NARAYANA IIT/PMT ACADEMY

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1 CPT-_XI (LJ) NARAYANA IIT ACADEMY ANSWER KEY XI STUD (LJ) IITJEE MAINS MODEL Exam Date : physics Chemistry Mathematics. (C). (C) 6. (A). (A). (B) 6. (C). (B). (A) 6. (B) 4. (A) 4. (D) 64. (B) 5. (C) 5. (C) 65. (A) 6. (A) 6. (B) 66. (C) 7. (D) 7. (C) 67. (A) 8. (A) 8. (D) 68. (B) 9. (A) 9. (A) 69. (A) 0. (A) 40. (B) 70. (B). (B) 4. (C) 7. (A). (B) 4. (D) 7. (A). (C) 4. (D) 7. (B) 4. (B) 44. (B) 74. (A) 5. (C) 45. (B) 75. (D) 6. (A) 46. (B) 76. (C) 7. (C) 47. (C) 77. (A) 8. (A) 48. (D) 78. (D) 9. (A) 49. (D) 79. (C) 0. (B) 50. (A) 80. (A). (A) 5. (B) 8. (A). (C) 5. (A) 8. (C). (C) 5. (A) 8. (A) 4. (A) 54. (A) 84. (A) 5. (B) 55. (C) 85. (B) 6. (B) 56. (B) 86. (D) 7. (C) 57. (B) 87. (A) 8. (B) 58. (C) 88. (D) 9. (B) 59. (A) 89. (C) 0. (B) 60. (A) 90. (A) Page No.

2 CPT-_XI (LJ) (C) KA t m A l Q ml m A l. (A) HINTS & SOLUTION PHYSICS Q Q t t BC CA KA T T KA TC T l l. (B) KA t mlice d KA6a t ice a Lice d Here, a, d are side and thickness of cube. Heat conducts through six faces. 4. (A) dt L 0 dt 5. (C) dt 0 ; R 0 dt 6. (A) dq KA d dt arc length 7. (D) Area of graph = E E 4 T and E 4 T 8. (A) 9. (A) Consider a concentric spherical shell of radius r and thickness dr as shown in the figure. Page No.

3 CPT-_XI (LJ) The radial rate of flow heat through his shell in steady state will be dq dt dt H KA K 4 r dt dr dr r dr 4 K T dt r r H T Which one integration and simplification gives dq 4 Kr r T T H dt r r dq r r dt r r 0. (A) A A t. (B) T t T. (B) L ; L L L t t. (C) The work done = area of P- diagram, P a b P P P W 4.: (B) du dq dw dw dw 0; AB BC CA 5. (C) rms N RT d M T T k 6. (A) Line equation for wavelength y mx c Page No.

4 CPT-_XI (LJ) P0 nrt P P0 0 P0 T P 0 nr 0 dt To get max up temp 0 d 0 & sub.in eq.() for T max 7. (C) U 4 P kt P mrt RT 4 kt T R T 8. (A) nrt0 i P0 At constant pressure as temp doubles volume doubles so nrt0 f P 0 Work done f i W P 9. (A) Isothermal process, du=0 0. (B) nrt T T dw. (A) R CP C M. (C) R R CP ; C. (C) du dq P 4. (A) dw dq 5. (B) Q nc T; P P C C R C C R P P Page No.4

5 CPT-_XI (LJ) U nc T 6. (B) U a bp; But CP C R; CP C 7. (C) T k dt kd Or dt nrt d ; P ; k W Pd 8. (B) dq nc dt dq ncdt dq nc dt 9. (B) dq nc dt 0. (B) P C C r where P r mt. C EN : B Tl In Ga Al. B Improper shielding effect. A BN n CHEMISTRY 4. D Na B4O OH.8H 4 O 5. C 6. B p p bonding between B and F 7. C 8. D Borax bend test must be performed for metals which can form coloured metaborates. 9. A 40. B A = HBO, B HB4O7 4. C 4. D 4. D Due to similar polarising power 44. D Diborane contains four B-H and two B-H-B bonds 45. B Tetrahedral 46. B 47. C Page No.5

6 CPT-_XI (LJ) D 49. D 50. A 5. B 5. A A MATHEMATICS 6. A. Let the tangent to parabola be y=mx+ a/m, if it touches the other curve, then D=0, to get the value of m. For parabola, y 4x Let y mx be tengent line and it touches the parabola m x y. x mx m x mx 0 m D=0 m 4 0 m / 8 m m=/ 6. C. The given equation can be written as (x+) = (y ). Shifting the origin at (, ) this equation becomes X = Y, Where x= X, y = Y +. The vertex of this parabola is at (, ) and the tangent at the vertex is Y = 0 i.e. y =. 6. B t t t 64. B. Clearly, A = (8p, 8p) and B = (8p, 8p) Also (0, 0) m of A = ; m of B = Therefore, A B. 65. A A 8p 8p y = 8px Page No.6

7 CPT-_XI (LJ) Given line is y = x 5. So, in this case m = and c = 5. The line is a tangent to the parabola 4 iff c = a m 5 a a = 5 = 5/ C 67. A Any point on the parabola is (x, x + 7x + ) Its distance from the line y = x is given by P x x 7x x 4x x 4x 5 as x 4x 5 0 for all x R 0 dp 0 x dx The required point = (, 8). Hence (A) is the correct answer. 68. B Since length of latus rectum = 8/7 Latus rectum is the smallest focal chord. Hence focal chord of length 4/7 does not exist. Hence (B) is the correct answer. 69. A Equation of the circle p x y r It touch the directrix x + a = 0 then r = p p So equation circle is x y p Coordinates of the intersection of () and y p = px is, Hence (A) is the correct answer. 70. B t t Slope of PQ = t t t t coordinates of point R (h, k) then p Page No.7

8 CPT-_XI (LJ) t t 4t t h and k 8 4 Using (), k h So locus is y x 9 9 Hence (B) is the correct answer. 7. A FA = 4, FB = We know that a 4a a AF FB 9 9. Hence (A) is the correct answer. 7. A Equation of normal to the parabola y = 4ax at the point (at, at ) is y+ tx = at +at.() () cuts the parabola again at (at, at) Then, at + t at = at +at a( T t) = at ( T t ) = t ( T + t ) [ t T] t + tt + = 0 t is real T T 8. Hence (A) is the correct answer. 7. B Any normal of parabola is y = - tx + t + t. If it pass through (6, 0), then 6t + t + t = 0 t = 0, t = 4, A (4, 4) thus for non common tangents AC > r 4 6 r r < 0 Hence (B) is the correct answer. 74. A Since the normal at (ap, ap) to y = 4ax meets the parabola at (aq, aq), Page No.8

9 CPT-_XI (LJ) q p...() p ap 0 aq 0 Since OP OQ, pq 4 p p 4 (using (i)] ap 0 aq 0 p p Hence (A) is the correct answer. 75. D t,t be any point t 4t 4 t 4 t K 4 Area = C Pt, Qt is focal chord t t = A x 6 y tangent is It is passing through (4, 0) focus of parabola y m x m 6 0 m m m 4m m m 78. D Point is point of intersection of directrix and tangent 79. C,, Point of intersection of tangent att, a t t h, k p at at and Q at at is, (-a, b) are collinear. a att bt t h k a a b. a a 80. A Let, be the point w.r.t, PQ is chord of contact 8. A Line joining midpoint of PQ & T is parallel to axis of the parabola. 8. C Any tangent to circle is y m x m y 4x Any tangent to parabola is y mx m If this line is tangent to circle then m m m m m but P,Q Page No.9

10 CPT-_XI (LJ) A Any tangent to the parabola y x is y mx m A If P,Q,R are conormal points on parabola y 4ax and normals of which concurrent at T then SP.SQ.SR = ast., where S is focus. For 85. B The equation of normal at, As () passes trhough P(h,k), so y x focus is 8( ) (0,0) at at is y tx at at... at t a h k 0 t t () Here a= t t t 0..() Given t t... 4 t t From () and (4) t h Put t in, we get Locus of P(h,k) is x-y= 86. D t k 0 h k 0 The minimum distance will be long the common normal. If normal at P am (, am) ie. y mx am am passes through C(6,0) which is centre of circle given with radius 5, t then m 0,, then P (4,4),(4, 4),(0,0) The imum dis ce min tan (6 4) A Circle should intersect or touch the directrix of the parabola i.e,. x+y 4 =0 88. D The locus is directrix of the parabola 89. C 0,0) is focus of the parabola. The circle on focal chord as diameter always touches directrix. x A Eqn of Directrix is x y 0 Page No.0

( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y.

PROBLEMS 04 - PARABOLA Page 1 ( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x - 8. [ Ans: ( 0, - ), 8, ] ( ) If the line 3x 4 k 0 is