lgk;d gksaxh D;ksafd geus bu iqLrdksa esa fo|kfFkZ;ksa dks vR;f/kd Hkjkslsean v/;;u&lkexzh iznku dh gSA vksloky NCERT ,XtsEIyj lWkY;w'ku ds dqN fo'ks"k fcanq gSa% z z z z z z z z

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(5)

POSITIVE AFFIRMATIONS “Affirmations are like a seed planted in soil. Poor soil, poor growth. Rich soil, abundant growth. The more you choose to think thoughts that make you feel good, the quicker the affirmations work.”

- Louise Hay

I am confident.

I am strong.

I am joyful.

I love who I am.

I can achieve my goals.

I care about others.

I am compassionate.

I make good decisions.

I am important.

I am responsible.

I am diligent.

I am a leader.

I am thoughtful.

I like myself. It’s going to be a great day.

I believe in my dreams.

I am talented.

I learn from my mistakes.

I am brave.

I am loved.

I make friends easily.

I choose a positive attitude.

I am generous.

I am enough.

I accept and love myself.

I am worthy. I am open to new experiences.

I am great just the way I am.

I am unique.

I am beautiful.

I work hard.

I am wonderfully made.

I am deserving of good things.

I radiate joy and love.

I am creative.

I am grateful.

I am honest.

Good things happen to me.

I believe in me.

I am patient.

I am loving.

I help my family.

I am kind.

I respect myself and I respect others.

Our mind starts believing what we repeatedly think or say. We, at Oswaal Books, resonate with this belief. So, we want all our readers to create their own positive affirmations! A positive affirmation is something spoken aloud that you want to believe or want to be true. Repeating positive affirmations daily can help shift your internal dialogue from negative to positive. So let’s get started! (6)

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izOk`Gfr ds ewyHkwr cy

eq[; fo"k;

fpjlEer HkkSfrdh LFkwy ?kVuk ls lacf/kr gS vkSj blesa ;kaf=dh] bysDV™ksMk;usel] izdkf'kdh vkSj iz; k stu rFk k m Ÿ k stu k ≈"ekizoSfxdh tSls fo"k; 'kkfey gSaA DokaVe HkkSfrdh ijek.kqvksa] v.kqvksa vkSj ukfHkd ds lw{kre iSekus ij lw{e ?kVuk ls lcaf/kr gSA

H k k Sf rd h d k

izkSn~;ksfxdh ubZ HkkSfrdh dks tUe nsrh gS] blh izdkj HkkSfrdh ubZ rduhdksa dks tUe nsrh gSA

detksj cy dh cgqr NksVh lhek (10–16 eh- ) xq#Rokd"kZ.k cy ds leku detksj ugha gS ysfdu etcwr ukfHkdh; cy vkSj fo|qr pqacdh; cyksa dh rqyuk esa cgqr detksj

vius ?kVd ds xq.kksa ls cM+h vkSj vf/kd tfVy iz.kkyh ds xq.kksa dks ljy Hkkxksa esa izkIr djukA

izd`fr ds ewy fu;eksa dk v/;;u vkSj fofHkUUk izkd`frd ?kVukvksa dh vfHkO;fDr

xq# R ok d"kZ. k cy

cgqr NksVh lhek] 'kfDr'kkyh cy izOk`Gfr esa vkd"kZ.k lhek&10&15ehlHkh ewyHkwr cyksa ds chp lcls 'kfDr'kkyh

vo/kkj.kkvksa vkSj fu;eksa ds lanHkZ esa fofo/k HkkSfrd ?kVukvksa dh O;k[;k djukA

O;ofLFkr voyksdu] fu;af=r iz;ksx] xq.kkRed vkSj ek=kRed rdZ] xf.krh; izfr:i.k] iwoZ lwpukvksa vkSj flkrksa dk lR;kiu ;k feF;kdj.k

fdlh Hkh fo"k; dks foKku dgk tkrk gS tc mls vuqÿe izfr:i ds vk/kkj ij v/;;u fd;k tkrk gSA ge vius vkl&ikl tks ns[krs gS] mldk iz;ksx] [kkst vkSj Hkfo";ok.kh djrs gSaA

fdUgha nks fi.Mkas ds chp muds nzO;ekuksa ds dkj.k yxus okyk vkdZ"k.k cy cM+s iSekus ij egRoiw.kZ Hkwfedk fuHkkrk gSA cz·akM dh ?kVuk,°] tSls fd flrkjksa vkSj vkdk'kxaxkvksa vkSj vkdk'kxaXkk lewgksa dk cuuk rFkk fodkl xq#Rokd"kZ.k cy ds n~okjk gksrk gSA

vkosf'kr d.kksa ds chp cy vkd"kZ.k rFkk izfrdkjd cy nksuksa ;g fdlh Hkh fuf'pr nwjh ds fy, nks izksVkWu ds chp xq#Rokd"kZ.k cy ls 1036 xquk vf/kd 'kfDr'kkyh gksrk gSA

v/;k; & 1 HkkSfrd txr

ekbaM eSi | 9

mean

a1

δa

n

a2

a mean 100 amean

izfr'kr =qfV

amean

n

...

an

a1 + a2 + ...... + an

amean amean

lkis{k =qfV

a

an = an – amean

fujis{k =qfV

Z=

A

izd k j

B

,d fuf'pr varjjk"V™h; Lrj ij Lohd`r lanHkZ ekud dks ek=d dgk tkrk gSA lanHkZ ekud dks HkkSfrd jkf'k;ksa dks ekius ds fy, Á;ksx fd;k tkrk gSA

Z Z

A A

If Z=A/B B B

=qfV dk la;kstu

ekih xbZ ek=k ds ladYi dh lhek

xq.k

O;qRi Uu bd kbZ

Z Z

If

p

A A

q

B B

r

Z A p B q / Cr C C

ekSfyd rFkk O;qRiUu ek=dksa dk lewg CGS&lsaVhehVj] xzke] lsdaM FPS&QqV] ikmaM] lsdaM MKS&ehVj] fdyksxzke] lsdaM S.I&varjjk"V™h; iºfr (varjkZ"V™h; Lrj ij LohOk`Gr)

lkoZHkkSfed LohOk`Gfr xSj fouk'k'khy vPNh rjg ls ifjHkkf"kr le; ds lkFk ugha cnyrk gSA

lery dks.k rFkk Bksl dks.k jkf'k;ksa ds ek=d jsfM;u rFkk LVsjsfM;u gSaA

m/s, m/s2

tks ek=d ewyHkwr ek=d ls O;qRiUu gksrs gSa O;qRiUu ek=d dgykrs gSaA HkkSfrd jkf'k;k° tSls xfr] Roj.k O;qRiUu ek=d j[krs gSa tSls

nzO;eku] yackbZ] le;] rki] fo|qr /kkjk] nhfIr rhozrk] vkSj inkFkZ dh ek=k ds ewyHkwr ek=d ÿe'k% fdyksxzke] ehVj] lsdaM] dsfYou] ,sfEi;j] dsaMyk vkSj eksy gSaA

lR; eku dh ekis x, eku dh utnhdh

;FkkFkZr k

=qfV=lR; eku – ekik x;k eku

ekiu

i f j'kqn~/k rk

ek=d vkSj ekiu

izdkj

lw= tks fn[kkrk gS fd dSls vkSj dkSu lh vk/kkj jkf'k;k° HkkSfrd jkf'k;ks dh foekvksa dks n'kkZrh gS] vk;ke lw= dgykrh gSA mnkgj.k cy = MLT –2

ek=d xq.kk ;k Hkkx

lHkh xSj&'kwU; vad nks xSj&'kwU; vadks ds chp lHkh 'kwU; ;fn la[;k 1 ls de gS rks n'keyo fcanq ds nkbZ a vksj 'kwU; gksrk gS ysfdu xSj&'kwU; vadksa ds ckbZ a vksj n'keyo egRoiw.kZ ugha gksrk gSA n'keyo fcanq ds fcuk la[;k esa VfeZuy ;k vuqxkeh 'kwU; egRoiw.kZ ugha gSa tSls ln 020342-010 es ;gka 20342-01 egRoiw.kZ gSaA

v/;k; & 2 ek=d vkSj ekiu

10 | Oswaal NCERT Exemplar Problems-Solutions, HkkSfrd foKku] Class-XI

r

at v = v+ 0

A

r vAB r vBn

B

r r vA vB rA r vB vA

n-1)

e q‰ :i

v k Sl r

ls fxj

R oj. k

uk

sf{ vk i

sx kd o

osx ds ifjorZ u r r dh nj a vt

ljy js[kk esa xfr

vavg

r

x t

dqy foLFkkiu dqy fy;k x;k le;

nh xbZ fn'kk esa le; ds lkFk fdlh oLrq dh fLFkfr ds ifjorZu dh njA lfn'k jkf'k

x f r ek u o L rq oj. k l s R u k e aË k h l e h d j . k , dl rd h lac f x 'k qº dk

foijhr fn'kk eas ;g vUrj gksxk leku fn'kk eas ;g ;ksx gksxkA

(ii)

(i)

a (iv) xnth = v0+ 2

2 2 (iii) v = v0 + 2ax

(ii) x = v0t + at

(i)

2

i`Foh ds xq#Rokd"kZ.k ds dkj.k fxjus okyh oLrq (g= 9.8m/s ) ol ok;q ÁfrjksËk dh mis{kk djus ij] ;g ,d leku Roj.k ds lkFk ,d xfr dh fLFkfr gS A tSls lsc ,d isM+ ls fxjrk gSA

v t

osx eas dqy ifjorZu dqy le;kUrjky r

Roj.k

aavg

osx

Ádkj

t

0

lim

r

dv dt

f o L F k k iu

r

vinst

r0 dx dt t

lim

r x t

v 1t 1 v2 t2 ..... vn tn t 1 t 2 ..... t n

tc oLrq vyx&vyx le; ds varjky esa vyx&vyx xfr ls nwjh r; djrh gSA

S1 + S2 + S3+....Sn t1 + t2 + t3+....tn

tc oLrq vyx&vyx xfr ls vyx&vyx nwjh r; djrh gSA

;g vfn'k jkf'k gSA

fdlh fiaM }kjk r; fd, x, iFk dh dqy yEckbZ dks bldh nwjh dgk tkrk gSA

tc le; ds lacaËk esa osx dh fn'kk dk ifjek.k cny tkrk gSA

leku le; ij leku nwjh r; dh tkrh gSA

r v t

r; dh x;h nwjh @ yxk;k x;k le;A vfn'k jkf'k

pky

n wj h

vlek u xfr

a inst

r

v/;k; & 3 ljy js[kk esa xfr

ekbaM eSi | 11

r A

A

{kSfrt lhek

vf/kdre

2

,R = u sin2θ g

mM+ku dk dqy le;

→ R → P

Á { k si d

le ry es x fr

lery esa xfr

→ P

→ R

prqHkqZt dk fu;e

s iFk d k l e h d j

.k

y=(u sinθ) t - 1 gt 2

x=(ucosθ)t;

le

;t

2

ds i '

fdlh fiaM dh Qsads tkus ;k Á{ksfir fd, tkus ds ckn ≈apkbZ ij xfr

l fn'k d s Ád k j

→ → → R=P+Q → → Q Q

f=Hkqt dk fu;e

g 2 y=x tanθ– x 2u2cos2

bZ l fn' k

leku lfn'k

bd k

Tf = 2u sinθ g ≈°pkbZ ,Hmax = u2sin2θ 2g

osDVj leku fcUnq ls ÁkjEHk gksrs gSa

osDVj ftudh ifjek.k leku rFkk fn'kk foijhr gksrh gSA r r mnk- A dk Ω.kkRed gS B r r ;fn, A = – B

osDVj ftudh leku fn'kk vkSj ifjek.k gksrk gSA

A =

^

;g ,d ;k ,drk ds :i es ifjek.k j[krk gSA r

blesa 'kwU; ifjek.k vkSj d{kh; fn'kk gS A

p k r fL Fk f

r

ax = 0,ay = g

→ → |VAB|=| VBA| &

→ → VAB = – VBA

→→ → → V BA = VB –VA

→ → → V AB =VA –VB

lkis{k osx

ac=v2/r = r

2

= 4π2 r

2

o`Ÿkh; xfr ds dsaÊ dh vksj funsZf'kr Roj.k }kjk ,d o`Ÿkh; xfr esa ,d fiaM }kjk fd;k x;k dk;ZA

dks.kh; osx , = θ/t dks.kh; Roj.k=Δ /Δt mnkgj.k& pDdjnkj >wyk

o`Ÿ k h ; xfr tc dks oLrq ,d fu;r xfr ls ,d o`Ÿkkdkj iFk dk vuqlj.k djrh gS] rks oLrq dh xfr dks ,dleku o`Ÿkh; xfr dgk tkrk gSA

u= x ucosθ,u= y u sinθ

fdlh Hkh le;

o sx ds ? k V d Á k j fH k d o sx

f}foeh;