TARGET COURSE FOR IIT-JEE 2011 ALL PHASE TEST-2 (TAKE HOME) PAPER – II Name : _________________________________________________________ Roll No. : __________________________ INSTRUCTIONS TO CANDIDATE A.GENERAL : 1. Please read the instructions given for each question carefully and mark the correct answers against the question numbers on the answer sheet in the respective subjects. 2. The answer sheet, a machine readable Optical Mark Recognition (OMR) is provided separately. 3. Do not break the seal of the question-paper booklet before being instructed to do so by the invigilators. B. MARKING SCHEME : Each subject in this paper consists of following types of questions:- Section - I 4. Multiple choice questions with only one correct answer. 3 marks will be awarded for each correct answer and –1 mark for each wrong answer. 5. Multiple choice questions with multiple correct option. 4 marks will be awarded for each correct answer and –1 mark for each wrong answer. Section - II 6. Column Matching type questions. 8 marks will be awarded for the complete correctly matched answer (i.e. +2 marks for each correctly matched row) and no negative marking for wrong answer. Section - III 7. Numerical response questions. 4 marks will be awarded for each correct answer and –1 mark for each wrong answer in this section. Answers to this Section are to be given in the form of single digit integer type. C.FILLING THE OMR : 8. Fill your Name, Roll No., Batch, Course and Centre of Examination in the blocks of OMR sheet and darken circle properly. 9. Use only HB pencil or blue/black pen (avoid gel pen) for darking the bubbles. 10. While filling the bubbles please be careful about SECTIONS [i.e. Section-I (include single correct, reason type, multiple correct answers), Section –II ( column matching type), Section-III (include integer answer type)] Section –I Section-II Section-III For example if only 'A' choice is correct then, the correct method for filling the bubbles is A B C D E For example if only 'A & C' choices are correct then, the correct method for filling the bublles is A B C D E the wrong method for filling the bubble are The answer of the questions in wrong or any other manner will be treated as wrong. For example if Correct match for (A) is P; for (B) is R, S; for (C) is Q; for (D) is P, Q, S then the correct method for filling the bubbles is P Q R S T A B C D Ensure that all columns are filled. Answers, having blank column will be treated as incorrect. Insert leading zeros (s) 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 '6' should be filled as 0006 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 '86' should be filled as 0086 0 0 0 0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 '1857' should be filled as 1857 Corporate Office : CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: 0744-3040000 (6 lines), Fax (0744) 3040050 email : [email protected]; Website : www.careerpointgroup.com SEAL 4 CHEMISTRY, MATHEMATICS, PHYSICS Date : 6/02/2011 Time : 3 : 00 Hrs. MAX MARKS: 240
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TARGET COURSE FOR IIT-JEE 2011
ALL PHASE
TEST-2 (TAKE HOME)
PAPER – II
Name : _________________________________________________________ Roll No. : __________________________
INSTRUCTIONS TO CANDIDATE
A. GENERAL : 1. Please read the instructions given for each question carefully and mark the correct answers against the question
numbers on the answer sheet in the respective subjects. 2. The answer sheet, a machine readable Optical Mark Recognition (OMR) is provided separately. 3. Do not break the seal of the question-paper booklet before being instructed to do so by the invigilators.
B. MARKING SCHEME : Each subject in this paper consists of following types of questions:- Section - I 4. Multiple choice questions with only one correct answer. 3 marks will be awarded for each correct answer and –1 mark for
each wrong answer. 5. Multiple choice questions with multiple correct option. 4 marks will be awarded for each correct answer and –1 mark for
each wrong answer. Section - II
6. Column Matching type questions. 8 marks will be awarded for the complete correctly matched answer (i.e. +2 marks for each correctly matched row) and no negative marking for wrong answer.
Section - III
7. Numerical response questions. 4 marks will be awarded for each correct answer and –1 mark for each wrong answer in this section. Answers to this Section are to be given in the form of single digit integer type.
C. FILLING THE OMR : 8. Fill your Name, Roll No., Batch, Course and Centre of Examination in the blocks of OMR sheet and darken circle properly. 9. Use only HB pencil or blue/black pen (avoid gel pen) for darking the bubbles. 10. While filling the bubbles please be careful about SECTIONS [i.e. Section-I (include single correct, reason type, multiple
Section - I Questions 1 to 4 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
Q.1 When copper sulphate solution is electrolysed in a copper voltameter for 30 sec, then m gram of copper was deposited. Time current graph for the electrolysis is
200
100
10 20 30 time (sec)
Cur
rent
(mA)
The electrochemical equivalent of copper from
above plot will be -
(A) Z = m (B) Z = 2m
(C) Z = 5m (D) Z = 2m
[k.M - I iz'u 1 ls 4 rd cgqfodYih iz'u gSaA izR;sd iz'u ds pkj
Q.4 When NaCl is added gradually to the saturated solution of AgCl then which of the following plot is correct ?
(A)
Cl–
[Ag+] (B)
Cl–
[Ag+]
(C)
Cl–
[Ag+] (D)
Cl–
[Ag+]
Questions 5 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct. Mark your response in OMR sheet against the question number of that question. + 4 marks will be given for each correct answer and –1 mark for each wrong answer.
Q.5 If equal volumes of 0.1 M HBr and 0.1M KOH are mixed, then which of the following is/are correct about the resulting solution ?
bl [k.M esa 2 iz'u (iz'u 1, 2) gSaA izR;sd iz'u esa nks LrEHkksa esa dFku fn;s x;s gSa] ftUgsa lqesfyr djuk gSA LrEHk-I (Column I ) esa fn;s x;s dFkuksa (A, B, C, D) dks LrEHk-II (Column II) esa fn;s x;s dFkuksa (P, Q, R, S,T) ls lqesy djuk gSA bu iz'uksa ds mÙkj uhps fn;s x;s mnkgj.k ds vuqlkj mfpr xksyksa dks dkyk djds n'kkZuk gSA ;fn lgh lqesy A-P, A-S, A-T; B-Q, B-R; C-P, C-Q rFkk D-S, D-T gS, rks lgh fof/k ls dkys fd;s x;s xksyksa dk 4 × 5 eSfVªDl uhps n'kkZ;s vuqlkj gksxk :
ABCD
P Q R S T
T S
P
P P Q R
R R
Q Q
S S T
T
P Q R S T
vr% OMR 'khV esa iz'u dh iz'u la[;k ds le{k viuk mÙkj [k.M-II esa vafdr dhft;sA izR;sd iw.kZ lgh mÙkj ds fy;s +8 vad fn;s tk;saxs ¼vFkkZr~ izR;sd lgh iafDr feyku ds fy, +2 vad fn, tk,saxs½ o xyr mÙkj ds fy, dksbZ _.kkRed vadu ugha gSA
Q.9 Which of the following is correct regarding equilibrium
(A) At equilibrium ∆G = 0 (B) It is dynamic in nature (C) At equilibrium ∆Gº = –RTlnK (D) Equilibrium can be attained from either of the
side
Section - II This section contains 2 questions (Questions 1, 2). Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :
A B C D
P Q R S T
T S
P
P P Q R
R R
Q Q
S S T
T
P Q R S T
Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.
Section - III This section contains 8 questions (Q.1 to 8).+4 marks will be given for each correct answer and –1mark for each wrong answer. The answer to each of thequestions is a SINGLE-DIGIT INTEGER, rangingfrom 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook like the following :
0 1 2
3
4
5 6
7
8
9
0 1 2
3
4
5 6
7
8
9
012
3
4
56
7
8
9
0 1 2
3
4
5 6
7
8
9
X Y Z W
Q.1 If the equilibrium constant of the reaction of weakacid HA with strong base is 109 then pH of 0.1 MNaA is -
Q.2 What is the minimum pH required to prevent theprecipitation of ZnS in a solution i.e., 0.01 M ZnCl2
and saturated with 0.1 M H2S ? Ksp(ZnS) = 10–21,
1aK × 2aK (H2S) = 10–20
[k.M - III
bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s +4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys fd;s x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA
012
3
4
56
7
8
9
012
3
4
56
7
8
9
0 1 2
3
4
5 6
7
8
9
0 1 2
3
4
5 6
7
8
9
X Y Z W
Q.1 ;fn nqcZy vEy HA dh izcy {kkj ds vfHkfØ;k dk lkE;
fLFkjkad 109 gS rks 0.1 M NaA dh pH gSA
Q.2 ,d foy;u esa 0.01 M ZnCl2 rFkk ftls 0.01 M H2S ds lkFk larIr fd;k x;k gS blls izkIr foy;u esa ZnS ds vo{ksi.k dks jksdus ds fy, vko';d U;wure pH D;k gS ?
will precipitate at limiting pH of ––––– . Q.4 20% of N2O4 molecules are dissociated in a sample
of gas at 27°C and 760 torr. Mixture has the densityat equilibrium equal to -
Q.5 In an experiment, 0.04 F was passed through 400
mL of a 1 M solution of NaCl. What would be the pOH of the solution after the electrolysis ?
Q.6 A current of 2 amp when passed for 5 hour through
a molten salt deposits 22.2 g of metal of atomicmass 177. The oxidation state of the metal in themetal salt is -
Q.7 What weight of solid ammonium carbamate
(NH2COONH4) when vaporized at 200°C will havea volume of 8.96 litre at 1 atm ? Assume that solidcompletely decomposes into CO2 and NH3 at 200°C and 1 atm.
Q.8 Find the pH of 0.5×10–5 H2SO4 solution
Q.3 Mg(OH)2 dk Ksp = 1 × 10–12 gSA 0.01 M MgCl2 fdl lhekUr pH ij vo{ksfir gksxkA
Q.4 20% , N2O4 v.kq] 27°C o 760 VkWj ij xSl ds uewus esa
Questions 1 to 4 are multiple choice questions. Eachquestion has four choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct. Mark your response inOMR sheet against the question number of thatquestion. + 3 marks will be given for each correct answerand – 1 mark for each wrong answer. Q.1 Range of the function
f(x) = 2347498142
24
24
+−−+−−
xxxxxx is
(A) [1, 3] (B) [2, 3] (C) (2, 3] (D) (1, 2]
Q.2 Number of solutions of the equation [y + [y]] = 2 cosx
is, where y = 31 [sinx + [sinx + [sinx]]] and [.]
denotes the greatest integer function (A) 1 (B) 2 (C) 3 (D) none of these
Questions 5 to 9 are multiple choice questions. Eachquestion has four choices (A), (B), (C) and (D), out ofwhich MULTIPLE (ONE OR MORE) is correct. Mark your response in OMR sheet against the questionnumber of that question. + 4 marks will be given for eachcorrect answer and –1 mark for each wrong answer.
Q.5 Let f (x) = sin–1x + cos–1x. Then 2π is equal to-
(A) f
21– (B) f(k2 – 2k + 3), k ∈ R
(C) f
+ 211k
, k ∈ R (D) f(–2)
Q.6 If 100C50 can be prime factorised as 2α 3β . 5γ . 7δ ….
where α, β, γ, δ, …. are non negative integers, thencorrect relation is/are -
rks f(x) gksxk (D) ekuk f : (–1, 5) → [0, 3] ; (S) vO;qRØe.kh;
f(x) = 245 xx −+ , }kjk
ifjHkkf"kr gS] rks f(x) gksxk (T) vukorhZ
Q.2 LrEHk-I LrEHk-II
(A) 31
33.)2(3.lim 1 =
−+− +∞→ nnn
n
n nxnn (P) 0
rc x gksxk (;fn n ∈ N)
(B) ;fn2
2
1 ))2((lim
xnbaxx
x −++
→ l fo|eku gS (Q) 1
rks vUrjky (a, b + l) esa iw.kk±d
gksaxs] tgk¡ l lhek dk eku gS
Q.1 Column –I Column –II
(A) Let f : R → R be defined as (P) one-one
f(x) = 3 x + tan–1x, then f(x) is
(B) Let f : (–∞, ∞) → {–1, 0, 1} (Q) into be defined as f(x) = sin3π (sgn (x2 + 3x + 5)) then f(x) is (where sgn x denotes signum function of x) (C) Let f : [–2, 2] → (0, e2] be (R) odd
defined as f(x) = 2xe , then f(x) is (D) Let f : (–1, 5) → [0, 3] be (S) non invertible
bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s +4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys fd;s x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA
012
3
4
56
7
8
9
012
3
4
56
7
8
9
0 1 2
3
4
5 6
7
8
9
0 1 2
3
4
5 6
7
8
9
X Y Z W
(C) l=−
→ xxx
x 20 tan2coscos1lim then (R) 2
integral value of l
(D) x
bae x
x
−→0
lim = 2 then a, b, a + b (S) 3
can be (T) 4
Section - III
This section contains 8 questions (Q.1 to 8).+4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of thequestions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook like the following :
Q.1 If range of the function f(x) = sin–1 x + 2 tan–1x + x2 + 4x + 1 is [p, q] then
find the value of (p + q)………
Q.2 Let f(x) = π2 (sin–1[x] + tan–1[x] + cot–1 [x]) where
[x] denotes greatest integer less than or equal to x. If A and B denote the domain and range of f(x) respectively, then the number of integers in (A ∪ B) is………
Section - I Questions 1 to 4 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
Q.1 A hollow vertical cylinder of radius r and height h has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point A, and given a horizontal speed u, tangential to the rim. It leaves the lower rim at point B, vertically below A. If n is an integer then-
A u
h
r
B
(A) g/h2r2
uπ
= n (B) r2
hπ
= n
(C) h
r2π = n (D) gh2
u = n
[k.M - I iz'u 1 ls 4 rd cgqfodYih iz'u gSaA izR;sd iz'u ds pkj
Q.2 3r f=kT;k ds fpdus di ij nks leku nzO;eku ds Hkkjh xksys n'kkZ;s vuqlkj j[ks gS tgka r izR;sd xksys dh f=kT;k gS rks di o fdlh Hkh xksys ds e/; izfrfØ;k cy o nks xksyksa ds e/; izfrfØ;k cy dk vuqikr gS–
r r
3r 3r
O
(A) 1 (B) 2 (C) 3 (D) buesa ls dksbZ ugha
Q.3 yEckbZ l < πR/2 dh ,d pSu ,d fpduh lrg ij
j[kh gS ftldk dqN Hkkx {kSfrt rFkk dqN Hkkx
fp=kkuqlkj R f=kT;k ds ,d pkSFkkbZ&oÙk ij gSA izkjEHk
esa pSu dk iwjk Hkkx oÙkh; Hkkx esa jgrk gS ftldk
,d fljk oÙkh; lrg ds 'kh"kZ fcUnq ij gSA ;fn pSu
dk nzO;eku m gS rc iwjh pSu dks {kSfrt Hkkx ij
/khjs&/khjs [khapus esa fd;k x;k vko';d dk;Z gS -
O
R
R
Q.2 Two identical heavy spheres of equal mass are placed on a smooth cup of radius 3r where r is radius of each sphere. Then the ratio of reaction force between cup and any sphere to reaction force between two sphere is –
r r
3r 3r
O
(A) 1 (B) 2 (C) 3 (D) None of these
Q.3 A chain of length l < πR/2 is placed on a smooth surface whose some part is horizontal and some part is quarter circular of radius R as shown. Initially the whole part of chain lies in the circular part with one end at top most point of circular surface. If the mass of chain is m then the work required to pull very slowly the whole chain on horizontal part is -
Q.5 uhps n'kkZ;k x;k ,d ydM+h CykWd dh xfr dks n'kkZrk gS ftldk nzO;eku 1 kg gS o ftls {kSfrt Vscy ij t = 0 ij ,d izkjfEHkd /kDdk fn;k x;k gS-
4(0, 0)
4
v (m
s–1)
t (s)
(A) l
m gR2
Rsin l (B)
l
m gR2
Rcos l
(C) l
m gR2
−
Rsin
Rll
(D) None of these
Q.4 A swimmer is swimming with constant velocity 22 m/s due North-East in a calm lake. He
observes his image in a mirror fitted at the rear of a boat moving with constant velocity 1 m/s due East. Velocity of his image as observed by him in the mirror will be -
(A) 2 m/s (B) 2 2 m/s(C) 52 m/s (D) 3 m/s
Questions 5 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct. Mark your response in OMR sheet against the question number of that question. + 4 marks will be given for each correct answer and –1 mark for each wrong answer.
Q.5 The velocity-time graph of the figure shows the motion of a wooden block of mass 1 kg which is given an initial push at t = 0 along a horizontal table-
[k.M - II bl [k.M esa 2 iz'u (iz'u 1, 2) gSaA izR;sd iz'u esa nks LrEHkksa esa dFku fn;s x;s gSa] ftUgsa lqesfyr djuk gSA LrEHk-I (Column I ) esa fn;s x;s dFkuksa (A, B, C, D) dks LrEHk-II (Column II) esa fn;s x;s dFkuksa (P, Q, R, S,T) ls lqesy djuk gSA bu iz'uksa ds mÙkj uhps fn;s x;s mnkgj.k ds vuqlkj mfpr xksyksa dks dkyk djds n'kkZuk gSA ;fn lgh lqesy A-P, A-S, A-T; B-Q, B-R; C-P, C-Q rFkk D-S, D-T gS, rks lgh fof/k ls dkys fd;s x;s xksyksa dk 4 × 5 eSfVªDl uhps n'kkZ;s vuqlkj gksxk :
ABCD
P Q R S T
T S
P
P P Q R
R R
Q Q
S S T
T
P Q R S T
Q.9 If one of the slits of a standard young‘s double slit experiment is covered by a thin parallel slit glass so that it transmits only one half the light intensity of the other, then:
(A) The fringe pattern will get shifted towards the covered slit
(B) The fringe pattern will get shifted away from the covered slit
(C) The bright fringes will become less bright and the dark ones will become more bright
(D) The fringe width will remain unchanged
Section - II This section contains 2 questions (Questions 1, 2). Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :
Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.
Q.1 The equation of one dimensional motion of particle is described in column I. At t = 0, particle is at origin and at rest. Match the column I with the statements in column II.
Column -I Column-II
(A) x = (3t2 + 2)m (P) velocity of particle at t = 1 s is 8 m/s
(B) v = 8t m/s (Q) particle moves with uniform acceleration
(C) a = 16 t (R) particle moves with variable acceleration
(D) v = 6t – 3t2 (S) particle will change its direction some time (T) None
Q.2 Refraction of plane surface (FG is parallel to MN)
Column I Column II (A) Which ray is not possible (P) A
(B) 3
2
2
1 >µµ (Q) B
(C) 12
1 ≤µµ (R) C
(D) 12
1 ≥µµ (S) D
(T) None
Section - III This section contains 8 questions (Q.1 to 8).+4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkening of bubbles willlook like the following :
0 1 2
3
4
5 6
7
8
9
0 1 2
3
4
5 6
7
8
9
012
3
4
56
7
8
9
0 1 2
3
4
5 6
7
8
9
X Y Z W
LrEHk I LrEHk II (A) dksulh fdj.k LEHko ugha gS (P) A
(B) 3
2
2
1 >µµ (Q) B
(C) 12
1 ≤µµ (R) C
(D) 12
1 ≥µµ (S) D
(T) dksbZ ugha
[k.M - III
bl [k.M esa 8 (iz-1 ls 8) iz'u gaSA izR;sd lgh mÙkj ds fy;s +4 vad fn;s tk,saxs rFkk izR;sd xyr mÙkj ds fy, 1 vad ?kVk;k tk,sxkAbl [k.M esa izR;sd iz'u dk mÙkj 0 ls 9 rd bdkbZ ds ,d iw.kk±d gSaA OMR esa iz'u la[;k ds laxr uhps fn;s x;s cqYyksa esa ls lgh mÙkj okys cqYyksa dks dkyk fd;k tkuk gSA mnkgj.k ds fy, ;fn iz'u la[;k ¼ekusa½ X, Y, Z rFkk W ds mÙkj 6, 0, 9 rFkk 2 gkas, rks lgh fof/k ls dkys fd;s x;s cqYys ,sls fn[krs gSa tks fuEufyf[kr gSA
Q.1 An insect moves with a constant velocity v from one corner of a room to other corner which is opposite of the first corner along the largest diagonal of room. If the insect can not fly and dimensions of room is a × a × a, then the minimum time in which the insect can move is a/v times the square root of a number n, then n is equal to ?
Q.2 A track has two inclined surfaces AB and AC each
of length 3 m and angle of inclination of 30º with the horizontal and a central horizontal part of length 4 m as shown in figure. A block of mass 0.2 kg slides from the rest from point A. The inclined surfaces are frictionless. If the coefficient of friction between the block and the horizontal flat surface is 0.2, where will the block finally come to rest from point B? [in 10–1 m]
30ºθ =30º3 m3 m
A D
C B 4 m
Q.3 A block of mass m = 1kg moving on horizontal surface with speed u = 2m/s enters a rough horizontal patch ranging from x = 0.10 m to x = 2.00m. If the retarding force fr on the block in this range is inversely proportional to x over this range i.e.
Q.1 ,d dhMk ,d fu;r osx v ls ,d cM+s dejs ds ,ddksus ls nwljs dksus (tks izFke dksus ds Bhd lkeus gS)rd dejs ds lcls cM+s O;kl ds vuqfn'k xfr djrk gSA;fn dhMk mM+ ugha ldrk rFkk dejs dk vk;ke a × a ×a gS rks og U;wure le; ftlesa dhMk xfr dj ldrkgSA ,d la[;k ds n ds oxZewy dk a/v xquk gS rks n dkeku D;k gS ?
Q.2 ,d Vªsd nks vkur lrg AB o AC j[krk gS] izzR;sd dh
yEckbZ 3m gS o {kSfrt ls vkur dks.k 30º gS o dsUnzh;
{kSfrt Hkkx dh yEckbZ 4 m gS (ns[ksa fp=k)A ,d 0.2 kg
nzO;eku dk ,d CykWd fcUnq A ls fojke ls fQlyuk
'kq: gksrk gSA vkur lrgsa ?k"kZ.kghu gSA ;fn CykWd o
lery lrg ds e/; ?k"kZ.k xq.kkad 0.2 gS] rks fcUnq B ls
fdruh nwjh ij CykWd ifj.kkeh :i ls fojke esa vk
tk;sxk ? [in 10–1 m]
30ºθ =30º3 m3 m
A D
C B 4 m
Q.3 ,d CykWd ftldk nzO;eku m = 1kg ,d {kSfrt lrgij u = 2m/s dh pky ls xfr'khy gSA xfr djrs gq,;g x = 0.10 m ls x = 2.00m ijkl ds [kqjnjs {kSfrtHkkx esa izos'k djrk gSA ;fn ,d vojks/kd cy fr blCykWd ij bl ij nh xbZ ijkl esa CykWd ij dk;Zjr gSAvFkkZr
= 0 for x < 0.10 and x > 2.00 If k = 0.5 J then the speed of this block as it crosses
the patch is (use ln 20 = 3) in m/s is –
Q.4 A particle of mass 7
10 Kg is moving in the
positive direction of x. Its initial position x = 0 &initial velocity is 1 m/s. The velocity at x = 10 is -
4
x (in m) 10
Power (in watts)
Q.5 Two blocks of mass 2 kg and 4 kg are connected
through a massless inextensible string. Coefficientof friction between 2 kg block and ground is 0.4and between 4 kg block and ground is 0.6. Twoforces F1 = 10 N and F2 = 20 N are applied on theblock as shown in figure. Friction force (in N)acting on 4 kg block minus 10 N is
4 kg 20 N 2 kg 10 N
µ = 0.6 µ = 0.4
fr = xk− 0.10 < x < 2.00
= 0 x < 0.10 o x > 2.00 ds fy, ;fn k = 0.5 J rks bl CykWd dh pky (m/s esa) tc ;g
bl {kSfrt Hkkx dks ikj dj ysrk gS] D;k gksxh (fn;k gSln 20 = 3) in m/s is –
Q.4 ,d d.k ftldk nzO;eku 7
10 Kg gS ,d /kukRed x
fn'kk esa xfr'khy gSA bldh izkjfEHkd fLFkfr x = 0 gS o izkjfEHkd osx 1 m/s gSA x = 10 ij bldk osx D;k gS -
4
x (in m) 10
Power (in watts)
Q.5 nks CykWd ftuds nzO;eku 2 kg o 4 kg gS o ,d
nzO;ekughu vfoLrkj.kh; Mksjh }kjk vkils esa tqMs+ gSA2 kg CykWd o tehu ds e/; ?k"kZ.k xq.kkad 0.4 o 4 kg CykWd o tehu ds e/; ?k"kZ.k xq.kkad 0.6 gSA nks cyF1 = 10 N o F2 = 20 N CykWdks ij n'kkZ, vuqlkj yx jgs gsA 4 kg CykWd ij dk;Zjr ?k"kZ.k cy (N esa) – 10 N dk eku D;k gksxk
Q.6 Two rays are incidents on a spherical concavemirror of radius R = 5cm parallel to its optical axisat perpendicular distances 3cm and 4cmrespectively. Determine the value ∆x if distancebetween the points at which these rays intersect theoptical axis after being reflected from the mirror is
∆x × 245 cm.
Q.7 A circular beam of light of diameter d = 2cm falls on a plane surface of glass. The angle of incidenceis 60º and refractive index of glass is
µ =23 . Find the diameter of the refracted beam in
cm. Q.8 In a modified YDSE the region between screen and
slits is immersed in a liquid whose refractive index
varies with time as µl = 25 –
4T until it reaches a
steady state value 45 . A glass plate of thickness 36
µm and refractive index 23 is introduced infront of
one the slits. The speed of the central maximawhen it is at O is …….. × 10–3 m/s
Q.6 nks izdk'k fdj.ksa ,d xksyh; vory niZ.k ftldh oØrk R = 5cm ij bldh izdkf'k; v{k ds lekUrj o yEcor~ nwjh;ksa 3cm o 4cm ij vkifrr gks jgh gSA nwjh ∆x Kkr dhft, ;fn ijkorZu ds i'pkr nksuksa fdj.kksa }kjk izdkf'k; v{k dks dkVus okys fcUnqvksa ds e/; dh