HALF COURSE TEST VII. Time Allotted: 3 Hours Maximum Marks: 360. School Program & 4423 Students from All Programs have qualified in JEE Advanced, 2016

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1 In JEE Advanced 016, FIITJEE Students bag 36 in Top 100 AIR, 75 in Top 00 AIR, 183 in Top 500 AIR Students from Long Term lassroom/ Integrated School Program & 443 Students from All Programs have qualified in JEE Advanced, 016 FIITJEE JEE (Main), 017 ALL INDIA INTEGRATED TEST SERIES HALF OURSE TEST VII Time Allotted: 3 Hours Maximum Marks: 360 Pleas e r ead th e instructions carefully. You are allotted 5 m inutes specifically for this purpose. You are not allowed to leave the Exam ination Hall before the end of the test. INSTRUTIONS A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is hemistry and Part-III is Mathematics. 4. Each part has only one section: Section-A. 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed. B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.. On the OMR sheet, darken the appropriate bubble with black pen for each character of your Enrolment No. and write your Name, Test entre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.. Marking Scheme For All Three Parts. (i) Section-A (01 to 30) contains 30 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and 1 mark for wrong answer. Name of the andidate Enrolment No.

2 AIITS-HT-VII-PM-JEE(Main)/17 Useful Data PHYSIS Acceleration due to gravity g = 10 m/s Planck constant harge of electron Mass of electron h = J-s e = me = kg Permittivity of free space 0 = /N-m Density of water water = 10 3 kg/m 3 Atmospheric pressure Pa = 10 5 N/m Gas constant R = J K 1 mol 1 HEMISTRY Gas onstant R = J K 1 mol 1 = Lit atm K 1 mol 1 = al K 1 mol 1 Avogadro's Number Na = Planck s constant h = Js = ergs 1 Faraday = coulomb 1 calorie = 4. joule 1 amu = kg 1 ev = J Atomic No: H=1, He =, Li=3, Be=4, B=5, =6, N=7, O=8, N=9, Na=11, Mg=1, Si=14, Al=13, P=15, S=16, l=17, Ar=18, K =19, a=0, r=4, Mn=5, Fe=6, o=7, Ni=8, u = 9, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=8, U=9. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, =1, N=14, O=16, F=19, Na=3, Mg=4, Al = 7, Si=8, P=31, S=3, l=35.5, K=39, a=40, r=5, Mn=55, Fe=56, o=59, Ni=58.7, u=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=17, Xe=131, Ba=137, Pb=07, U=38.

3 3 AIITS-HT-VII-PM-JEE(Main)/17 Physics PART I SETION A Straight Objective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices, (B), () and, out of which only ONE is correct 1. A wedge of mass M and dimensions as shown in the figure is lying completely inside a region (I) of zero pressure. The pressure inside region II is 1 Pa. All the surfaces are smooth. The wedge is imparted an initial velocity v0 so that it just travels a distance b inside region II before finally coming to rest. The value of v0 is abh M () 4 abh 3 M (B) 3 abh 4 M 4 abh 3 M h b Region - I a Region - II. A block A of mass m and a box B of same mass are lying on a horizontal surface as shown in the above figure. The coefficient of kinetic friction between the block and horizontal surface is A, while that between the box and surface is B. Given that B > A. At t = 0, the position is as shown in the figure and both are simultaneously given a velocity v0 to the right. The time after which block will collide with the right end of the box is L L (B) g g () B A 4L g B A B A 4L g B A A B L

4 AIITS-HT-VII-PM-JEE(Main)/ The figure shows a hollow circular tube fixed to a frictionless horizontal table. It is the top view of the arrangement. A ball is shot into end A of the tube to leave the other end B at high speed. The balls diameter is slightly less than the internal diameter of the tube. Which of the paths below will the ball follow on the table after it leaves the tube? B A (B) () None of these 4. A mass m on the end of an ideal spring stretches the spring to a length when at rest. The mass is now set into motion so that it executes up and down vibrations while swinging back and forth as a simple pendulum. The mass moves in a figure eight patterns in a vertical plane a shown in the figure. The force constant of the spring assuming small oscillations is mg () 4mg (B) mg k mg m m 5. A narrow tunnel is made through the earth of mass M and radius R from the centre to the surface. The speed (in m/s) with which a particle should be projected from the centre of the earth through the tunnel so that it escapes to the space is gr (B) gr () 3gR gr

5 5 AIITS-HT-VII-PM-JEE(Main)/17 6. A cubical block of volume v and density 3 is placed inside a liquid of density and attached to a spring of spring constant k as shown in the figure. Assuming ideal spring and pulley and spring is attached at A which is at R/ from centre. The compression in the spring at equilibrium is k A 4 vg k () 3 vg k (B) vg k vg k 7. A light thread is wound on a disk of mass m and other end of thread is connected to a block of mass m, which is placed on a rough ground as shown in diagram. Find the minimum value of coefficient of friction for which block remain at rest: 1 1 (B) 3 4 () m r m 8. A horizontal spring mass system of mass M performs simple harmonic motion of amplitude a0 and time period T0. When the mass M passes through mean position another stationary mass M sticks to it and both move together. If a and T be new amplitude and time period. Then () a 0 a (B) a a0 T 0 T None 9. System is shown in figure. Assume the cylinder remains in contact with the two wedges. The velocity of cylinder is u m/s 30 o 30 o u m/s u m/s (B) v m/s () 3v m/s 7u m/s

6 AIITS-HT-VII-PM-JEE(Main)/ onsider the following statements for a particle moving in an elliptic orbit under the influence of a central force: (1) The radius vector covers equal area in equal time. () The motion takes place in a plane. (3) The angular momentum is constant of motion. Which of options given above are correct? 1 & only (B) & 3 only () 1 & 3 only all 11. Two equal masses hang on either side of a pulley at the same height from the ground. The mass on the right is given a horizontal speed, after some time. The mass on the left will be nearer to ground. (B) The mass on the right will be nearer to ground. () Both the masses will be at equal distance from the ground. Nothing can be said regarding their positions. 1. O is the centre of mass of a body of mass M as shown in the figure. A, B, are three different point on the body. OB = 8 cm, O = 10 cm, B = 6 cm and OA = 10 cm. Which of the following can be written by using parallel axis theorem? I0 is the moment of inertia about the axis passing through point O and perpendicular to plane of object. IB = I + M(B) (B) I = IB + M(B) () IA = I0 + M(OB) None of these O B u Ground A 13. The temperature of a mono-atomic gas in an uniform container of length L varies linearly from T0 to TL as shown in the figure. If the molecular weight of the gas is M0, then the time taken by a wave pulse in travelling from end A to end B is A T 0 L B T L L ( T T ) L 0 3M 5R (B) 3(T T ) L 0 5RM L 0 () L ( T T ) L 0 3M 5R L M 0 R(T T ) L A uniform metallic disc of radius r and mass m is spinning with angular speed 0 about an axis passing through its centre and perpendicular to its plane. If its temperature is increased (slightly) by T without disturbing the disc, its new angular speed is (The coefficient of linear expansion of the metal is ) 0 1 T (B) 0 1 T () 0 1 T T

7 7 AIITS-HT-VII-PM-JEE(Main)/ A rod of mass M and length L is placed on a smooth horizontal table and is hit by a ball moving horizontally and perpendicular to length of rod and sticks to it. Then conservation of angular momentum can be applied About any point on the rod (B) About a point at the centre of the rod () About end point of the rod None 16. A wedge whose curved surface is parabolic in shape and has equation x = 4y starts accelerating with acceleration g m/s when a block is at the bottom of wedge and is located at (0, 0). The maximum height attained by the block (assume the curved surface is sufficiently long) 1m (B) m () 4m 8m a= g m/s (0, 0) 17. The ratio of magnitude of work done in moving slowly a block of mass m on a rough inclined surface of inclination 45 (tan ) from bottom to top and from top to bottom is 5. The coefficient of friction between the block and surface is 1 (B) 3 () Four identical particles of mass m are projected along the plane towards the centre of a square from the corners of the square simultaneously with constant speed V0. Then If the two spheres comes to rest after collision then the other two must also come to rest after collision. (B) If the three spheres comes to rest after collision then the fourth one must also stop after collision. () If all comes to rest after collision then loss of energy is 4m V 0. If all comes to rest after collision then it will violate the law of conservation of momentum.

8 AIITS-HT-VII-PM-JEE(Main)/ Figure shows the pressure P versus volume V graphs for a certain mass of an ideal gas at two constant temperatures T1 and T. Which of the following option is correct? T1 = T (B) T1 > T () T1 < T no inference can be drawn due to insufficient information. P V T 1 T 0. Two identical vessels A and B contain mass m and m of same gas respectively. The gases in the vessels are heated keeping their volumes constant and equal. The Temperature-Pressure curve for mass m makes angle with T-axis and that for mass m makes an angle with T-axis then tan = tan (B) tan = tan () tan = tan None of these 1. If the moment of inertia of a isosceles right angle plate is I about an axis shown in figure. Then moment of inertia of a square plate of same material and thickness shown in figure about the given axis is 30I (B) 3I () 64I 90I a a a a. Two simple pendulum of length and 16 are released from the same phase together. They will be at the same phase after a minimum time. 8 (B) 3 g 3 g () s none of these

9 9 AIITS-HT-VII-PM-JEE(Main)/17 3. Two springs, each of spring constant k = 100 N/m are attached to a block of mass kg as shown in figure. The block can slide smoothly along horizontal platform clamped to the opposite walls of trolley of mass 5 kg. The block is slightly displaced and then released. The period of oscillation is (in seconds). (all surfaces are smooth). k kg 5kg k = 0 7 T (B) T () T T Two particles are executing SHM of equal amplitude along parallel lines with same time period. Their velocity vectors are always oppositely directed to each other. The minimum phase difference between the two particles is 0 (B) 90 () Which of the following statements is incorrect? Work done is zero if the point of application of force does not move. (B) Total work done by static friction is zero in rolling without slipping for the complete system. () Work done by friction must be zero in pure rolling for the rolling body. For an isolated system momentum of the system is conserved for any type of collision. 6. Three small spheres A, B and of masses 1kg, kg and 3kg are rotating with a circular disc with angular velocity 3 radian/sec and are connected with strings to O as shown in figure. oefficient of friction between spheres A, B, and disc is 0.4, 0.3 and 0. respectively. Friction force acting on sphere B is 6 N. (B) Tension in the string connecting sphere A and B is 9 N () Tension in the string connecting sphere and O is 8 N Data insufficient A B O 50cm 100cm =3 rad/sec 50cm 7. A block of mass kg is kept gently on a moving tape of a machine in which the rotating cylinders have angular speed of 0 rad/sec and there radius is 0cm. If coefficient of friction between the tape and block is 0.5 and there is no slipping between tape and cylinder. Then (take g = 10 m/s ) The distance travelled by the block before relative motion with tape ceases is 1.6 m (B) Work done by friction on the block is 8 N () Work done by friction on the block is 16 N Linear velocity of tape is 40 m/s

10 AIITS-HT-VII-PM-JEE(Main)/ A rod of mass m kg and length meter is hinged about its end A and is vertical initially. Now the end A is accelerated horizontally with acceleration a0 = g m/s. The hinge reaction when the rod becomes horizontal is 4mg mg mg mg Rx N, Ry N (B) Rx N, Ry N mg mg mg () Rx N, Ry N Rx 4mgN, Ry N B A a 0 9. The temperature at which the speed of sound wave in helium gas is same as that in hydrogen gas at 7, is 504 (B) 45 () A triangular wave pulse on a taut string travels in positive x-direction with speed v. The tension in the string is F, and linear mass density of string is. At t = 0, the shape of pulse is given by 0 if x L h(l x) for L x 0 L y(x,0) h(l x) for 0 x L L 0 for x L choose the correct statement. Magnitude of instantaneous power is zero for L < (x vt) < 0 h (B) Magnitude of instantaneous power is Fv L h () Magnitude of instantaneous power is Fv L h Magnitude of instantaneous power is Fv L for (x vt) < L for (x vt) > L for 0 < (x vt) < L

11 11 AIITS-HT-VII-PM-JEE(Main)/17 hemistry PART II SETION A Straight Objective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices, (B), () and, out of which only ONE is correct 1. Arrange the following compounds in correct order of basic strength: NH NH H N NH H 3 NH H 3 OH H 3 H 3 (I) (II) (III) (IV) I > II > III > IV (B) I > IV > II > III () IV > III > II > I I > III > IV > II. A compound with molecular formula 4H10O3 is converted by the action of acetyl chloride to a compound with molecular weight 190. The original compond has one OH group (B) two - OH groups () three OH groups non OH groups 3. Which of the following pairs contains amphoteric oxides? BeO, BaO (B) BeO, AlO3 () AlO3, PO5 FeO, uo NH NH 4. The compound which can not exihibit geometrical isomerism is 6H5 N = N 6H5 (B) H 5 6 H 5 6 N OH () H = = H H5 H 3 H 3

12 AIITS-HT-VII-PM-JEE(Main)/ In the compound: H 3 N (Y) NH 3 (Z) HOO (X) orrect order of acidicity of position X, Y, Z are X > Y > Z () X = Y = Z (B) Y > X > Z X < Y < Z 6. Which of the following molecule has the highest value of dipole moment? (B) () 7. The dipole moment of which of the following compounds increase on heating H3Hl (B) lhhl () Hl3 H3HHl 8. Which of the following compound is added to boric acid in order to titrate it completly with NaOH, i.e. to increase its acidic strength? HO OH (B) H OH H H H H HO () H3HOH HOHHHO 9. Stereoisomers possible for following compounds: H H H H 3 H H 8 (B) 4 () 16 3

13 13 AIITS-HT-VII-PM-JEE(Main)/ The order of basic strength of the compounds: O O H O NH (I) (II) (III) (IV) IV > II > I > III (B) III > II > IV > I () II > III > IV > I II > III > I > IV 11. In which of the following molecule, the resoance effect is not present? (B) NH NH 3 () OH l 1. The major product when n-butane is treated with bromine in present of light is H 3 H H H Br (B) H 3 H H H 3 Br () H 3 H 3 H 3 H H H 3 H 3 Br H The reagent not used for softening of the temperory hardness of HO is/are a3(po4) (B) a(oh) () NaO3 NaOl 14. rystalline burn (B) is obtained form borax is the following steps: X Borax H PO B O Y B X & Y are respectively : Hl, Mg (), Al (B) Hl, l Hl, Al

14 AIITS-HT-VII-PM-JEE(Main)/ Which of the following structrues are aromatic? H H H H (1) () (3) (4) Select the correct answer using the codes given below: 1, and 4 (B) 1, 3 and 4 () 1 & 3 & Which of the following is the strongest reducing agent in aqueous solution? Na (B) K () s Li 17. O O NOl products Product is NO (B) N OH () l l l l OH N OH 18. The conjugate base of NH3 is NH 4 () NH (B) N3H NH

15 15 AIITS-HT-VII-PM-JEE(Main)/ Which of the following in most stable? H (B) H () H l H NO OOH 0. Which of the following will not give white ppt. with aqueous AgNO3 l (B) l () l H l 1. Which of the following pair is correct with respect to chlorination of given alkene? l major product h (B) () l l l h major product h l major product All of the above correct l

16 AIITS-HT-VII-PM-JEE(Main)/ Which of these does have gretest second ionization energy? B (B) () Sr Ba 3. How many structral isomers are possible with molecular formula 7H16? 6 (B) 8 () Which of the following statement in true about boron compounds? BF3 least acidic among the boron halides (B) BF3 does not hydrolysis () BH6 does not have banana bond all are correct 5. Which of the following carbocation will be relatively less stable than benzyl carbocation? H (B) PhH + () H 3 Ph H 3 6. The number of possible enantiomeric pair that can be formed by monochlorination of -methyl butane is (B) 3 () The number fo structural isomers of 6H14 is 3 (B) 4 () 6 5

17 17 AIITS-HT-VII-PM-JEE(Main)/17 8. onsider the following reaction: H 3 i NaNH ii H (X) l (X) will be H 3 NH (B) H 3 NH () H 3 H 3 NH 9. Which of the following carbides give allylene on hydrolysis? a (B) Be () Mg3 Mg 30. Which of the following compound will not undergoes hydrolysis? l4 Sil4 () Bl3 SiH4

18 AIITS-HT-VII-PM-JEE(Main)/17 18 Mathematics PART III SETION A Straight Objective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices, (B), () and, out of which only ONE is correct 1. The slope of the line which belongs to family of lines (1 + )x + ( 1)y + (1 ) = 0 and makes shortest intercept on x = 4y 4, is 1 (B) 1 () 0. If (sin, cos ); ( [0, ]) and (1, 4) lie on the same side of the line 3 x y + 1 = 0, then maximum value of sin will be 1 (B) 0 () 1 3. If a circle of radius 3 units is touching the lines length of chord of contact to this circle is () The minimum value of the expression 1 3 3y 4xy 3x 0 in the first quadrant then (B) E z z 3 z 6i is m then the value of m 6 is 3 (B) 4 () 5 none of these

19 19 AIITS-HT-VII-PM-JEE(Main)/17 5. If n = (1999)! then 1999 logn x is x1 0 (B) 1 () 3 none of these 6. The number of ways of dividing 15 men and 15 women into 15 couples, each consisting of a man and a woman is 140 (B) 1840 () (3x 4y 7) The length of the major axis of the ellipse (5x 10) (5y 15) 4 is 10 (B) 0 3 () If foci of hyperbola lie on y = x and one of the asymptote is y = x, then equation of the hyperbola, given that it passes through (3, 4), is x y 5 xy + 5 = 0 (B) x y + 5xy + 5 = 0 () x + y 5xy + 10 = 0 none of these 9. If tan x tan x = 1, then the value of tan 4 x tan 3 x tan x + tan x + 1 is 1 (B) () For any real, the maximum value of cos (cos) + sin (sin) is 1 (B) 1 + sin 1 () 1+ cos 1 does not exist 11. If points corresponding to the complex numbers z1, z, z3 and z4 are the vertices of a rhombus, taken in order, then for a non-zero real number k z1 z3 = i k( z z4) (B) z1 z = i k( z3 z4) () z1 + z3 = k( z + z4) z1 + z = k( z3 + z4)

20 AIITS-HT-VII-PM-JEE(Main)/ From a 60 meter height tower angles of depression of the top and bottom of a house are and 60sin respectively. If the height of the house is, then x is x sin sin (B) cos cos () sin cos cos sin 13. If coefficient of x n in (1 + x) 101 (1 x + x ) 100 is non zero, then n can not be of the form (t N) 3t + 1 (B) 3t () 3t + 4t Radius of the larger circle touching the coordinate axis and the line y + x + 1 = 0 is () (B) If both roots of the quadratic equation x kx + (k + k 5) = 0 are less than 5 then k lies in interval (5, 6) (B) (6, ) () (, 4) [4, 5] 16. In a AB if medians from B and are perpendicular then minimum value of cot B + cot is (B) 3 () The sum of () upto 10 terms is equal to (B) none of these 18. If there exists a value of between 0 and that satisfies the equation sin 4 sin 1 = 0, then must be equal to (B) () 3 none of these

21 1 AIITS-HT-VII-PM-JEE(Main)/ If a, b, c are three consecutive positive integers, then loge a loge c ac 1 3 ac 1... loge a (B) loge b () loge c loge abc 3 n n 1 0. If an = n then r 1 n equals r0 nan n () an 1 r r0 r (B) (n+1)an none of these 1. The diagonals of a parallelogram PQRS are along the straight lines ax + by = 50 and 4bx ay = 100. Then PQRS must be a rhombus (B) rectangle () square none of these. If log10x + log10 y then the smallest possible value of x + y is 0 (B) 00 () The number is divisible by 10 n then maximum value of n is (B) 3 () If a1, a, a3, a4 are the roots of the equation x 4 + px 3 + qx + px + q = 0, then a 1 a1 1 a 1 a3 1 a 4 equals 0 (B) q + p () q p 1 5. If 0 a 3, 0 b 3 and the equation x cos (ax + b) = x has atleast one solution then the value of a + b equals 0 (B) / () none of these

22 AIITS-HT-VII-PM-JEE(Main)/17 6. The equations of x + ax + a = 1 and x + bx + b = 1 have exactly one common root; then a b equals 0 (B) () If z +1 = z + 1, where z is a complex number, then the locus of z is a straight line (B) a ray () a circle an arc of a circle 8. The equation x + y + sin x + cos y belongs to 0, (B) 4, 4 (), none of these 4 4 log10 x 3 log10 x1 9. If x 1000, then x belongs to (10, ) (B) (10 3, ) () (10 4, ) none of these = 0 represents a real circle if 30. Number of three digit numbers which are of the form xyz with x < y, z < y and x 0 are 04 (B) 140 () 44 none of these