ALL INDIA TEST SERIES

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1 From Long Term Classroom Programs and Medium / Short Classroom Program 4 in Top 0, 0 in Top 0, 43 in Top 00, 75 in Top 00, 59 in Top 500 Ranks & 354 t o t a l s e l e c t i o n s i n I I T - J E E 0 FIITJEE JEE (Main), 03 ALL INDIA TEST SERIES CNCEPT RECAPITULATIN TEST (Set VI) Time Allotted: 3 ours Maximum Marks: 360 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination all before the end of the test. INSTRUCTINS A. General Instructions. Attempt ALL the questions. Answers have to be marked on the MR sheets.. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry 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 MR Sheet. Ensure matching of MR sheet with the Question paper before you start marking your answers on MR sheet.. n the MR sheet, darken the appropriate bubble with black pen for each character of your Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. MR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts. (i) Section-A (0 to 30) contains 30 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and mark for wrong answer. Name of the Candidate Enrolment No.

2 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 Useful Data PYSICS Acceleration due to gravity g = 0 m/s Planck constant h = J-s Charge of electron e = C Mass of electron m e = kg Permittivity of free space ε 0 = C /N-m Density of water ρ water = 0 3 kg/m 3 Atmospheric pressure P a = 0 5 N/m Gas constant R = 8.34 J K mol CEMISTRY Gas Constant R = 8.34 J K mol = 0.08 Lit atm K mol =.987 Cal K mol Avogadro's Number N a = Planck s constant h = J s = erg s Faraday = coulomb calorie = 4. joule amu = kg ev = J Atomic No: =, e =, Li=3, Be=4, B=5, C=6, N=7, =8, N=9, Na=, Mg=, Si=4, Al=3, P=5, S=6, Cl=7, Ar=8, K =9, Ca=0, Cr=4, Mn=5, Fe=6, Co=7, Ni=8, Cu = 9, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=8, U=9. Atomic masses: =, e=4, Li=7, Be=9, B=, C=, N=4, =6, F=9, Na=3, Mg=4, Al = 7, Si=8, P=3, S=3, Cl=35.5, K=39, Ca=40, Cr=5, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=08, Sn=8.7, I=7, Xe=3, Ba=37, Pb=07, U=38.

3 3 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 Physics PART I SECTIN A Single Correct Choice Type This section contains 30 multiple choice questions. Each question has four choices,, and (D) out of which NLY NE is correct.. Determine the region of the electron spectrum which liberates photo-electrons from potassium. Given that the work function of potassium is.4 ev. < 555Å > 555 Å < 5.43 Å (D) none of the above. The refractive indices for violet and red colour are.54 and.5 respectively, the angular dispersion of a prism of angle 0 and made of such glass will be (D) In an interference experiment the separation between the st and the th bright fringe on a screen is.5 mm. The screen is at a distance of 3 m from the interfering sources. If λ = 5000Å, Then ratio of intensity at 0. mm from central max and maximum intensity is 4π π sin cos 5 5 π π sin (D) cos A ball of mass m, attached to a light wire of length l, is rotated in a horizontal circle. The area of cross-section of the wire is A and its breaking stress is S then maximum angular velocity is ω AS rad s ml AS rads 4 ml (D) AS ml rads AS ml rads l m

4 AITS-CRT(Set-VI)-PCM-JEE(Main)/ A uniform solid cylinder of mass M and radius R is pulled horizontally by a force F acting at its center of mass from rest. Then indicate the correct direction of friction, assuming that it rolls without sliding on a rough horizontal surface F F f f (D) cannot be interpreted F f=0 F 6. A small block of mass m, having charge q is placed on frictionless inclined plane making an angle θ with the horizontal. There exists a uniform magnetic field B parallel to the inclined plane but perpendicular to the length of spring. If m is slightly pulled on the inclined in downward direction, the time period of oscillation will be (assume that the block does not leave contact with the plane) π m m π K K π qb qb (D) π. K K B θ 7. The first over tone of an open organ pipe and the fundamental tone of a closed organ pipe closed organ give 5 beats per second when sounded together. If the length of the closed pipe is 5 cm, what are the possible lengths of the open organ pipe? (speed of sound in air = 340 m/s): 90 cm and 00 cm 98.5 cm and 0.5 cm 00 cm and 03 cm (D) 0 cm and 05 cm 8. A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration a away from the block as shown in the figure. Find the maximum extension in the spring. Assume that initially block and spring is at rest w.r.t ground frame ma k ma k ma k (D) 4ma. k m A a

5 5 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 9. In an A.C. circuit when applied voltage is V = V 0 sin (ωt π/4) then resulting current is I = I 0 sin (ωt + π/4) then average power developed in the circuit is VI 0 0 V 0 I 0 zero (D) None of the above 0. A balloon of mass M with a light rope having monkey on the rope is in equilibrium. If the monkey starts moving up with acceleration a w.r.t. rope. Then the acceleration of centre of mass of the system is a(m m) Zero (M + m) M a (D) am m. m. For what value of R, power developed across 6 Ω resistor is equal to the power developed across 4 Ω resistor? Ω 6 Ω 4 Ω (D) 8 Ω i 6 Ω R 4 Ω i. A cell of emf V is connected across a resistance 5Ω. The potential difference between the terminals of the cell is found to be.5 V. The internal resistance is 5 8 Ω 0 3 Ω 3Ω (D) none of these. 3. In a parallel plate capacitor of plate area A, plate separation d and charge Q, the force of attraction between the plates is F, then F Q F A F d (D) F d

6 AITS-CRT(Set-VI)-PCM-JEE(Main)/ As arrangement shown in the figure at t = 0 switch S is closed, find current i through battery at t = 0 v R v R + R v R (D) None of the above R L C R + r t = 0 S 5. The time period of a simple pendulum in air is T. The time period of the same simple pendulum in another medium which offers a Buoyant force on the bob, one third of its weight, is 3 T 3 T 3 T (D) 3 T 6. A sealed tank containing a liquid of density ρ moves with a horizontal acceleration a 0, as shown in the figure. The difference in pressure between the points A and B is hρg lρa 0 hρg lρa 0 (D) hρg + lρa 0 B A h a 0 7. Identify the correct definition of gravitational potential at a point. it is defined in terms of the force required to displace a unit mass from infinity to that point it is defined in terms of the force required to move a unit mass from the surface of earth to that point it is defined in terms of the force required to displace a unit mass from that point to infinity (D) none of these

7 7 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 8. The density (ρ) versus temperature (T) graph of an ideal gas undergoing a process AB is as shown in the figure. Choose the incorrect option P A V A = P B V B P B > P A W A B is positive (D) DU AB = 0 ρ A B T 9. An ideal gas of adiabatic exponent γ is supplied heat at a constant pressure. Then ratio dq : dw : du is equal to γ : γ : γ : : γ γ : γ - : (D) γ : : γ 0. In a thermodynamic process helium gas obeys the law TP /5 = constant. The heat given to the gas when the temperature of moles of the gas is raised from T to 4T (R is the universal gas constant) is 9 RT 8 RT Zero (D) Data insufficient. A particle moves with a speed v in a circle of radius R. The x-component of the average velocity of the particle in a halfrevolution, as shown in figure, is v v π π v 4 π (D) π v final position y 60º initial position x. ne end of a rope is bound to a vertical wall. The other end is pulled with a horizontal force of 30 N. An additional force of 0N is applied to the right at the point A in the middle of the rope. Which of the following is true about tensions at points P and Q P A T P = T Q = 40N T Q = T P = 0N T P T Q = 0N (D) T Q = 0N T P = 40 N 0 N Q 30 N

8 AITS-CRT(Set-VI)-PCM-JEE(Main)/ A particle of specific charge q = π C/kg is projected from the origin towards positive x axis with a m velocity of 0 m/s in a uniform magnetic field B = kˆ T. The velocity v of particle after time t = s will be (in m/s) 5[ ˆ i + 3 ˆ j ] 5( 3i ˆ+ ˆj ) 5[ 3i ˆ ˆj ] (D) 5[ ˆ i + ˆ j ] 4. The effective charge experienced by an M( n = 3) electron in an atom of atomic number z is about (z 7.4) e. The frequency of L α X-rays of such an element is ( ) 3cR z 4 5cR z ( ) (D) 3cR ( z) 4 ( ) 5cR Z Wavelength of K α X-ray of an element A is λ and wavelength of K α X-ray element B is λ. λ λ is equal to 4 and Z and Z are the atomic numbers of element A and B respectively. Then relation between Z and Z are given by Z Z = Z Z = Z 4 Z = (D) Z 4 Z = 6. In Young s experiment, light of wave length 6000 Å is used to produce fringes of width 0.3 mm. If the whole apparatus is dipped in a liquid of refractive index.6 then fringe width will be 0.5 mm 0.6 mm 0.4 mm (D) 0. mm 7. A converging lens of focal length 30 cm and a converging mirror of focal length 40 cm are placed with their principal axis at a distance of 40 cm from the lens an object is placed. It is found that final image is formed at focus of lens, then distance between lens and mirror is 60 cm 00 cm bject 40cm 0 cm (D) None of these S ///////////////////////

9 9 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 8. The point masses m and m are placed at the two ends of a rigid massless rod of length l. The system is set into rotation with an angular velocity ω about an axis which is at a distance x from the mass m and perpendicular to rod. The value of x for which the work done in the process is minimum is l m ml m + m (D) m l m l m + m m m l 9. A block of mass m is connected to two springs of spring constants k and 3k respectively, as shown in the diagram, with both the springs being vertical and fixed at their other ends. Both springs are initially unstretched and the mass m is given an initial velocity u in the downward direction. The block oscillates. The amplitude of oscillation of the block is given by mu mg + mg 5K 5K 5K m k 3k mu 5K mg + 5K (D) mu 5K mg 5K 30. In a resonance-column experiment to measure the velocity of sound, the first resonance is obtained at a length l and the second resonance at a length l, (end correction is taken into consideration), then l > 3l l = 3l l < 3l (D) may be any of the above depending on the frequency of the tuning fork used.

10 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 0 Chemistry PART II SECTIN A Straight bjective Type This section contains 30 multiple choice questions numbered to 30. Each question has 4 choices,, and (D), out of which NLY NE is correct.. Which of the following is the correct IUPAC name of the following compound Cl C N C 3 p-acetamido chlorocyclohexane N-methyl amido chlorocyclohexane 4-chloro-N-methylcyclohexane carboxamide (D) None of the above. Compare relative stability of the following resonating structure: (p) C (q) C (r) C p > q > r q > r > p N N q > p > r (D) p > r > q N 3. ow many distinct monochlorinated products (including stereoisomers) may be obtained when the alkane shown below is heated in presence of Cl (D) 8 4. Which of the following statement is incorrect? [NiCl 4 ] - is Ni 4 both are tetrahedral in shape [NiCl 4 ] - is paramagnetic while Ni 4 is diamagnetic [NiCl 4 ] - shows colour while Ni 4 is colourless (D) [NiCl 4 ] - and Ni 4 both contains nickel in + oxidation state Rough Work

11 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 5. The E product of the following reaction will be? Br C 3 Na C 3 (D) C 3 C 3 C 3 6. C D R ( ) ( A ) ( ) C C Find out the reactivity order with LiAl 4 is: CCl B ( ) A > B > C > D D > C > B > A B > C > D > A (D) B > D > C > A 7. 4 C 3 I base ( A) 3 C ( dilute A + ) B Product B in the above reaction is: C 3 4 C C 4 (D) 4 C 3 Br C Rough Work

12 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 8. C 3 C Et Ac Product of the reaction is ( d) dextrorotatory C 3 C 3 C Et C Et ( d ) 3 C d& (D) 3 C ( ) ( ) C Et C C 3 C 9. Which of the following product will be obtained in the given (consider minor product also) Backmann-type rearrangement? (i) Me () i N ( ),Cl ii PCl 5, Products are: (ii) N Me N Me (iii) N (i) and (ii) (i) and (iii) Me (ii) and (iii) (D) (i), (ii) and (iii) 0. Which of the following will react fastest with sodium? C C C (D) (C 3 ) 3 C Rough Work

13 3 AITS-CRT(Set-VI)-PCM-JEE(Main)/3. Arrange decreasing order of reactivity of given compounds with NBS (N-Bromosuccinimide) (I) C 6 5 C 3 (II) C 6 5 C C C 3 (III) C 6 5 C C = C (IV) C65 C C = C C 3 Select the correct answer from the codes given below codes: IV, III, I & II IV, III, II & I I, II, III & IV (D) I, III, II & IV. An excited hydrogen atoms returns to the ground state. The wavelength of emitted photon is λ. The principal quantum number of the excited state will be: / / λr λ R+ λr λr / λr( λ R+ ) / (D) λr( λ R+ ) 3. Binding energy per nucleon versus mass number for w, x, y, z are indicated on the curve: Binding energy per nucleon (MeV) z y x w Mass number The process that would release energy is: y z w y w x + z (D) x y + z 4. Figure shows two spherical containers P and Q connected by a tap T. P contains an ideal gas at pressure N/m and temperature 300 K. Q contains same gas at pressure 0 5 N/m and temperature 400 K. If the tap is opened the final pressure becomes m 0 5 N/m. What is the value of m? The volume of Q is four time the volume of P: T P Q (D).8 5. It is believed that non Stoichiometric compound Fe 0.93 formed by dopping of Fe 3+ ions in Fe crystal by replacement of Fe +. The total no. of cationic vacancies in 0. mole of Fe 0.93 are: 0.07 moles moles 0.0 moles (D) 0.04 moles Rough Work

14 AITS-CRT(Set-VI)-PCM-JEE(Main)/ Insulin (C ) n dissolved in a medium shows osmotic pressure π at C gm/cm 3 concentration and 300 K temperature. The slope of π against C is Molecular mass of insulin is (D) Calculate the cell potential of the following cell: Pt(s) (g) (0. bar) B (0. Meq.) A(0. M) (g) ( bar) Pt. Given: K a = 0-7 K b = V 0.93 V 0.36 V (D) 0.63 V 8. According to VSEPR theory, the most stable arrangement is X X X (D) X X X X X 9. ( ) ( ) ( ) 3 AgBr s + S3 aq. Ag S3 ( aq. ) + Br ( aq. ) Given: K ( AgBr) = ; K Ag( S ) = sp f 3 What is the molar solubility of AgBr in 0. M Na S 3? 0.5 M M 0.45 M (D) None of these 0. The heat liberated when.89 g of benzoic acid is burnt in a bomb calorimeter at 5 o C, increase in temperature of 8.94 g water in calorimeter is 0.63 o C. If the specific heat of water is at 5 o C is cal/g deg. The value of heat of combustion of benzoic acid is 88. k cal 77.4 k cal 98. k cal (D) 87. k cal. n heating a mixture of S Cl and C, two equilibria are simultaneously established: SCl( g) S( g) + Cl( g) C( g) + Cl( g) CCl( g) n adding more S at equilibrium what will happen? Amount of C will decrease Amount of S Cl and CCl will increase Amount of C will remain unaffected (D) Amount of S Cl and C will increase Rough Work

15 5 AITS-CRT(Set-VI)-PCM-JEE(Main)/3. The number of isomers possible for disubstituted borazine B 3 N 3 4 X is (D) g of bleaching powder on reaction with KI required 50 ml of N hypo solution. Thus percentage of bleaching powder is: (D) Which of the following statement is incorrect: ICl is a good conductor of electricity in fused state Cl 7 is an anhydride of perchloric acid Melting and boiling points of Br is more than Cl (D) F form stable oxoacids 5. Functionally active form of vitamin D is: Cholecalciferol Ergocalciferol dehydro cholesterol (D) Calcitriol 6. A complex is prepared by mixing CoCl 3 and N 3 0. M solution of the complex was found to freeze at 0.37 o C. The formula of the complex is (K f =.86 o C/m for ) [Co(N 3 ) 6 ]Cl 3 [Co(N 3 ) 4 Cl ]Cl [Co(N 3 ) 5 Cl]Cl (D) [Co(N 3 ) 3 Cl 3 ] Rough Work

16 AITS-CRT(Set-VI)-PCM-JEE(Main)/ ( ) 4 A colourless salt A + Mn / delocalisation of permegnate solution occurs eat x+ y + z, z 'B' ( gases) Gas y + B Milkiness Gas burns with blue flame. Mark the correct choice. A x y z B CaC 3 C C Ca Ca() CaC 4 C C Ca Ca() CaC 4 C C Ca Ca() (D) CaCl Cl Ca Ca() C 3 8. Product (P) Wolff Κishner reduction C C NMe 3 Cl The structure of (P) is C 3 C 3 C C NMe 3 Cl C 3 C (D) C 3 C C 9. Arrange Ce +3, La +3, Pm +3 and yb +3 in increasing order of their size yb +3 < Pm +3 < Ce +3 < La +3 Ce +3 < yb +3 < Pm +3 < La +3 yb +3 < Pm +3 < La +3 < Ce +3 (D) Pm +3 < La +3 < Ce +3 < yb When an impurity in metal has greater affinity for oxygen and is more easily oxidized the metal itself then the metal is refined by: Cupellation Zone refining Poling (D) Electrolytic process Rough Work

17 7 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 Mathematics PART III SECTIN A Straight bjective Type This section contains 30 multiple choice questions numbered to 30. Each question has 4 choices,, and (D), out of which NLY NE is correct.. In a very particular language code for a true statement is and for a false statement is. (i) Image of the point (, 3) in the line y + x = 0 is ( 3, ) (ii) Maximum distance between the two points lying on the two given circles x + y + x + 4y + 4 = 0 and x + y 0x 4y + 59 = 0 is 0 (iii) No tangent can be drawn from the (3, ) to the ellipse 9x + 6y = 44 (iv) Total four circles can be drawn which touch all the sides of a triangle formed by x = 0, y = 0 and 3x + 4y = 4 If codes of the above statements are written in the form of a natural number in the same order then that number is (D). A function f(x) is given by f( x) = ( ) ( ) ( + sin x + cos x + tan x) ( ) ( ) ( ) cosec x + sec x + cot x then range of f(x) lies in the internal (0, 60 ) [ 0, 60 ] ( 60, 80 ) (D) [ 0, 80 ] 3. If c is the shortest distance between the lines x z =, y = 0 and y + z =, x = 0 then which n m n of the following is true + = + + = m n c m n c m + mn + n = (D) + m + n = c c

18 AITS-CRT(Set-VI)-PCM-JEE(Main)/ The exhaustive set of conditions on a and b such that the ellipse x a y + = and the hyperbola b x y = have exactly four tangents in common are 5 6 a ( 5, 5) {0}; b R {0}; a b a ( 5, 5) {0}; b ( 4, 4) {0} b ( 4, 4) {0}; a R {0}; a b (D) a ( 5, 5); b ( 4, 4) {0}; a b y x 5 5. A system of curves is given by x y = 8. Find the range of values of α and β such y 3 x that the points (, α) and (β, ) lies in the largest region enclosed by the above system of curves α ( 4 5, ) and β (, ) ( 4 6, ) α and β (, ) α ( 4 6, ) and β (, ) (D) ( 4 6, ) α and β (, ) 6. In how many ways Ram can distribute 40 applies in his six children named A, B, C, D, E and F such that A gets two more than B, C gets 3 more than F and D gets five less than E and any one must have atleast one fruit (D) A book is having 500 pages printed back to back numbered from to 000. The number of sides where digit 3 is printed. Exactly once, exactly twice and thrice is respectively 8, 9, 43, 7, 33, 8, (D) 300, 6, 8. Number of planes containing the two family of lines x y z + = = and x + 3 y z = = k 0 k k no such plane exactly one plane exactly two planes (D) exactly three planes

19 9 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 9. If y = (sin x + cosec x) + (cos x + sec x) + (tan x + cot x) where x R {x ; x = nπ, (n + )π/ n I} and minimum value of y = p then denotes the greatest function (D) 8 p 3 is where [.] 0. Let C and C be two curves on the complex plane defined as C : z+ z = ( z ) C : arg (z + + i) = α Where α (0, π) such that the curves C and C touches each other at P(z 0 ) then the value of z 0 is 3 (D) 4. Roots of a quadratic equation x + 5x + 3 = 0 are 4cos α + a, and 4sin α + a. Another quadratic equation is given as x + px + q = 0 where p, q N and p, q [, 0]. If roots of second quadratic equation are real then the probability that they are 4cos 4 α + b and 4sin 4 α + b is Let a = ˆi + j ˆ 3kˆ, b = i ˆ+ ˆj kˆ (D) 5 00 length then the vector x satisfying a x = a b and a x = 0 is of 3. Number of integral values of k such that the equation cos x + cot x = k possesses solution is 5 0 (D) 8 (D) 5 4

20 AITS-CRT(Set-VI)-PCM-JEE(Main)/ If we know that sin A = and sin B = 5 but the actual values of A and B are not given, then 3 7 how many different values of cos(a B) are possible depending upon the actual values of A and B 3 (D) 4 5. For a triangle if inradius is six units and the distance of the vertices of a triangle from the nearest pqr point of contact of the incircle with the sides be p.q and r respectively then p+ q+ r is (D) 6 6. If f(x) = 3x 9 x 4 + x 3 3x + x + cos x + 5 and g(x) = f (x) then find the value of g (6) (D) 4 7. Let ( ) = ( + ) x f x t t dt and the mean value theorem says that there must be atleast one c (4, 9) 0 such that f (c) is equal to the average slope of f(x) on [4, 9] then for this number c, c+ c is equal to (D) 35 4 x y 9 8. For the following system of equations y = x z 4z 3 x + y + z =? (D) find the value of

21 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 9. n n n n n n S Let S n = C0 C + C C Cn Cn where n N if n+ 5 = the sum of all possible Sn 4 values of n is (D) 5 0. If z be a complex number such that z α + z 4α = 5 where α R + always represents an ellipse then the number of integral values of α is 3 4 (D) 5. Let z be a non zero complex number and w ( ) be a non real can be root of unity. If the area of triangle formed by A(Z), B(wz) and C(w z) be 48 3 then z is (D) 8 3. If the coefficient of x 7 and x 8 x in the expansion of (D) 55 n are equal the value of n is 3. Let A(z ), B(z ) and C(z 3 ) be the vertices of a triangle ABC such that z 3 + iwz = ( + iw)z where w is the cube root of unity not, then ABC is π π isosceles triangle with A = isosceles triangle with A = 6 3 right angle isosceles (D) equilateral n 0 4. r + 3 n 7. Given Cr = then value of n is r + 0 r= (D) 9

22 AITS-CRT(Set-VI)-PCM-JEE(Main)/3 5. Consider the triangle with sides as a = n +, b = n + and c = n with tan C = 4 3 and n N then area ABC is (D) Number of solutions of the equation cos x + sin x = + in the internal [ π, π] is (D) 8 7. Three vertices of a triangle ABC are given as A(, ), B(7, ), C(3, 4) images of this triangle are taken in x axis, y axis and the line y = x. Now G, G and G 3 are the centroids of the three image triangles then the area of the G G G 3 is 0 0 (D) 3 8. For which of the following functions lim f(x) exists x 0 ( ) x { f x = ( ) x} f x = { sin x} sin x ( ) x [ f x = (D) ( ) x] f x = [ sin x] sin x 9. If the equation 3 x bx cx 0, = ( b c) ( ) ( ) tan cosecα + tan sinαsec α, is π π <, has only one real root α. Then the value of π (D) π 30. Square ABCD is inscribed in a circle point E is on the circle. If AB = 8, then the value of AE + BE + CE + DE is (D) 364