02. If 2 p = 1 + i then p 6 + p 4 + p =? [ 2 p = 1 + i n j p 6 + p 4 + p =?]

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1 01. If A = {x : x N, 10 < x 2 < 90}, B = {x : x: prime number x <10} then A B =? [hw` A = {x : x N, 10 < x 2 < 90}, B = {x : x: gšwjk msl v x <10} nq, Zvn j A B =?] 02. If 2 p = 1 + i then p 6 + p 4 + p =? [ 2 p = 1 + i n j p 6 + p 4 + p =?] =?

2 04. Find the coefficient of x 5 in the expansion of (1+2x+3x α) 3/2 [(1+2x+3x α) 3/2 Gi we wz Z x 5 Gi mnm wby q Ki ] 05. The coordinates of points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If the area of triangle POA drawn through P is twice the area of triangle POB then find the locus of point P. [O, A Ges B Gi vbv¼ h_vµ g (0, 0), (0, 4) Ges (6, 0) hw` P we `y Øviv MwVZ POA Gi Îdj POB Gi wø Y nq Zvn j P we `yi mâvic_ ei Ki ] 06. Find the middle point of the portion of the line x sinα + y cosα = sin2α intercepted with axes. [x sinα + y cosα = sin2α ilvi A Ø qi LwÊZ As ki ga we `y KZ?] 2

3 07. Find the equation of a circle of radius 5 and which touches the circle x 2 + y 2 2x 4y 20 = 0 externally at point (5,5). [ h e Ëi e vmva 5 Ges x 2 + y 2 2x 4y 20 = 0 e Ë K (5, 5) we `y Z ewn: úk K i Zvi mgxkiy wby q Ki ] 08. For what value of c the line y = 2x + c is tangent to the hyperbola y 2 = 16x. [c KZ n j y = 2x + c ilvwu y 2 = 16x cive Ë Gi úk K n e? ] 09. Solve [mgvavb Ki] cos θ + sin θ = 2 3

4 10. If a = 2, b = 1+ 3, C = 60 0, solve the triangle. [hw` a=2, b=1+ 3, C = 60 0 nq, Z e wîfzrwu mgvavb Ki ] π π 11. Find the value of y 4 y dy. [gvb wby q Ki : y 4 y dy ] Evaluate: [gvb wby q Ki:] 1 3 x cot 1 x dx 4

5 13. Evaluate the integral [ hvmrwui gvb wby q Ki]: π / 4 sin 2xdx 4 sin x + cos 0 4 x 14. Three persons can solve a problem independently. The probability that the problem is solved by three persons are 1/3, 1/4 and 1/5 respectively. Find the probability that the problem not to be solved. [ wzbrb jvk ^vaxbfv e GKwU mgm v mgvavb K i Zv `i mgm vwu mgvavb Kivi m ve Zv h_vµ g 1/3, 1/4 I 1/5 n j mgm vwu mgvavb bv niqvi m ve Zv KZ? ] 15. lim π x 4 sin x cos x =? π x 4 5

6 a x 16. If y = tan 1 1+ ax dy then =? dx 17. A 6kg weight is tied with a 20cm long light string and hanged from a point. When a horizontal force F is applied it will moves to a distance 16 cm from a vertical line passing through the point. Find the value of F and string tension. [6 KwR IR bi GKwU e K 20 mwg. `xn GKwU nvjkv myzvi mvnv h GKwU wbw` ó we `y Z Ave Kiv n q Q Zvi Dci f wg Z ji mgvš ivj F gv bi e ji wµqvi d j Zv wbw` ó we `y w` q Aw¼Z Lvov ilv n Z 16 mwg. `~ i w ive vq Av Q F Gi gvb Ges myzvi Uvb KZ? ] 18. The mass of a cycle along with its passenger is 90kg. It is moving with a velocity 5 m/s. Find at what distance will it stops if he stops paddling. The total resistance of road and air is 4.5 kg wt. [mvb Kjmn 90 KwR f ii Av ivnx 5 m/s e M MwZkxj Ae vq hw` mvb Kj Pvjv bv eü K i Z e m KZ `~i wm q _vg e? iv v I evzv mi gvu evav 4.5 KwR IRb ] 6

7 19. A boat can cross a river straight at time t and travels equal distance along the direction of current at time t 1. When there is no current in the river the velocity of boat is u and velocity of current is v then t:t 1 =? [GKLvwb bškv t mg q GKwU b`x mvrvmywr cvwo w` Z cv i Ges t 1 mg q mªv Zi AbyK j mgvb `~iz AwZµg Ki Z cv i kvš b`x Z bškvi em u I mªv Zi em v n j t:t 1 =?] 20. A man can carry a weight W with the help of a pole placed on his shoulder. If the distance between his shoulder to hand and weight is x and a respectively, then find the minimum pressure on his shoulder. [GKRb jvk Zvi Kuv ai Dci GKwU jvwv eu a W IR bi GKwU evsv enb Ki e Kuva n Z Zvi nvz I evsvwui `~iz h_vk&ª g x I a n j Zvi Kuv ai Dci b~ bzg Pvc KZ n e? ] 21. If a body travels half its total path in the last second of its fall from rest, find the time and height of its fall. Explain the unacceptability of the solution if any. [ Kvb e w ive v _ K covi mgq me kl m K Û gvu AwZµvš `i Z i A a K `iz AwZµg K i cz bi mgq I DPPZv wby q Ki mgvav bi AMÖnY hvm Zv _vk j Zv e vl v Ki ] 7

8 22. The base of an insect's leg is spherical in shape with a radius of m. The gm mass of the insect is supported equally by the six legs on the surface of water. Calculate the angle of contact of the insect's leg with the water. Surface tension of water is Nm -1 and g = 9.8 ms -2. [ Qq cv wewkó MÖvg f ii GKwU cvkv cvwbi DcwiZ j `vwo q _vk Z cv i QqwU cv mgvb fi enb Ki j Ges cvkvi cv qi Zjv wg. e vmv a i MvjK AvK wzi n j, cvwbi mv _ cvkvi cv qi ck KvY KZ n e?) [cvwbi c ôuvb Nm -1 I g = 9.8 ms -2 ] 23. Two equiconvex lenses, each of focal length 20 cm, are placed in contact and the space between them is 3 filled with water. Find the focal length of the combination. [Refractive index of glass =, refractive index 2 4 of water =. [20 cm dvkvm `~iz wewkó `ywu mg-dëj jý ci úi K úk K i Av Q jý `ywui ga v b cvwb Øviv c~y jý ms hvr bi dvkvm `~iz wby q Ki (Kuv Pi cöwzmiv¼ =, cvwbi cöwzmiv¼ = ) ] A carnot refrigerator takes heat from water at 0 C and discards it to a room at a temperature of 27 C. If 100 kg of water at 0 C is to be changed to ice at 0 C, what is the work required? (Latent heat of ice = J/kg) [ Kvb Kv b v iwd«rv iui 0 C ZvcgvÎvi cvwb _ K Zvc MÖnY K i 27 C ZvcgvÎvi GKwU K Qv o 0 C ZvcgvÎvi 100 kg cvwb K 0 C ZvcgvÎvi ei d cwiyz Ki Z KZ Kv Ri cö qvrb n e? (eid Mj bi myßzvc = J/kg)] 8

9 25. An electron of mass kg revolves round a nucleus in a circular orbit of radius m. Find the centripetal acceleration and angular velocity of the motion of the electron. [ kg f ii GKwU B j±ªb wbdwk qvm K K `ª K i m e vmv a i GKwU e ËvKvi c _ Nyi Q N~Y biz B j±ª bi K `ªgyLx Z iy Ges KŠwYK em wby q Ki ] 26. The resistances of the first and the second arms of a Wheatstone bridge are 10 Ω and 12Ω respectively. The third arm contains an unknown resistance. When two parallel resistances each of 20 Ω are connected to the fourth arm of the bridge, it attains the null condition. Find out the value of the unknown resistance. [GKwU ûbu vb eªx Ri cö_g I wøzxq evûi iva h_vµ g 10 Ω Ges 12 Ω. Gi Z Zxq evû Z GKwU ARvbv iva jvmv bv Av Q hlb eªx Ri PZz_ evû Z `ywu mgvšivj iva, hv `i cö Z Ki gvb 20 Ω, jvmv bv nq ZLb eªxrwu wb c ` Ae vq _v K ARvbv ivawui gvb KZ? ] 27. An alien spaceship passed the BUET football playground along the length of the ground at a speed of 0.6c (as measured by the players on the field). The football playground is 110 metres long and 50 metres wide. What are the length and width of the football playground according to the alien of the spaceship? [wfbœ MÖ ni GKwU b fvhvb 0.6c MwZ Z (gv Vi L jvqvo `i cwigvc Abyhvqx) ey qu dzuej gv Vi ˆ`N eivei AwZµg K i dzuej gvvwu 110 wguvi j ^v Ges 50 wguvi cök b fvhv bi wfbmönevmxi cwigvc Abyhvqx dzuej gvvwui ˆ`N I cö KZ n e?] 9

10 28. Two coherent light sources of intensity ratio 25: 4 are employed in an interference experiment. What is the ratio of the intensities of the maxima and minima in the interference pattern? [ Kvb e wzpvi cix vq `ywu mymsmz Av jvk Dr mi cöve j i AbycvZ 25:4 e wzpvi m¾vi Pig we `y I Aeg we `yi cöve j i AbycvZ wby q Ki ] 29. A balloon of radius 1.0 m at 298K and kpa is released from sea-level. At a certain altitude the radius and temperature of the balloon is 3.0 m and 252 K respectively. Find the pressure inside the balloon? [298 K ZvcgvÎv I kpa Pv c 1.0 m e vmv a i GKwU ejyb K mgy`ªc ôzj n Z Q o `Iqv nj GKwU wbw` ó D PZvq ejybwui e vmva 3.0 m n j H D PZvq Ges 252 K ZvcgvÎvq ejybwui wfz ii Pvc KZ n e? ] 30. Magnetic flux of Wb is produced when current of 4A flows through a coil of 400 turns. If the current reduces to zero in 2ms, calculate (a) the induced emf in the coil, (b) self-inductance of the coil and (c) energy stored in the coil. [400 cv Ki GKwU KzÛjxi ga w` q 4A Zwor cöevwnz n j Wb PŠ ^K ej ilv Drcbœ nq hw` Zwor cöevn 2ms G k~ b b g Av m Z e wby q Ki KzÛjxi (a) Avweó Zwo PvjK ej (b) ^Kxq Av ek YvsK (c) mwâz kw³ ] 10

11 31. What will be the density of lead at N m 2 pressure if it has normal density 11.4 g cm 3 and bulk modulus N m 2? [mxmvi ^vfvwek NbZ 11.4 g cm 3 Ges AvqZb bvsk N m 2 n j N m 2 Pv c mxmvi NbZ KZ n e?] 32. In a Fraunhofer s class of diffraction experiment due to a single slit a light wavelength of 5890Å is used. If the width of the slit is 0.2mm then determine the angle of diffraction for the second dark band. [GKwU d«bndvi kªyxi GKK wp oi `i Y AceZ b cix vq 5890Å Zi½ ˆ` N i Av jv e envi Kiv nj wpowui ea 0.2mm n j wøzxq Ae gi Rb AceZ b KvY wby q Ki ] 33. Two tuning forks A and B when sounded together produce 5 beats per second. If A is slightly loaded, the number of beats is reduced. Find the frequency of A, if the frequency of B is 256 per second. [`ywu myi-kjvkv A I B K GKB mv _ Kuvcv j cöwz m K Û 5wU ^ik ci m wó nq hw` A Gi Dci wkqyuv IRb `qv hvq, Z e ^ik ci msl v K g hvq hw` B Gi K cv¼ cöwz m K Û 256 nq, Z e A Gi K cv¼ wby q Ki ] 11

12 34. Calculate the terminal velocity of a rain drop of radius 0.01mm. The coefficient of viscosity of air is N-sm 2 and its density is 1.2 kgm 3. Density of water = kgm 3. [0.01mm e vmv a i GK duvuv e wói cvwbi cövš em wby q Ki evzv mi mv `ªZv YvsK N-sm 2 Ges NYZ 1.2 kgm 3 cvwbi NYZ kgm 3 ] 35. A river 240 m wide is flowing downwards at the velocity of 1800 m per hour and a swimmer who can swim at the velocity of 3600 m per hour wishes to reach a point just opposite. Find the direction along which will he swim and find the time to reach that point. [cöwz N Uvq 1800 m e M 240 m cök GKwU b`x bx Pi w` K cöevwnz n PQ Ges cöwz N Uvq 3600 m e M muvzv i m g GKRb mvzviy GKwU wecixz we `y Z h Z BPQyK m Kvb w`k eivei muvzvi ` e Ges mb we `y Z h Z KZ mgq b e?] 36. A body executing linear simple harmonic motion has a velocity 3 ms 1 when its displacement is 4 m and velocity is 4 ms -1 when its displacement is 3 m. (a) Find the amplitude and period of the oscillation. (b) If the mass of the body is 50 kg, calculate the total energy of oscillation. [mij Qw `Z ú `bm úbœ GKwU e i em 3ms -1 hlb miy 4m Ges em 4 ms -1 hlb miy 3 m. (a) `vj bi we vi I chv qkvj wby q Ki (b) e wui fi 50kg n j `vj bi gvu kw³ wby q Ki ] 12

13 37. A photon of wavelength λ = 4000 A falls on a metal surface causing photoelectrons of maximum Kinetic energy 0.4 ev to be emitted from the metal surface. Calculate the work function of the metal. [ λ = 4000 A Zi½ ˆ` N i dvub Kvb avze c ô AvcwZZ n q m ev P 0.4 ev MwZkw³i d UvB jkuªb wbm Z K i H avzzi Kvh A c K wby q Ki ] 38. A spherical oil drop, carrying a charge of C, has a potential of 500 V at its surface. If such two drops combine to form a single spherical drop, what will be the potential at the surface of this drop? [ 0 = C 2 /N-m 2 ] [ C Avavbhy³ GKwU MvjKvKvi Z ji duvuvi Z ji wefe 500 V. hw` GiKg `ywu duvuv wg j GKwU MvjKvKvi duvuvi m wó nq, Zvn j D³ duvuvi Z ji wefe KZ n e? [ 0 = C 2 /N-m 2 ] 39. What is the distance of an object from a concave mirror of 27cm focal length to create a real image of three times the original size? [27cm dvkvm `~i Z i GKwU AeZj `c Y n Z KZ `~ i GKwU e vcb Ki j ev e cöwzwe ^i AvKvi e i AvKv ii wzb Y n e? ] 13

14 V-1000 W is marked on an electric iron. If it is connected to a 200 V line and works for 2 hours, then how many units of electricity will be consumed by it? [GKwU ˆe`y wzk B x Z 220 V-1000 W jlv Av Q B xwu 200 V jvb b hy³ n q 2 NÈv Pj j KZ BDwbU we`y r kw³ LiP Ki e?] ml Molar NaOH solution is required to titrate 60ml H 2 SO 4. Find the Molarity of H 2 SO 4. [GKwU 60ml AvqZ bi H 2 SO 4 `ªeY K UvB UªU Ki Z 43.7 ml AvqZ bi gvjvi NaOH `ªe Yi cö qvrb nq H 2 SO 4 `ªe Yi gvjvwiwu ei Ki ] 42. Find the wavelength of that particle of mass 1g and 100m/s velocity. [1g fi Ges 100m/s em wewkó KYv KZ Zi½ `N m úbœ?] 14

15 43. Determine the C C bond enthalpy per mole from the following data. Here C H bond enthalpy is 416 kjmol 1. [wb Pi cö`ë Z_ _ K cöwz gvj C C eüb kw³ wby q Ki G Î C H eüb kw³ 416 kjmol 1 ] 2C (s) + 3H 2 (g) C 2 H 6 (g) H = kj C (s) C (g) H = kj H 2 (g) 2H (g) H = kj 44. (a) Show the formation of sigma (σ) bond by overlapping s-s, s-p, and p-p orbitals of two atoms. [`ywu cigvyyi s-s, s-p, Ges p-p AiweUvj AwaµgY K i wmmgv (σ) eüb MVb-Gi cöwµqv `LvI ] (b) Is the second electron affinity exothermic or endothermic? Give reason. [wøzxq B j±ªb Avmw³ wk Zvc Drcv`x bv Zvcnvix? hyw³ `LvI ] 45. (a) Write down e configuration: [B jkuªb web vm wjl:] (i) Fe 2+ (ii) Cu 2+ (iii) Cr (b) (i) Mn 7+ +?? H +?? (ii) Mn 7+ +?? H 2 O?? (iii) Mn 7+ +?? OH?? 15

16 46. (a) Write down the formula: [ms KZ wjl:] (i) Freon-114 (ii) Freon-12 (iii) Freon-11 (b) What is bending? How to prevent? [ ewûs wk? wkfv e iva Kiv hvq?] 47. Write down the cell reaction: [ Kvl wewµqv wjl :] i) Lead-Acid battery ii) Nickel oxide cell iii) Necklance cell 48. At 350K temperature the equilibrium constant Kp = atm for the dissociation of N 2 O 4. If pressure is 15 atm at equilibrium then compute the dimension of dissociation constant of N 2 O 4. [350K ZvcgvÎvq N 2 O 4 Gi we qvr bi mvg aª ek Kp = atm mvg ve vq Pvc 15 atm n j N 2 O 4 Gi we qvrb gvîv wby q Ki ] 16

17 49. Illustrate with a figure, how does a catalyst reduce the activation energy, E A for a chemical reaction. [wp Îi mvnv h `LvI, wkfv e cöfvek Øviv wewµqvi mwµqb kw³, E A Gi n«vm cvq ] 50. Write the balanced equations to explain: [mylg mgxki Yi mvnv h e vl v `vi t] (i) Colour change occurs when HCl is added to a solution of Cu (II) and Ammonia. [G gvwbqv I Cu (II) `ªe Yi g a HCl Pvjbv Ki j is-gi cwiez b nq ] (ii) ++ Z n (aq) can be separated from Fe +3 (aq) by the addition of excess OH. ++ n [AwZwi³ HO ms hv M Z (aq) K Fe +3 (aq) _ K c _K Kiv ] 51. Fill up the following equations. [wb Pi wewµqv jv c~y KiÑ] (i) HC CH Fe (ii) C 2 H 5 NH 2 + HNO 2 + HCl C (iii) CH 3 COOH + Cl 2 O h ν (iv) + CHCl 3 + KOH 700 C 17

18 52. Transformation: [iƒcvš i Ki :] (i) Hexamine [ n vwgb] Cyclonite [mvb K vbvbu] (ii) Nitro Benzene [bvb Uªv ebwrb] Phynile Amine [wdbvbj A vwgb] 53. Write down the formulae: [ms KZ wjl :] (i) Paragyline [c vivrvbwjb] (ii) Sulphanikic Acid[mvjdvwbwjK GwmW] (iii) Ninhydrine [wbbnvbwwªb] (iv) Cyclohexanone [mvb K v n v bvb] 54. Answer the followings: [wb Pi cökœ jvi DËi `viñ] (a) Explain order of solubility of Sulfate compound of group II elements? [MÖ c II Gi gšjmg~ ni mvj d Ui `ªve Zvi µg e vl v Ki ] (b) What is Devardas alloy metal? For which test this metal is used? [ WfviWvm mski avzz wk? Kvb cix vi Rb GB avzz e envi Kiv nq? ] 18

19 55. Write down the synthesis of Strakar and Hell-Volhart-zelinsky reaction. [ ªKvi ms k lb Ges nj fvjnvu R j b x wewµqv wjl ] 56. Write short note on the identification of Glycerol. [UxKv wjl: wm mvij mbv³kiy ] 57. (a) Prepare Shif base and Anil compound. [wmd vik I A vwbj hšm cö Z Ki ] (b) Complete the reaction with mentioning the name of reactant and product. [wewµqk Ges Drcv `i bvg D j Lmn wewµqv m ú~y Ki ] (i) n HOOC(CH 2 ) 8 COOH + n H 2 N(CH 2 ) 6 NH 2? (ii) n H 2 C CH 2 + n HOOC COOH? OH OH (iii) gjv Wvi O C OH (c) 2 C + R CH COOH =? C OH NH 2 O (d) What is Catoferosis, Anaferosis and Isoelectric point? [K v Uv d ivwmm, A v bv d iwmm I AvB mvb jkwuªk c q U wk?] 19

58. Write down the following reactions [wb Pi wewµqv jv wjl:] (i) Benzophenone from Benzene ( ebwrb n Z eb Rv dbb) (ii) Phenol and Propanone from Benzene ( ebwrb n Z dbj I cövcvbb) 59.

] (a) Potassium Ferrocyanide (cuvwmqvg d ivmvqvbvbw) (b) Mohr s Salt ( gv ii jey) (c) Sodium Cobaltinitrite ( mvwwqvg KvevwëbvBUªvBU) (d) Dolomite ( Wv jvgvbu) (e) Chrome alum ( µvg A

20 58. Write down the following reactions [wb Pi wewµqv jv wjl:] (i) Benzophenone from Benzene ( ebwrb n Z eb Rv dbb) (ii) Phenol and Propanone from Benzene ( ebwrb n Z dbj I cövcvbb) 59. wb Pi hšm jvi ivmvqwbk ms KZ wjl [Write the chemical formulae of the following compounds.] (a) Potassium Ferrocyanide (cuvwmqvg d ivmvqvbvbw) (b) Mohr s Salt ( gv ii jey) (c) Sodium Cobaltinitrite ( mvwwqvg KvevwëbvBUªvBU) (d) Dolomite ( Wv jvgvbu) (e) Chrome alum ( µvg A vjvg) 60. (A) Name the following glasswares: [bx Pi Kuv Pi hš cvwz jvi bvg wjl:] (i) (ii) (iii) (iv) (B) Write the structural formula for the following compounds: [bx Pi hšm jvi MvVwbK ms KZ wjl:] (i) Menthol ( gb_j) (ii) Glycerine (wm mvwib) (iii) Paracetamol (c vivwmuvgj) ivd ivd 20

- 1 - (1) (2) B 0.80 g /cm 3. C 1.33 g /cm 3. D 2.0 g /cm 3 (3)

- 1 - (1) (2) B 0.80 g /cm 3. C 1.33 g /cm 3. D 2.0 g /cm 3 (3) - 1 - (1) An astronaut has a mass of 80 kg on Earth. He can jump 10 cm high off the surface of the Earth. When he is on the Moon he can jump higher than this. This is because, on the Moon, (c w_ex Z GKRb