Physics, Chemistry, Mathematics & Logical Aptitude. 3. Each section ... Four
alternatives have been given with each of the objective questions. You have to ...
FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
FOUND ATION COURSE FOR IIT FOUNDA IIT-- JEE (For Class X to XI moving Students) [Time : 03:00 Hrs.]
[Maximum Marks : 300]
INSTRUCTIONS TO CANDIDATES 1.
Attempt all questions.
2.
The question paper has Four sections viz. Physics, Chemistry, Mathematics & Logical Aptitude.
3.
Each section consists of following sections : (a) Short write ups followed by Objective Questions. (b) Objective Questions not based on write ups.
4.
Four alternatives have been given with each of the objective questions. You have to select the single correct alternative. Each correct answer carries three marks.
5.
There is No negative marking and no deduction will be made for WRONG attempt.
6.
The answer sheet is supplied with this question paper and you are advised to indicate your answer on this Answer Sheet only.
7.
Rough work should be done only on the blank spaces provided. Extra paper will not be supplied.
8.
Logarithm table will not be supplied. Use of calculators, slide rule is not permitted.
9.
There are different types of questions, you will find special direction for each set of questions. Be sure you have understood the direction before attempting to answer any question.
10.
Do not spend too much time on questions that are difficult for you. Go on the other questions and come back to the difficult ones later.
11.
Before you start marking your answer, write your Name at the top of the answer sheet.
12.
Do not help your neighbour in your own interest.
Name............................................................................Roll Number................................................ Space for Rough Work
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
PART : 1 PHYSICS Each correct answer carries three marks. Passage 1.(Q.No. 1 to 5) Archimedes principle applies to fluids. It states : "When a body is partly or wholly immersed in a fluid (liquid or gas) at rest, it undergoes an apparent loss in the weight which is equal to the weight of the fluid displaced by the body." According to the principle of floatation, when a body floats in a liquid, its weight is equal to the weight of the liquid displaced by it. If the volume of the floating body is V, its density D, the volume of the portion of the body immersed in the liquid v and density of the liquid d, then V×D=v×d Based on above passage answer the following questions :
izR;sd lgh mÙkj ds 3 vad fu/kkZfjr gS x|ka'k 1.(iz- l- 1 ls 5) vkfdZfeMht dk fl¼kUr rjyksa ij ykxw gksrk gSA blds vuqlkj: "tc ,d oLrq vkaf'kd ;k iw.kZ :i ls fojke rjy (nzo ;k xSl) esa Mwch gqbZ gks] rks blds Hkkj esa deh izrhr gksrh gS tks fd oLrq }kjk gVk;s x;s rjy ds Hkkj ds cjkcj gksrh gSA" rSjus ds fl¼kUr ds vuqlkj] tc ,d oLrq ,d nzo esa rSjrh gS] rks bldk Hkkj blds }kjk gVk;s x;s nzo ds Hkkj ds cjkcj gksrk gSA ;fn rSjrh gqbZ oLrq dk vk;ru V gks] bldk ?kuRo D gks, nzo esa Mwcs gq, blds Hkkx dk vk;ru v rFkk nzo dk ?kuRo d gks, rks V×D=v×d
mijks D r x|ka ' k ds vk/kkj ij fuEu iz ' uks a ds mÙkj nhft,%
Q.1
Two bodies have the same weight in a liquid. Then– (a) their densities must be same (b) their volumes must be same (c) their masses must be same (d) none of these
Q.1
nks oLrqvksa dk ,d nzo esa Hkkj leku gS] rks – (a) muds ?kuRo leku gksaxs (b) muds vk;ru leku gksaxs (c) muds nzO;eku leku gksaxs (d) buesa ls dksbZ ugha
Q.2
A boat of mass 650 kg floats on water. What volume of water does it displace ? (a) 0.65 m3 (b) 6.50 m3 3 3 (c) 6.50×10 m (d) 0.65 × 102 m3
Q.2
650 kg
What volume of alcohol (density = 0.75 g cm–3) is displaced by a cork of mass 4.2 g which floats in it– (a) 5.6 cm3 (b) 6.2 cm3 3 (c) 7.8 cm (d) 8.4 cm3
Q.3
Q.3
Q.4
Q.5
A cork of density 250 kg m–3 floats in a liquid with onethird of its volume below the surface of the liquid. What is the density of the liquid ? (a) 750 kgm–3
(b) 820 kgm–3
(c) 860 kgm–3
(d) 940 kgm–3
nzO;eku dh ,d uko ikuh ij rSjrh gSA ikuh ds fdrus vk;ru dks ;g foLFkkfir djsxh ? (a) 0.65 m3 (c) 6.50×103 m3
,sYdksgkWy (?kuRo = 0.75 g cm–3) dk fdruk vk;ru 4.2 g nzO;eku ds dkWdZ }kjk foLFkkfir gksrk gS] tks blesa rSjrk gS– (a) 5.6 cm3 (c) 7.8 cm3
Q.4
Q.5
(b) 6.2 cm3 (d) 8.4 cm3
250 kg m–3 ?kuRo
dk ,d dkWdZ ,d nzo esa bl izdkj rSjrk gS fd blds vk;ru dk ,d frgkbZ nzo dh lrg ds uhps jgrk gSA nzo dk ?kuRo D;k gS ? (a) 750 kgm–3 (c) 860 kgm–3
A body floating in oil always displaces its own– (a) volume of oil (b) weight of oil (c) surface area of oil (d) depth of oil
(b) 6.50 m3 (d) 0.65 × 102 m3
(b) 820 kgm–3 (d) 940 kgm–3
rsy esa rSjrh gqbZ dksbZ oLrq lnSo foLFkkfir djrh gS vius – (b) Hkkj dk rsy (a) vk;ru dk rsy (c) i`"B {ks=kQy dk rsy (d) xgjkbZ dk rsy
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FOUNDATION COURSE FOR IIT-JEE Following Questions are not based on passage : (Each correct answer carries three marks) Q.6
A ball is thrown vertically upwards. Neglecting the air resistance, the velocity time graph of the ball during it's time of flight will be -
SAMPLE TEST PAPER
fuEu iz'u x|ka'k ij vk/kkfjr ugha gS : (izR;sd lgh mÙkj ds 3 vad fu/kkZfjr gS) Q.6 ,d ckW y dks Å/okZ / kj Åij dh vks j Qs a d k tkrk gS A ok;q izfrjks/k dks ux.; ekurs gq, mM+ku dky ds nkSjku ckWy dk osx le; xzkQ gksxk -
v
v
(a)
v
v
(b)
(a)
(b)
t
t
t
t
v
v v
(c)
(d)
t
Q.7
Q.8
Q.9
v
(c)
(d)
t
t
Light year is the unit of – (a) intensity of light
(b) time
(c) distance
(d) velocity of light
A train passes an electric pole in 8 second and a bridge of length 1 km in 108 seconds. The speed of the engine is – (a) 10 ms–1
(b) 12 ms–1
(c) 8 ms–1
(d) 5 ms–1
Q.7
izdk'k o"kZ fdldh bdkbZ gS – (a) izdk'k dh rhozrk (b) le; (c) nwjh (d) izdk'k dk osx
Q.8
,d Vsªu 8 lsd.M esa ,d fctyh ds [kEHks ls xqtjrh gS rFkk 1 km yEckbZ ds ,d iqy dks 108 lsd.Mksa esa ikj djrh gSA batu dh pky gksxh – (a) 10 ms–1 (c) 8 ms–1
If 10 gm of ice at 0°C is mixed with 10g of water at 10°C, the final temperature t is – (a) –35°C (b) –10°C (c) 5°C (d) 0°C
Q.10 In the circuit shown in fig, the ammeter ‘A’ reads 5 amperes and the voltmeter ‘V’ reads 20 volt. The correct value of resistance R is :
t
Q.9
(b) 12 ms–1 (d) 5 ms–1
;fn 0°C ij 10g cQZ dks 10°C okys 10 g ikuh ds lkFk feyk;k tkrk gS] rks vafre rki t gksxk – (a) –35°C (c) 5°C
Q.10
fp= esa fn[kk;s x;s ifjiFk esa vehVj ‘A’, 5 ,sfEi;j i r2) dh o`Ùkh; d{kkvksa esa pDdj yxk jgs gSAa fuEu esa ls muds osxksa v1 o v2 ds lEcU/k esa dkSulk dFku lR; gS \ (a) v1 = v2 (b) v1 < v2 (c) v1 > v2
Q.26
(b) 273°C (d) –273°F
(d)
v1 v 2 = r1 r2
,d iz l kj.k LVs ' ku 71 × 10 4 Hz vko` f r dh rja x ks a dks 3 × 108 ms–1 dh pky ls Hkstrk gSA rjaxksa dh rjax nS/;Z gS– (a) 412. 8 m
(b) 324.6 m
(c) 208.4 m
(d) 422.5 m
Q.27 The distance travelled by a freely falling body is proportional to the – (a) mass of the body (b) time of fall (c) square of the time of fall (d) square of the acceleration due to gravity
Q.27
eqDr :i ls fxjrs gq, fi.M }kjk r; dh xbZ nwjh fdlds lekuqikrh gS – (a) fi.M ds nzO;eku ds (b) fxjus esa yxs le; ds (c) fxjus esa yxs le; ds oxZ (d) xq:Roh; Roj.k ds oxZ
Q.28 The metal bob of a simple pendulum swing to and fro with simple harmonic motion. Which of the following quantities does not become zero at any time throughout the oscillation ? (a) acceleration (b) momentum (c) kinetic energy (d) weight
Q.28
,d ljy yksyd dk /kkfRod xksyd ljy vkorZ xfr ds lkFk bnZ&fxnZ xfr djrk gSA nksyu ds nkSjku fdlh Hkh le; ij fuEu esa ls dkSulh jkf'k 'kwU; ugha gksxh ? (b) laosx (a) Roj.k (c) xfrt ÅtkZ (d) Hkkj
Q.29 A body of mass 2 kg moves 30 m against a frictional force of 100 N. If the work is completely converted into heat, the amount of heat expressed in joules will be – (a) 3000 J (b) 6000 J (c) 2000 J (d) 1500 J
Q.29
2 kg nzO;eku
Q.30 When 1 g of water at 373 K is converted into steam at the same temperature, the approximate change in volume is (a) 1 cm3 (b) 1000 cm3
Q.30
(c) 1670 cm3
dh ,d oLrq 100 N ds ?k"kZ.k cy ds fo:¼ 30 m rd xfr djrh gSA ;fn lEiw.kZ dk;Z] Å"ek es ifjofrZr gks tk;s rks Å"ek dh twy esa O;Dr ek=k gksxh – (a) 3000 J (c) 2000 J
(b) 6000 J (d) 1500 J
tc 373 K ij 1 g ikuh leku rki ij Hkki esa :ikUrfjr gks tk;s rks vk;ru esa yxHkx ifjorZu gksxk – (a) 1 cm3 (c) 1670 cm3
(b) 1000 cm3 (d) 3000 cm3
(d) 3000 cm3
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
PART : 2 CHEMISTRY Each correct answer carries three marks.
izR;sd lgh mÙkj ds 3 vad fu/kkZfjr gS x|ka'k 1.(iz- l- 1 ls 5)
Passage 1.(Q.No. 1 to 5)
Q.1
Cathode rays are a stream of particles, consisting of electrons, emerging from the cathode in a discharge tube at low pressure. Electrons are negatively charged particles with a mass 1/1840 that of a hydrogen atom. Proton is a fundamental paritcle with a positive charge and mass equal to that of a hydrogen atom. A neutron is another fundamental particle with no charge but mass equal to that of a hydrogen atom or proton. The sum of the number of neutrons and protons in the nucleus of an atom of an element is mass number. Total number of protons or electrons in a neutral atom of an element is atomic number. An atom of an element has 10 electrons, 10 protons and 12 neutrons. The atomic mass of the element is– (a) 32 (b) 22 (c) 44 (d) 20
dSFkksM fdj.ksa bySDVªkWuksa ;qDr d.kksas dh /kkjk gS tks fd de nkc ij foltZu uyh esa dsFkksM ls fudyrh gSA bySDVªku ½.kkosf'kr d.k gS ftudk nzO;eku ,d gkbMªkstu ijek.kq dk 1/1840 gSA izksVksu Hkh ,d /kukRed vkosf'kr ewy d.k gS ftldk nzO;eku ,d gkbMªkstu ijek.kq ds cjkcj gSA U;wVªku ,d vU; ekSfyd d.k gS ftl ij dksbZ vkos'k ugha gS ysfdu nzO;eku gkbMªkstu ijek.kq ds cjkcj gSA ,d rRo ds ijek.kq ds ukfHkd esa mifLFkr U;qVªku rFkk izksVksuks dh la[;k dk ;ksx] nzO;eku la[;k dgykrh gSA ,d rRo ds mnklhu ijek.kq esa izksVksu ;k bySDVªkWuksa dh dqy la[;k ijek.kq la[;k dgykrh gSA
Q.1
,d rRo ds ,d ijek.kq es a 10 bys D Vª k u] 10 iz k s V ks u rFkk 12 U;q V ª k u gS A rRo dk ijek.kq nz O ;eku gS – (a) 32 (c) 44
(b) 22 (d) 20
Q.2
The fluorescence on the walls of discharge tube is due to (Cathode ray experiment) – (a) Cathode rays (b) X-rays (c) γ−rays (d) None of the above
Q.2
foltZu uyh dh fnokjksa ij izfrfnIrh dk dkj.k gS (dSFkksM+ fdj.k ifj{k.k esa) – (a) dSFkksM (b) X-fdj.ks (c) γ−fdj.ksa (d) buesa ls dksbZ ugha
Q.3
The charge carried by an electron is – (a) 1.602 × 10–7 coulombs (b) 1.602 × 10–9 coulombs (c) 1.602 × 10–19 coulombs (d) 1.76 × 10–11 coulombs The addition of a neutron to the nucleus of an atom results in – (a) increase in nuclear charge (b) increase in atomic mass (c) formation of an isobar (d) none of above
Q.3
,d bySDVªku dk vkos'k gS – (a) 1.602 × 10–7 dqyke (b) 1.602 × 10–9 dqyke (c) 1.602 × 10–19 dqyke (d) 1.76 × 10–11 dqyke
Q.4
,d ijek.kq ds ukfHkd esa ,d U;qVªku dks tksMus ds ifj.kke Lo:i – (a) ukfHkdh; vkos'k ck gqvk pwuk
Q.21 The NH3 molecule has – (a) no lone pairs (b) one lone pair (c) two lone pairs (d) three lone pairs
Q.21 NH3 v.kq j[krk gS – (a) dksbZ ,dkdh ;qXe ugha (c) nks ,dkdh ;qXe
(b) ,d ,dkdh ;qXe (d) rhu ,dkdh ;qXe
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
Q.22 Which of the following properties is different for solids, liquids and gases ? (a) movement of molecules (b) particle size of the substance (c) mass of substance (d) energy exchanges
Q.22 fuEu esa ls dkSulk xq.k Bkslks] nzoks rFkk xSlks esa fHkUu&fHkUu gS? (a) v.kqvksa dh xfr (b) inkFkZ ds d.k dk vkdkj (c) inkFkZ dk nzO;eku (d) ÅtkZ fofue;
Q.23 Which of the following electronic configuration is wrong? (a) Be(3) = 2, 1 (b) O(8) = 2, 6 (c) S(16) = 2, 6, 8 (d) P(15) = 2, 8, 5
Q.23 fuEu es ls dkSulk bySDVªkfud foU;kl xyr gS ? (a) Be(3) = 2, 1 (b) O(8) = 2, 6 (c) S(16) = 2, 6, 8 (d) P(15) = 2, 8, 5
Q.24 Which of the following solvent will dissolve an ionic compound – (a) Benzene (b) Cyclohexane (c) Water (d) Ether
Q.24 fuEu es ls dkSulk foyk;d ,d vk;fud ;kSfxd dks ?kksysxk– (a) csUthu
(b) lkbDyks gsDlsu
(c) ty
(d) bZFkj
Q.25 ijek.kq la[;k 15 okyk rRo gS – (b) }hla;ksth (a) ,d la;ksth (c) f=la;ksth (d) prq% la;ksth
Q.25 The element with atomic number 15 is – (a) monovalent (b) bivalent (c) trivalent (d) tetravalent Q.26 The acidity and alkalinity of a compound is represented on a scale known as – (a) pH scale (b) Hess's scale (c) Kelvin scale (d) none of these
Q.26 ,d ;kSfxd dh vEyh;rk rFkk {kkjdrk dks ,d iSekus ls iznf'kZr djrs gS tks dgykrk gS– (a) pH Ldsy (b) gSl Ldsy (c) dsfYou Ldsy (d) buesa ls dksbZ ugha
Q.27 CuSO4 solution will turn – (a) Red litmus blue (b) blue litmus red (c) phenolphthalein (d) NaOH solution yellow
Q.27 CuSO4 foy;u ifjofrZr djsxk – (a) yky fyVel dks uhys esa (b) uhys fyVel dks yky esa (c) fQukY¶Fksyhu (d) NaOH foy;u dks ihyk Q.28 Vsfjyhu cgqyd gS – (a) ,d vekbM dk (c) ,d bZFkj dk
Q.28 Terylene is a polymer of – (a) an amide (b) an ester (c) an ether (d) acetylide
Q.29 Q.29 The purest form of C is – (a) diamond (b) wood charcoal (c) coal (d) coffee
dkcZu dk 'kq¼re :i gS – (a) ghjk (c) dks;yk
Q.30 In which of the following process CO2 is not emitted– (a) Respiration (b) Combustion (c) burning coke in air (d) Photosynthesis
(b) ,d ,LVj dk (d) ,flfVykbM
(b) ydMh dk pkjdksy (d) dkWQh
Q.30 fuEu esa ls fdl izØe esa CO2 ugha fudyrh gS – (a) 'olu (b) ngu (c) dks;ys dks ok;q esa tykuk (d) izdk'k la'ys"k.k
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
PART : 3 MATHEMATICS Each correct answer carries three marks. Passage 1.(Q.No. 1 to 5) We define a set as a collection of well defined objects, known as elements. A set containing a finite number of elements is called a finite set, otherwise it is called an infinite set. Let A and B are two sets. Then (i) Difference A – B = {x: x ∈ A, x ∉ B} (ii) Cartesian product A × B = ((a, b): a ∈ A, b ∈ B) n (A × B) = n(A) · n(B) A relation R from A to B is a non-empty subset of A × B. It is called a ‘function’ if every element of A is related to some unique element of B. A relation ƒ from A to B is called a function from A to B if no two ordered pairs of the relation have the same first component. On the basis of above passage answer the following questions:Q.1
Q.2
Q.3
izR;sd lgh mÙkj ds 3 vad fu/kkZfjr gSa x|ka'k 1.(iz- l- 1 ls 5) ge ,d leqPp; dks ifjHkkf"kr djsaxs tks fd lqifjHkkf"kr oLrqvksa] ftUgs vo;o dgrs gSa] dk laxzg.k gSA ,d leqPp; tks lhfer la[;k esa vo;o j[krk gS ifjfer leqPp; dgykrk gS] ugha rks ;g ,d vifjfer leqPp; dgykrk gSA ekuk A rFkk B nks leqPp; gSa] rks (i) vUrj A – B = {x: x ∈ A, x ∉ B} A × B = ((a, b): a ∈ A, b ∈ B) (ii) dkrhZ; xq.ku n (A × B) = n(A) · n(B) A ls B esa ,d laca/k R, A × B dk ,d vfjDr mileqPp; gksrk gSA ;g ^Qyu^ dgykrk gS ;fn A dk izR;sd vo;o] B ds ,d vf}rh;
vo;o ls lacaf/kr gksA A ls B esa ,d laca/k ƒ, A ls B esa Qyu dgykrk gS ;fn
laca/k ds dksbZ Hkh nks Øfer ;qXe leku izFke vo;o u j[krs gksaA fuEu x|ka'k ds vk/kkj ij fuEufyf[kr iz'uksa ds mÙkj nhft,:-
If A = {1, 2, 3}, B = {1, 2, 3, 4},then A– B is equal to– (a) {4} (b) φ (c) {1, 2, 3, 4} (d) None of these
Q.1
If A = {0}, the number of elements in A × A is – (a) 0 (b) 1 (c) 2 (d) 3
Q.2
Which one of the following graphs represents a function from A to B ?
Q.3
;fn A = {1, 2, 3}, B = {1, 2, 3, 4},rks A– B cjkcj gSa – (a) {4} (c) {1, 2, 3, 4}
(b) φ (d) buesa ls dksbZ ugha
;fn A = {0}, rks A × A esa vo;oksa dh la[;k gS – (a) 0
(b) 1
(c) 2
(d) 3
fuEu esa ls dkSulk ys[kkfp= A ls B esa ,d Qyu dks iznf'kZr djrk gS ?
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FOUNDATION COURSE FOR IIT-JEE Q.4
Which of the following sets is finite ? (a) The set of the people living on earth (b) The set of natural numbers (c) The set of real numbers (d) None of these
Q.5
A relation from A to B is – (a) a subset of A × B (b) a superset of A × B (c) equal to A × B (d) not associated to A×B
Following Questions are not based on passage : (Each correct answer carries three marks) Q.6 Four triangles are formed by joining the midpoints of the three sides of a triangle, then –
SAMPLE TEST PAPER
Q.4
fuEu esa ls dkSu lk leqPp; ifjfer leqPp; gS ? (a) i`Foh ij jgus okys O;fDr;ksa dk leqPp; (b) izkd`r la[;kvksa dk leqPp; (c) okLrfod la[;kvksa dk leqPp; (d) buesa ls dksbZ ugha
Q.5
A ls B esa ,d laca/k – (a) A × B dk ,d mileqPp; gSA (b) A × B dk ,d vf/k leqPp; gSA (c) A × B ds cjkcj gSA (d) A × B ls lacaf/kr ugha gSA
fuEu iz'u x|ka'k ij vk/kkfjr ugha gS : (izR;sd lgh mÙkj ds 3 vad fu/kkZfjr gS) Q.6
,d f=Hkqt dh rhu Hkqtkvksa ds e/; fcUnqvksa dks tksMdj pkj f=Hkqt cuk, x, gS] rks – (a) nks f=Hkqt lokZaxle gksaxs (b) rhu f=Hkqt lokZaxle gksaxs (c) lHkh lok±xle gksaxs (d) dksbZ lok±xle ugha gksxk
Q.7
layXu fp= esa] lHkh dks.kksa dk ;ksx K ledks.kksa ds cjkcj gS] rks K cjkcj gS –
(a) Two triangles are congruent (b) Three triangles are congruent (c) All are congruent (d) None are congruent Q.7
In the adjoining figure, the sum of all the angles is equal to K right angles. K is equal to –
(a) 10 (c) 14
Q.8
(b) 12 (d) 16
(a) 10 (c) 14
ƒ(x) = | x – 100 |, x∈R. The minimum value of ƒ(x) is– (a) 0 (b) 100 (c) 1000
Q.8
(d) not defined
(b) 12 (d) 16
ƒ(x) = | x – 100 |, x ∈ R, rks ƒ(x) dk U;w u re eku gS – (a) 0 (b) 100 (c) 1000 (d) vifjHkkf"kr
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FOUNDATION COURSE FOR IIT-JEE Q.9
In the figure given below, find ∠QSR.
(a) 50° (c) 70°
SAMPLE TEST PAPER
Q.9
(b) 65° (d) 75°
fn, x, fp= esa ∠QSR gS &
(a) 50° (c) 70°
(b) 65° (d) 75°
Q.10 The sum of the squares of two consecutive even numbers is two more than two times the squares of their mean. This statement is – (a) never true (b) always true (c) true when the numbers are more than 100 (d) true when the numbers are less than or equal to 100
Q.10 nks Øekxr le la[;kvksa ds oxksZa dk ;ksx muds ek/; ds oxZ ds nksxqus ls nks vf/kd gksrk gSA ;g dFku– (a) dHkh lR; ugha gks ldrk (b) lnSo lR; gSA
Q.11 LCM of three numbers x, y, z is w. Then LCM of numbers y, z, w will be – (a) y (b) w (c) z (d) None of these
Q.11 rhu la[;kvksa x, y, z dk y-l-i w gS] rks la[;kvksa y, z, w dk y-l-i- gksxk – (a) y (b) w (c) z (d) buesa ls dksbZ ugha
Q.12 The equation 3y2 + y + 4 = 2 (6x2 + x + 2) where y = 2x, is satisfied by – (a) no value of x (b) all real values of x (c) x = 2 only (d) None of these
Q.12 lehdj.k 3y2 + y + 4 = 2 (6x2 + x + 2) tgk¡ y = 2x (a) x ds fdlh eku ls larq"V ugha gksrh (b) x ds lHkh okLrfod ekuksa ls larq"V gksrh gS (c) dsoy x = 2 ls larq"V gksrh gS (d) buesa ls dksbZ ugha
Q.13 A can do a piece of work in 15 days. B is 50% more efficient than A. A and B together will finish the same piece of work in – (a) 6 days (b) 9 days (c) 10 days (d) 12½ days
Q.13 A ,d dk;Z ds ,d Hkkx dks 15 fnuksa esa iwjk dj ldrk gSA B, A ls 50% vf/kd dq'ky gSA A rFkk B dk;Z ds Hkkx dks ,d lkFk iwjk djsaxs – (a) 6 fnuksa esa (b) 9 fnuksa esa (c) 10 fnuksa esa (d) 12½ fnuksa esa
Q.14 A wire of length 50 cm is to be bent in the form of a parallelogram of area 50 cm2. Determine its dimensions if the angle between two adjacent sides is 30° (a) 20 cm, 5 cm (b) 15 cm, 10 cm (c) 13 cm, 12 cm (d) 17 cm, 8 cm
Q.14 ,d 50 cm yEck rkj ,d lekUrj prqHkqZt ftldk {ks=Qy 50 cm2 gS] ds :i esa eksM+k x;k gSaA ;fn nks vklUu Hkqtkvksa ds e/; 30° dk dks.k gks] rks vklUu Hkqtk,¡ gksaxh & (a) 20 cm, 5 cm (b) 15 cm, 10 cm (c) 13 cm, 12 cm (d) 17 cm, 8 cm
(c) lR; gksxk tc la[;k,as100 ls vf/kd gksaA (d) lR; gksxk tc la[;k,sa ≤ 100 gksa
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FOUNDATION COURSE FOR IIT-JEE Q.15 Find the value of x in the given figure –
(a) 30° (c) 40° Q.16 If cos θ + sin θ = to– (a) 2 sin θ (c)
SAMPLE TEST PAPER
Q.15 fn, x, fp= esa x dk eku Kkr dhft, –
(a) 30° (c) 40°
(b) 35° (d) 45° 2 cos θ, then cos θ – sin θ is equal
2 – 1
(b)
2
(d)
2 + sin θ
(b) 35° (d) 45°
Q.16 ;fn cos θ + sin θ = 2 cos θ,rks cos θ – sin θ cjkcj gS – (a)
2 sin θ
(b)
2
(c)
2 –1
(d)
2 + sin θ
Q.17 What percent of 8.25 m is 75 cm ? (a) 150/11% (b) 75/11% (c) 80/11% (d) 100/11%
Q.17 8.25 m dk fdruk izfr'kr 75 cm gS ? (a) 150/11% (b) 75/11% (c) 80/11% (d) 100/11%
Q.18 Which of the following represents the shaded portion in the figure ? y
Q.18 fuEu esa ls dkSu Nk;kafdr fp= dks iznf'kZr djrk gS ? y
O
O
x
x ≤ 0 y ≤ 0
(b)
x < 0 y ≤ 0
(d)
x ≤ 0 (a) y ≤ 0
x ≤ 0 (b) y < 0
(a)
x < 0 (c) y ≤ 0
x < 0 (d) y < 0
(c)
Q.19 The roots of the equation 2kx2 + 5kx + 2 = 0 are equal if k is equal to – (a) 0 (b) 1 (c) 4/5 (d) 16/25
x
x ≤ 0 y < 0
x < 0 y < 0
Q.19 lehdj.k 2kx2 + 5kx + 2 = 0 ds ewy leku gksaxs ;fn k fuEu ds cjkcj gks – (a) 0 (b) 1 (c) 4/5 (d) 16/25
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FOUNDATION COURSE FOR IIT-JEE Q.20 sec2θ =
4 xy ( x + y)
2
SAMPLE TEST PAPER
Q.20 sec2θ =
is true, –
( x + y )2
lR; gksxk –
(a) tc x = y (b) tc x < y (c) tc x > y (d) x rFkk y ds izR;sd eku ds fy,
(a) when x = y (b) when x < y (c) when x > y (d) for every value of x and y
Q.21
4 xy
cot A + cos ecA − 1 is equal to – cot A − cosecA + 1
Q.21
cot A + cos ecA − 1 cot A − cosecA + 1
cjkcj gS –
1+ sin A (a) cos A
1+ cos A (b) sin A
(a)
1+ sin A cos A
(b)
1+ cos A sin A
sin A (c) 1 + cos A
1− cos A (d) sin A
(c)
sin A 1 + cos A
(d)
1− cos A sin A
Q.22 tan 50° – tan 40° is equal to – (a) tan 10° (b) 2 tan 10° (c) 1 (d) 2
Q.22 tan 50° – tan 40° cjkcj gS – (a) tan 10° (b) 2 tan 10° (c) 1 (d) 2
Q.23 If ƒ(x) = tan2 x + cot2 x, the minimum value of ƒ(x)is– (a) 0 (b) 1 (c) 2 (d) not defined
Q.23 ;fn ƒ(x) = tan2 x + cot2 x,rks ƒ(x) dk U;wure eku gS – (a) 0 (b) 1 (c) 2 (d) vifjHkkf"kr
Q.24 In this figure, which one is true ?
Q.24 fuEu fp= esa dkSu lk lR; gS ?
(a) (b) (c) (d)
(a) Ar∆(APS) = Ar∆(QRB) (b) PA = RB (c) Ar(PQS) = Ar (QRS) (d) mijksDr lHkh
Ar∆(APS) = Ar∆(QRB) PA = RB Ar(PQS) = Ar (QRS) all of these
Q.25 The value of
(0.6)0 − (0.1)−1 1 ( 3 / 2 ) ( 3 / 2) + − 3 3 −1
(a) 3/2
(b) –3/2
3
(c) 2/3
−1
Q.25
is –
(0.6)0 − (0.1)−1 1 ( 3 / 2 ) ( 3 / 2) + − 3 3 −1
(d) –1/2
(a) 3/2
3
(b) –3/2
−1
dk eku gS –
(c) 2/3
(d) –1/2
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FOUNDATION COURSE FOR IIT-JEE Q.26 The sum and difference of a number and its reciprocal are in the ratio 13:5. The number is – (a)
3 2
(b)
3+ 2
Q.27 If x = (a)
(c)
3− 2 5 6 −4 6 −4 5
9 4
(c)
4 5
(d)
and y = 1, the value of (b)
(d)
SAMPLE TEST PAPER
Q.26 ,d la[;k rFkk mlds O;qRØe dk ;ksx rFkk vUrj 13:5 ds vuqikr esa gS] rks la[;k gS–
25 16
(a)
x−y is – x − 3y
3 2
(b)
Q.27 ;fn x =
5
(a)
6 +4 6 +4 5
(c)
3+ 2 3− 2
9 4
(c)
rFkk y = 1, rks
5
(b)
6 −4 6 −4 5
(d)
4 5
(d)
x−y x − 3y
25 16
dk eku gS –
5 6 +4 6 +4 5
Q.28 If n is a whole number greater than 1, then n2(n2 –1) is always divisible by – (a) 12 (b) 24 (c) 12 and 24 (d) 36
Q.28 ;fn n,1 ls cMh ,d iw.kZ la[;k gS] rks n2(n2 –1) lnSo fuEu ls foHkkftr gksxk – (a) 12 (b) 24 (c) 12 rFkk 24 (d) 36
Q.29 What should be added to 1516 to make it divisible by 16 ? (a) 0 (b) 1 (c) 7 (d) 15
Q.29 1516 esa D;k tksMk tk, fd ;g 16 ls foHkkftr gks ? (a) 0 (b) 1 (c) 7 (d) 15
Q.30 If tan x = (a) 0° (c) 60°
1 , then x is 2 sin 60 °
Q.30 ;fn tan x = (a) 0° (c) 60°
(b) 30° (d) 90°
1 , 2 sin 60°
rks x gS (b) 30° (d) 90°
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
PART : 4 LOGICAL APTITUDE In each part of this question, four alternatives are given of which only one is correct. Select the correct alternative and write down the corresponding letter a, b, c, or d in your answer sheet against the question number : [10 x 3 = 30] Q.1
Q.2
Q.3
Q.4
Q.5
bl iz'u ds izR;sd Hkkx esa pkj fodYi fn;s x;s gSaA ftuesa ls flQZ ,d lgh gSA lgh fodYi pqfu;s vkSj mÙkj esa iz'u la[;k ds lEeq[k lacaf/kr v{kj a, b, c ;k d vafdr dhft,A [10 x 3 = 30]
Find the missing term in the following series : 2, 3, 5, 7, 11, ..........., 23 (a) 12 (b) 13 (c) 14 (d) 15
Q.1
Find the missing term in the following series : 6, 9, 18, 21, 42, 45, ......... (a) 93 (b) 90 (c) 98 (d) 96
Q.2
The following question are based on the letter series. In each series some letters are missing. The letters in the series are arranged in a proper sequence. Find the sequence and encircle the correct group of letters given in the choice − bcb − c − − cb − c (a) bbbbb (b) bccbc (c) ccbcb (d) cccbc
Q.3
In the following section, each question consists of five sets of group of letters in which one is different from the other four. Find the one which is different (a) REWSNA (b) ESICREXE (c) ELPMAXE (d) STUVGHI If FLOWER is coded GMPXFS, then GARDEN is coded as (a) HSBFEO (b) HBSEFO (c) ICTFGP (d) NEDRAG
Q.4
fjDr in Kkr dhft, & 2, 3, 5, 7, 11, ..........., 17 (a) 12 (c) 14
(b) 13 (d) 5
fjDr in Kkr dhft, 6, 9, 18, 21, 42, 45, ......... (a) 93 (b) 90
(c) 98
(d) 96
;g iz ' u v{kjks a dh fo'ks " k Js . kh ij vk/kkfjr gS A iz R ;s d Js . kh es a dq N v{kj fjDr gS A v{kj ,d fuf'pr Js . kh es a tes a gq , gS A fjDr inks a dh Js . kh Kkr djks & − bcb − c − − cb − c
(a) bbbbb
(b) bccbc
(d) cccbc
izR;sd iz'u esa ikap 'kCnkssa ds lewg fn;s x;s gSA buesa ls ,d lewg vU; pkjksa ls fHkUu gS rks fHkUu lewg gksxk & (a) REWSNA (c) ELPMAXE
Q.5
(c) ccbcb
(b) ESICREXE (d) STUVGHI
;fn FLOWER dks fy[kk tkrk gS GMPXFS, rks GARDEN dks fy[kk tk;sxk & (a) HSBFEO (c) ICTFGP
(b) HBSEFO (d) NEDRAG
Q.6
Q.6
bl fp= esa fdrus "kVHkqt gS & The number of hexagons in the above diagram is (a) 0 (b) 1 (c) 2 (d) 3
(a) 0
(b) 1
(c) 2
(d) 3
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
uhps fn, x, fp= dk /;kuiw o Z d v/;;u djrs gq , fuEu iz ' uks a ds mRrj nhft, (Q.7 to Q.9)
Study the following figure and choose the correct answer of the following question (Q.7 to Q.9)
Q.7
Q.8
Q.9
The number of parallelograms in the above figure is (a) 6 (b) 7 (c) 8 (d) 9
Q.7
The number of triangles in the figure above is (a) 10 (b) 12 (c) 14 (d) 16
Q.8
The number of pentagons in the above figure is (a) 3 (b) 4 (c) 5 (d) 6
Q.9
fn;s x;s fp= esa fdrus lekUrj prqHkqZt gksxs & (a) 6 (c) 8
fn;s x;s fp= esa fdrus f=Hkqt gksxs & ((a) 10 (c) 14
Q.10 The following question is based on sets of numbers in a certain order or logic. Candidates are required to find out a similar set from the choice which corresponds to the set given in the question The given set is (4 , 16, 36) (a) (8,13, 18) (b) (7,12, 15) (c) (5, 10, 15) (d) (15, 24, 35)
(b) 7 (d) 9
(b) 12 (d) 16
fn;s x;s fp= esa fdrus iapHkqt gksxs & (a) 3 (c) 5
(b) 4 (d) 6
Q.10 bl iz'u esa fn;s x;s lewg dh rhuksa la[;k,sa ,d fuf'pr Øe esa gSA
ml ;qXe dk irk yxkb;s ftldk Øe fn;s x;s lewg ds Øe dh rjg gSA fn;k x;k Øe gS (4 , 16, 36) (a) (8,13, 18) (c) (5, 10, 15)
(b) (7,12, 15) (d) (15, 24, 35)
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
ST AND ARD ANSWER KEY STAND ANDARD SAMPLE TEST PAPER
PHYSICS Q.1 (d)
Q.2 (a)
Q.3 (a)
Q.4 (a)
Q.5 (b)
Q.6 (c)
Q.7 (c)
Q.8 (a)
Q.9 (d)
Q.10 (b)
Q.11 (b)
Q.12 (c)
Q.13 (c)
Q.14 (c)
Q.15 (a)
Q.16 (b)
Q.17 (a)
Q.18 (d)
Q.19 (c)
Q.20 (a)
Q.21 (a)
Q.22 (a)
Q.23 (b)
Q.24 (c)
Q.25 (b)
Q.26 (d)
Q.27 (c)
Q.28 (d)
Q.29 (a)
Q.30 (c)
CHEMISTRY Q.1 (b)
Q.2 (a)
Q.3 (c)
Q.4 (b)
Q.5 (b)
Q.6 (a)
Q.7 (c)
Q.8 (a)
Q.9 (a)
Q.10 (d)
Q.11 (c)
Q.12 (c)
Q.13 (c)
Q.14 (c)
Q.15 (c)
Q.16 (a)
Q.17 (c)
Q.18 (a)
Q.19 (c)
Q.20 (d)
Q.21 (b)
Q.22 (a)
Q.23 (c)
Q.24 (c)
Q.25 (c)
Q.26 (a)
Q.27 (b)
Q.28 (b)
Q.29 (a)
Q.30 (d)
MA THEMA TICS MATHEMA THEMATICS Q.1 (d)
Q.2 (b)
Q.3 (c)
Q.4 (a)
Q.5 (a)
Q.6 (c)
Q.7 (d)
Q.8 (a)
Q.9 (b)
Q.10 (b)
Q.11 (b)
Q.12 (b)
Q.13 (a)
Q.14 (a)
Q.15 (a)
Q.16 (a)
Q.17 (d)
Q.18 (a)
Q.19 (d)
Q.20 (a)
Q.21 (b)
Q.22 (b)
Q.23 (c)
Q.24 (d)
Q.25 (b)
Q.26 (a)
Q.27 (d)
Q.28 (a)
Q.29 (d)
Q.30 (b)
Q.5 (b)
Q.6 (b)
Q.7 (d)
LOGICAL APTITUDE Space for Rough Work
Q.1 (b)
Q.2 (b)
Q.3 (a)
Q.8 (c)
Q.9 (d)
Q.10 (d)
Q.4 (d)
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FOUNDATION COURSE FOR IIT-JEE
SAMPLE TEST PAPER
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