IIT JEE 2010 6th Test Series Paper 1 P a g e | 1 www.vidyadrishti.com An educational portal for future IITians by current IITians IIT‐JEE 2010 6th Test Series PAPER 1 21st Feb 2010 to 7th March 2010 from www.vidyadrishti.com An educational portal for future IITians by current IITians Send your feedback to www.vidyadrishti.com/feedback.php IIT JEE 2010 6th Test Series Paper 1 P a g e | 2 www.vidyadrishti.com An educational portal for future IITians by current IITians IIT JEE 2010 6th Test Series Paper 1 P a g e | 3 www.vidyadrishti.com An educational portal for future IITians by current IITians Physics Paper 1 Section I Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices for its answer, out of which ONLY ONE is correct. 1. A particle is initially at rest at the top of a curved frictionless track. The x‐and y‐coordinates of the track are related in dimensionless units by 2 , 4 y x where the positive y‐axis is in the vertical downward direction. As the particle slides down the track, what is its tangential acceleration? (a) 0 (b) g (c) gx/2 (d) 2 . 4 gx x 2. A block is kept on the floor of an elevator of height 50 cm at rest. The elevator starts descending with an acceleration 12m/s2 . Find the displacement of the block during the first 0.2 s after the start. Take g10 cm/s2. (a) 20 cm (b) 24 cm (c) 44 cm (d) 4 cm 3. A body starts rolling drawn an inclination . The speed of the centre of mass is found to be v when it has covered distance l. Here 10 sin 7 v gl . The body is a (a) sphere (b) disc (c) ring (d) cylinder O y x Track IIT JEE 2010 6th Test Series Paper 1 P a g e | 4 www.vidyadrishti.com An educational portal for future IITians by current IITians 4. A liquid is contained in a vertical tube of uniform semicircular cross section. The contact angle is zero. The forces of surface tension on the curved part and on the flat part are in ratio. (a) : 2 (b) 2: (c) 1:2 (d) 1:1 5. If starting from the position drawn in figure, the loop is pulled rightward with constant velocity, all the way through the magnetic field of width d (d > L) then. Which graph best shows the magnetic flux through the rectangle as a function of time? (a) (b) (c) (d) d L m Magnetic field 0 flux time 0 flux time 0 flux time 0 flux time IIT JE www6 78EE 2010 6th Te w.vidyadrisht 6. A horizon strikes a angle thr (a) 1 (b) 2 (c) 3 (d) 4 7. A star ini 2 1 1 2 1 1 H H H H If the ave 2 1 M H M(n) 1 the orde (a) 106 se (b) 108 se (c) 1012 s (d) 1016 s 8. When lig graph of a) The v veloc b) The v veloc c) The c d) The c est Series Pa i.com ntal ray of lig vertical mirr rough which tially has 10 2 3 1 3 4 2 H He erage power 2.014 a.m 1.008 a. m. u r of ec ec sec sec. ght is inciden sin i versus velocity of lig city of light in velocity of lig city of light in critical angle critical angleper 1 An ght passes th ror M as sho the mirror s 040 deuterons pn r radiated by m.u., M(p) u, M(He4) nt on a medi s sin r is as s ght in secon n the first m ght in the fir n second me e of the two e of the two educational p hrough a pri own in the fi should be ro s. It produce y the star is 1.007 a.m.u 4.001a. m. um at angle hown. From d medium is medium rst medium i edium media is giv media is giv portal for fut ism of refrac gure. In orde otated is es energy via 1016W and m u. u. the deute i and refra m this one ca s 3 times t is 3 times t en by sin c i en by sin c i ture IITians by ctive index 1 er to have to a the proces masses of nu eron supply cted into a s n conclude t he the 13 1 . 2 P a g current IIT 1.5 whose ap otal deviatio ses. uclei are as f of the star i second med that 4e | 5 Tians pex angle is on equal to 1 follows. s exhausted ium at an an δδδ 4 and then 180 the in a time of ngle r , the M f IIT JEE 2010 6th Test Series Paper 1 P a g e | 6 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JE www This s MOR9111EE 2010 6th Te w.vidyadrisht section conta RE is/are corre 9. An ideal along a s a) The w taken b) In the c) In the d) In go decre 10. A block o friction b wall. Cho (a) The b (b) The b (c) Fricti (d) Fricti 11. Water flo sections through A (a) The s (b) The s (c) The s (d) The p 12. Two ide simultan unchange be said th (a) 2 T wa (b) 2 T wa (c) 1 T wa (d) 1 T waest Series Pa i.com ains 4 multipl ect. gas is taken traight line p work done b n from A to B e T‐V diagram e P‐T diagram oing from A eases. of mass 2 k being 0.5. An oose the cur block will no block will mo on force exc on force act ows through at A and B A, then choo speed of wat speed of wat speed of wat pressure diff ntical straig eously. On ed. Denoting hat while ma as decreased as increased as increased as decreasedper 1 An e choice ques from the sta path in the P y the gas in along the i m, the path m, the path to B, the t kg is pushed nother horiz rent option/t move ove ceeds net ap ts at an angle h a horizont are 4mm ose the curre ter at A is 25 ter at B is 50 ter at A = the ference A p ght wires ar changing t g by 1 T and aking the ab d d d. educational p SE Multiple C stions. Each q ate A (press PV diagram. the process isotherm. AB becomes AB becomes emperature d against a r ontal force /s. pplied force e 127 with 1 tal tube of v m2 and 2mm ent option/s 5cm/s 0 cm/s e speed of w B p zero re stretched the tension 2 T , the high bove change portal for fut ECTION II orrect Choic question has f ure P, volum Select the c A to B exce s part of a p s part of a hy e T of the g rough vertic of 15 N is ap by 5 N. 15 N force. variable cros m2 respective s. water at B = d so as to n slightly in her and the l s in tension ture IITians by ce Type four choices f me V) to the correct state eds the wor arabola. yperbola. as first incr cal wall with pplied on th ss section as ly. If 1 cub 25 cm/s produce 6 n one of th ower initial P a g current IIT for its answer state B (pre ement(s) from rk done by it eases to ma h a force 40 e block in a s shown in f ic cm of w beats per hem the b tensions in t e | 7 Tians r, out of whic ssure P/2, vo m the follow if the system aximum valu 0 N, coeffici direction pa figure. The a ater enters second wh eat frequen the strings, t ch ONE OR olume V/2) wing. m were ue and then ent of static arallel to the area of cross per second en vibrating ncy remain then it could n c e s d g s d IIT JEE 2010 6th Test Series Paper 1 P a g e | 8 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 9 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Comprehension Type This section contains 2 group of questions. Each group has three multiple choice questions based on a paragraph. Each question has four choices for its answer, out of which ONLY ONE is correct. Comprehension for questions 13‐15 Two points charges are placed at point a and b. The field strength to the right of the charge b Q on the line that passes through the two charges varies according to a law that is represented graphically in the figure. The electric field is taken positive if its direction is towards right and negative if its direction is towards left. 13. Choose the correct statement regarding the signs of the charges (a) Charge at point a is positive and charge at point b is negative (b) Charge at point a is negative and charge at point b is positive (c) Both charges are positive (d) Both charges are negative. 14. Ratio of magnitudes of charges ab QQ will be equal to (a) 1 1 l x (b) 2 1 1 l x (c) 2 1 1 l x (d) 4 1 1 l x E 1 x a b l 2 x xIIT JEE 2010 6th Test Series Paper 1 P a g e | 10 www.vidyadrishti.com An educational portal for future IITians by current IITians 15. The distance 2 x from point b where the field is maximum, will be (a) 2/3 1 1 1 l l x x (b) 1/3 1 1 1 l l x x (c) 2/3 1 12 1 l l x x (d) 1/3 1 12 1 l l x x SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 11 www.vidyadrishti.com An educational portal for future IITians by current IITians Comprehension for questions 16‐18 In the figure, light of wavelength 0 5000A is incident on the slits (in a horizontal fixed plane). Here d = 1mm, D = 1 m. O is the mid point of S1S2. Take origin at O and XY plane as shown in figure. The screen is released from rest at t = 0 from rest from the initial position as shown. Take g = 10 m/s2. Answer the following questions based on this passage. 16. The velocity of central maxima at t = 5s is a) 50 m/s along positive Y‐axis b) 50 m/s along negative Y‐axis c) 25 m/s along positive Y‐axis d) 3 x 108 m/s along positive Y‐axis 17. Velocity of 2nd maxima w.r.t., to central maxima at t = 2s is a) 8 cm /si20 m /sj b) 8 cm /s i c) 2 cm/s i d) 86 cm /s i 18. Acceleration of 3rd maxima w.r.t. 3rd maxima on other side of central maxima at t = 3s, is a) 2 0.02 m /s i b) 2 0.03 m /s i c) 10 m /s2 j d) 2 0.06 m /s i d Y S1 X D O S2 Screen IIT JEE 2010 6th Test Series Paper 1 P a g e | 12 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 13 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION IV Matrix Match Type 19. Match the following Column I Column II (a) W p dv (p) Isothermal process (b) 1 1 2 2 1 W pv pv (q) Adiabatic process (c) W Q (r) Isochoric process (d) WU (s) Isobaric process (t) Reversible process SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 14 www.vidyadrishti.com An educational portal for future IITians by current IITians 20. Match the following . Column I Column II (a) Frequencies of K X‐rays of different materials are observed. Plot between the frequency Y (y‐axis) and the atomic number Z (x‐axis). (p) (b) Let n A be the area enclosed by the nth orbit in a hydrogen atom. Plot of 1 ln n AA against ln n. (q) (c) The curve which may represent speed of the electron in a hydrogen atom as a function of the principle quantum number n. (r) (d) Half time 1/2 t vs. 1/(decay constant) i.e. 1 (s) (t) tan θ=4 θ Y θ tanθ = ln2. IIT JEE 2010 6th Test Series Paper 1 P a g e | 15 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 16 www.vidyadrishti.com An educational portal for future IITians by current IITians Chemistry Paper 1 SECTION I Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices for its answer, out of which ONLY ONE is correct. 1. A hypothetical reaction : 2 A + 2 B 2AB follows following mechanism as follows: A2 Kc A + A..........(fast) kc is equilibrium constant A + B2 K1 AB + B..(slow) k1 is rate constant A + B 23 kk AB..........fast k2 , k3 are rate constant The order of overall reaction is (a) 2.5 (b) 1 (c) 3/2 (d) zero 2. The spontaneous redox reaction(s) among the following is/are (a) 2Fe3 + Fe → 3Fe2 (b) 2 Hg Hg + Hg (c) 3AgCl +NO +2H20 3Ag +3Cl‐ + 3 NO +4H+ Given that : 3/2 oFe Fe E = 0.77V 2 /oFe Fe E = ‐0.44V 22 /oHg Hg E = 0.85V 2 2/2 oHg Hg E = 0.92 /o 0.22 AgCl Ag E V 3 /oNO NO E = 0.96 (A) a (B) a, b, c (C) a, b (D) a, c SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 17 www.vidyadrishti.com An educational portal for future IITians by current IITians 3. Which of the following statement(s) is true for the given species? N2, CO, CN‐and NO+ . (A) All species have linear shape. (B) All species have some dipole moment. (C) All species are isoelectronic. (D) All species have identical bond order and are paramagnetic in nature. 4. Which of the following does not react with AgCl? a) Na2S2O3 b) NH4OH c) NaNO3 d) Na3AsO3 5. The thermal decomposition of N2O5 occurs as: 2N2O5→4NO2 +O2 Experimental studies suggests that rate of decomposition of N2O5 ,rate of formation of NO2 ,and the rate of formation of O2 all becomes double if concentration of N2O5 is doubled .If the rate constant of decomposition of N2O5, formation of NO2 and O2 are K1, K2 , K3 respectively, then : (a) K1 = K2 = K3 (0b) 2K1 = K2 = 4K3 (c) K1 = 2K2 = K3 (d) K1 = K2 = 2K3 6. If the rate of formation of O2 is 16g/hr ,then rate of decomposition of N2O5 and rate of formation of NO2 respectively is : (a) cannot be calculated without knowing rate constants . (0b) 108gm/hr , 92gm/hr (c) 32gm/hr , 64gm/hr (d) 54gm/hr , 46gm/hr 7. Compounds I and II can be distinguished by using reagents: I: 4‐Hydroxy‐4‐methylpent‐2‐enoic acid II:5‐Hydroxypent‐2‐ynoic acid (a)NaHCO3 (b) Br2/H20 (c) HCl/ZnCl2(anhydrous) (d) Cu2Cl2/NH4OH 8. Select the correct statements: (A) C‐C single bond in ethene is shorter than ethane . (B) Ethanoic acid is stronger acid than ethanedioic acid. (C) In sodium acetate both the c‐o bond lengths are equal. (D) Stability of ortho‐nitrobenzoate ion is more than ortho‐methyl benzoate ion IIT JEE 2010 6th Test Series Paper 1 P a g e | 18 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION II Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has four choices for its answer, out of which ONE OR MORE is/are correct. 9. In the following reaction: 2SO2(g) + O2 2SO3(g) H=‐10 kcal The equilibrium concentration of SO3 is increased by A) decrease in volume at constant temperature B) increase in volume at constant temperature C) increase in temperature at constant volume D) adding He(g) at constant temperature and volume 10. The container of 2L contains 4mole of N2O5 . On heating to 100OC , N2O5 undergoes complete dissociation to NO2 and O2 .Select the correct answers if rate constant for decomposition for decomposition of N2O5 is 6.3x10‐1sec.(ln2 = 0.693). (a) The mole ratio before and after decomposition is 4:2. (b) Half life of N2O5 is 1100sec and it is independent of temperature. (c) Time required to complete 87.5% of reaction is 55 min. (d) if volume of container is doubled , the rate of decomposition becomes half of the initial rate. 11. Which of the following statements is/are correct for an electron of quantum numbers n=4 and m=2? A) The value of l may be 2 B) the value of l may be 3 C) the only possible value of s is +1/2 D) the value of l may be 0,1,2,3. 12. In the following gaseous phase first order reaction A(g) → 2B(g) + C(g) Initial pressure was found to be 400mm of Hg and is changed to 1000mm of Hg after 20 min . Then (A) Half life for A is 10 min (B) Rate constant is 0.0693min‐1. (C) Partial pressure of C at 30 min is 350mm of Hg (D) Total pressure after 30 min is 1150mm of Hg IIT JEE 2010 6th Test Series Paper 1 P a g e | 19 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Comprehension Type This section contains 2 group of questions. Each group has three multiple choice questions based on a paragraph. Each question has four choices for its answer, out of which ONLY ONE is correct. Comprehension for qs 13‐15 The thermal decomposition of N2O5 occurs as: 2N2O5→4NO2 +O2 Experimental studies suggests that rate of decomposition of N2O5 ,rate of formation of NO2, and the rate of formation of O2 all becomes double if concentration of N2O5 is doubled . 13. If the rate constant of decomposition of N2O5, formation of NO2 and O2 are K1 , K2 , K3 respectively, then : (a) K1 = K2 = K3 (0b) 2K1 = K2 = 4K3 (c) K1 = 2K2 = K3 (d) K1 = K2 = 2K3 14. If the rate of formation of O2 is 16g/hr ,then rate of decomposition of N2O5 and rate of formation of NO2 respectively is : (a) cannot be calculated without knowing rate constants . (b) 108gm/hr , 92gm/hr (c) 32gm/hr , 64gm/hr (d) 54gm/hr , 46gm/hr 15. The container of 2L contains 4mole of N2O5 . On heating to 100OC , N2O5 undergoes complete dissociation to NO2 and O2 .Select the correct answers if rate constant for decomposition for decomposition of N2O5 is 6.3x10‐4 sec‐1.(ln2 = 0.693). (a) The mole ratio before and after decomposition is 4:2. (b) Half life of N2O5 is 1100sec and it is independent of temperature. (c) Time required to complete 87.5% of reaction is 55 min. (d) if volume of container is doubled , the rate of decomposition becomes half of the initial rate. SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 20 www.vidyadrishti.com An educational portal for future IITians by current IITians Comprehension for Qs 16‐18 Calomel electrode: It consists of mercury at the bottom over which a paste of mercury‐mercurous chloride is placed. A saturated solution of potassium chloride is then placed over the paste. A platinum wire sealed in a glass tube helps in making the electrical contact. The electrode is connected with the help of the side tube on the left through a salt bridge with the other electrode to make a complete cell. The potential of the calomel electrode depends upon the concentration of the potassium chloride solution. If potassium chloride solution is saturated,the electrode is known as saturated calomel electrode (SCE) and if potassium chloride solution is 1N , the electrode is known as normal calomel electrode (NCE) while for 0.1N potassium chloride solution , the electrode is referred to as decinormal calomel electrode (DNCE).The electrode reaction when the electrode acts as cathode is : 1/2Hg2Cl2 + 1e Hg + Cl‐1 (given : 2.303RT/F = 0.06) 16. For the calomel half cell, Hg, Hg2Cl2|Cl‐1(aq) values of electrode oxidation potential are plotted at different log[Cl‐1]. Variation is represented by : 17. E.M.F. of the following cell is 0.67 V at 298 K Pt|H2(1 atm)|H+(pH = 6.5)||1N KCl|Hg2Cl2(s),Hg Calculate 2 2 0cl/Hg Cl,Hg E (calomel electrode). (A)0.28 V (B)0.30V (C)0.26V (D)0.4 V 18. For the cell Hg|Hg2Cl2|Cl‐(0.1M)||Cl‐(0.01M)|Pt(Cl2), 2 0 Cl /Cl E = 1.38 (use information from previous question) Hence, Ecell is: (A)1.15V (B)1.13V (C)1.07V (D) ‐1.04V IIT JEE 2010 6th Test Series Paper 1 P a g e | 21 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION IV Matrix Match Type Match the compound of column‐I with the reagent of column‐II which can distinguish the compounds of column‐I Column I Column II (a) Ethyne, acetaldehyde (p) Tollen’s reagent (b) Ortho-nitro phenol, Anisole (q) I2/NaOH (c) 2‐ethanol, acetone (r) Lucas reagent (d) 1‐phenyl ethanol, para ethylphenol (s) Neutral FeCl3 20. Match the following Column I Column II (a) ZnIZnSO4(1M)IIZnSO4(2M)IZn (p) Spontaneous cell reaction (b) Cu|CuCl2(1M)||CuSO4(2M)|Cu (q) Osmotic pressure of cathodic solution is greater than that of anodic solution (c) Ag|AgCl(sat. Sol)|| AgNO3(1M)|Ag (r) At equilibrium condition of the cell, freezing point Of anodic solution is higher than that of cathodic solution (d) Pt|H2|HCOOH|(IM)||HCl(1M)| H2|Pt (s) At equilibrium condition of the cell, boiling point Of cathodic solution is higher than that of anodic solution SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 22 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 23 www.vidyadrishti.com An educational portal for future IITians by current IITians Mathematics Paper 1 SECTION I Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices for its answer, out of which ONLY ONE is correct. 1. Given a triangle whose vertices are at (0, 0), (4, 4) and (10, 0). A square is drawn in it such that its base is on the x‐axis and its two corners are on the 2 sides of the triangle. The area of the square is equal to (a) 400 49 (b) 400 25 (c) 625 16 (d) 625 49 2. The value of integral 1 2 tan 2 1 1 e x x x dx x is 1 1 1 tantan tan (a) e (b) (c) (d) none of these x x xC xe C x e C 3. The area of the smaller region bounded by the circle x2y21 and the lines yx1 is (a) 1 4 2 (b) 1 2 (c) 2 (d) 1 2 IIT JEE 2010 6th Test Series Paper 1 P a g e | 24 www.vidyadrishti.com An educational portal for future IITians by current IITians 4. Sides of a triangle ABC are in A.P. If a min. b,c and c max. a,b , then cos A is equal to (a) 3 4 2 (b) 3 4 2 (c) 4 3 2 (d) 4 3 2 c b b c b c c b b c b c 5. Reflection of the line 1 2 4 1 3 1 x y z in the plane in the xyz 7 is a) 1 2 4 3 1 1 x y z b) 1 2 4 3 1 1 x y z c) 1 2 4 3 1 1 x y z d) 1 2 4 3 1 1 x y z 6. If f(x)(axn)1/n,a0and nN, then fof (x)is a) a b) x c) xn d) an . SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 25 www.vidyadrishti.com An educational portal for future IITians by current IITians 7. If 1 z and z2 are two complex numbers and a,bare real, then 2 2 1 2 1 2 az bz bz az equals a) 2 2 1 2 (ab)(z z ) b) 2 2 2 2 1 2 (a b)z z c) 2 2 1 2 a b z z d) none of these. 8. If a,b,care in A .P, the line axbyc 0 passes through a fixed point a) (1, ‐2) b) (‐1, 2) c) (1, 2) d) (‐1, ‐2) SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 26 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION II Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has four choices for its answer, out of which ONE OR MORE is/are correct. 9. 1 bc ac x dx c c equals a) 1 ( ) ba f x dx c b) ( ) ba f x dx c) ( ) ba c f x dx d) 22 ( ) . bc ac f x dx 10. If the imaginary part of the expression 1 1 i iz e e z be zero, then the locus of z is a) a straight line parallel to x axis b) a parabola c) a circle of radius 1 d) a straight line passing through (1,0) 11. If x 0 and 0 1 , 2 x x dx x AB where [.] denotes the greatest integer function, then a) Ax1 b) B x[x] c) A[x]1 d) B x[x] 12. If 2 ( ) 3 3 2 3.4 , 3 h x f x f x x where f"(x) 0x3, 4, then h(x)is a) Increasing in (3/2,4) b) Increasing in (‐3/2,0) c) Decreasing in (‐3,‐3/2) d) Decreasing in (0,3/2) IIT JEE 2010 6th Test Series Paper 1 P a g e | 27 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Comprehension Type This section contains 2 group of questions. Each group has three multiple choice questions based on a paragraph. Each question has four choices for its answer, out of which ONLY ONE is correct. Comprehension for Qs 13‐15 Let us consider that function f (x) is an integrable function in the interval [1, 3] has graph as shown in the figure, then answer the following questions. 13. 3 1 [f(x)]dx is equal to (here [.] represents greatest integer function) is equal to (a) 3 (b) 1 (c) 2 (d) 0 14. Area bounded by the curve y[f(x)] (here [.] represents the greatest integer function), lines x = 1, x = 3 and x‐axis is a) 3 b) 1 c) 2 d) 0 15. Which of following statement is correct ? 2 2 1 1 2 2 1 1 2 3 1 2 2 3 1 2 (a) ( ) 2 ( ) (b) [ ( )] [ ( )] (where [.] represents greatest integer function) (c) ( ) ( ) (d) ( ) ( ) 0 f x dx f x dx f x dx f x dx f x dx f x dx f x dx f x dx SPACE FOR ROUGH WORK 1 3 ‐1 0 ‐2 1 2 x f(x) 2 IIT JEE 2010 6th Test Series Paper 1 P a g e | 28 www.vidyadrishti.com An educational portal for future IITians by current IITians Comprehension for Qs 16‐18 If sinn cosn , n A nW (whole number) and θ R (Real number). On the basis of above information, answer the following questions. 16. If 31 A k, A then range of k is a) [1, 3] b) [1/2, 3/2] c) [‐3/2, ‐1/2] d) None of these. 17. The value of 6 4 6 4 3414 A A A A is equal to a) 15 b) 4 c) 5 d) 3 18. If 2 2 4 2 sin cos , n n A A A then value of equals a) n 4 b) n 8 c) n 6 d) n 10. SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 29 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION IV Matrix Match Type 19. Match the following Column I Column II (A) If sin 3,0 ;cos 12 , 3 , 5 2 13 2 A A B B then cos (A + B) and tan (A – B) are respectively (P) 528 , 672 697 697 (B) If cos( ) 4,sin( ) 5 5 13 AB AB such that 0 , , 4 then tan(A – B) and 2A are respectively (Q) 33 ,16 45 63 (C) If sin 8, cos 9 17 41 A B such that 2 A and 0 < B π/2, then sin (A + B) and sin(A – B) are respectively (R) 5 ,56 12 33 (D) If tan 5 2 2 A and tan 3 , 2 4 B then cos (A + B) and sin (A – B) are respectively (S) 7, 17 2 2 (T) 627 , 644 725 725 SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 30 www.vidyadrishti.com An educational portal for future IITians by current IITians 20. Let α, β, γ are three real numbers such that 2,222 6,3338. Now, match the entries from the following two columns Column I Column II (A) The value of 444 (P) 20 (B) (1 – α) (1 – β) (1 – λ) = (Q) 18 (C) If |x|< 1, then (x – α) (x – β) (x – λ) is (R) A quantity > 0 (D) 121212 (S) A quantity <0 (T) Zero SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 1 P a g e | 31 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK