TEST - 5 (Paper-I) ANSWERS

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1 TEST - 5 (Paper-I) ANSWERS PHYSICS CHEMISTRY MATHEMATICS. () 3. () 6. (). (3) 3. () 6. () 3. () 33. () 63. (3). () 3. () 6. () 5. () 35. () 65. (3) 6. () 36. (3) 66. () 7. (3) 37. () 67. () 8. (3) 38. () 68. () 9. () 39. () 69. (). (). () 7. (). (). () 7. (). (). (3) 7. () 3. () 3. () 73. (). (). () 7. () 5. () 5. () 75. () 6. () 6. () 76. () 7. () 7. () 77. () 8. () 8. (3) 78. (3) 9. () 9. (3) 79. (3). (3) 5. (3) 8. (). () 5. () 8. (3). (3) 5. (3) 8. () 3. (3) 53. () 83. (). () 5. () 8. (3) 5. () 55. () 85. () 6. () 56. (3) 86. () 7. () 57. () 87. () 8. () 58. () 88. () 9. (3) 59. () 89. (3) 3. () 6. () 9. (3) /7

2 . Answer () kq ka' b a a a' q b. Answer (3) 3. Answer (). Answer () 5. Answer () 6. Answer () 7. Answer (3) 8. Answer (3) 9. Answer (). Answer () Radius of the new sphere r 8, r mm 3 3 Total charge = = 9 C Capacitance = C = r PART - A (PHYSICS) W W U b V. SV W VSV 5. Answer () 6. Answer () 7. Answer () 8. Answer () 9. Answer () X R l l dx d X l l( l) W SV SV For minimum error l( l) is maimum l = 5 cm. Answer (3) Q U C. Answer () 7. mj A P C Potential at A = = 7 V Potential at A = Potential at P. Answer () 3. Answer (). Answer () R sin AC R P = q B A = R q U i = E S C /7 SV q S C SV q U f R qe R U qe A B

3 . Answer () 5. Answer (). Answer (3) R net across C = 3. Answer (3) = RC a R 3a R a Ey Ey E z y y z 6 6. Answer () E E R R V V L 3 a a L 3a a Ohm's law E J V V E E J 3 J S net net i qen qen i 3. Answer () ZnO is hot becomes yellow but in cold it is white. 3. Answer () MSO 3 SO K Cr O 7 + H SO + SO Cr (SO ) 3 Green 33. Answer () 3. Answer () 35. Answer () Ca + and Sr + same group cations. 36. Answer (3) Cu [Fe(CN) ] Cu [Fe(CN) ] 6 6 redbrown 3 V V = 8 V 6. Answer () 7. Answer () 8. Answer () 9. Answer (3) 3. Answer () PART - B (CHEMISTRY) 37. Answer () All are ambidentate ligands. 38. Answer () 39. Answer () EAN = 8 + ( ) = 3. Answer (). Answer () SCN is a weak ligand Co + No. of unpaired electrons is 3. So, 3(3 ) BM. Answer (3) In [NiCl ], Ni has sp 3 hybridisation. 3/7

4 3. Answer () Cr +3 The hybridisation of the comple is d sp 3. Answer () + Cl Cl en Co +3 en No plane of symmetry. 5. Answer () 6. Answer () 7. Answer () Mn + has 5 unpaired electrons. 8. Answer (3) 9. Answer (3) 5. Answer (3) 5. Answer () 5. Answer (3) 53. Answer () 5. Answer () 55. Answer () 56. Answer (3) 57. Answer () 58. Answer () 59. Answer () 6. Answer () PART - C (MATHEMATICS) 6. Answer () Number of subsets = C + C = 6 = Answer () It is very clear that 6 n(a B). Hence, if n((a B) C) is maimum than C (A B). 63. Answer (3) As 6 = 3 or 6 = 6 For maimum value of n(a B B A), n(a) =, n(b) = 3 and A B n(a B) = Maimum value of n(a B) = n(a B B A) = 6. Answer () ( y) + y ( y) = y, clearly relation is equivalence. 65. Answer (3) f() = k 3 k k 6 Least integral value of k = 66. Answer () log {} [] < [] {} < [] [] = [, )...(i) Also, {} >, {} integer...(ii) By (i), (ii), 3 Domain = (, ) 67. Answer () The given function can be written as ( )( 3) 3 f( ),, ( )( ) Let 3 y y y = 3 (y ) = y 3 /7

5 y 3 y y Also, if =, then If =, then Hence, A,, y y 5 37 Sum Answer () Clearly, g() is the inverse of f(). The domain of g() is the range of f(). As f() is increasing function a = f() = 3 and b = f() = = a + b = 3 + = 69. Answer () = =, = Hence, f() is symmetrical about the lies = and =. The period of f() = ( ) = = Hence, the period of f() = =. 7. Answer () Clearly, statement S, S and S 3 are true but S is incorrect. Because if g( + y) = g() + g(y) g() = g() + g( ) [Replacing y by ] Also, g() = g() + g() g() = Hence, g() + g( ) = g() is odd Similarly, h() is odd. Hence, in this case, f() will be an odd function. 7. Answer () The given it is 6 3 ( ) ( )( 3 = ) = 7. Answer () The given it is tan, where [ ] greatest integer function, but if + then < tan. Hence the value of it = 73. Answer () sin. cos sin. cos LHL = RHL = sin( h). cos h =. = 9/ h sin h cos h h = 9/. h 7. Answer () If { } represents fractional function, then f() can be written as f() = min.{{}, { }}. Y B C E X A 3 The graphs of y = {} represented by AB, CD. The graphs of y = { } represented by BC, DE. D Clearly f() is not differentiable at Sum = Answer () 3,, k cot ( tan { tan }), where { } represents fractional functional k cot { tan } Hence, [, 5/7

6 76. Answer () For g()r, {[g()]} = [{g()}] =, then f() =, which is continuous and differentiable everywhere. 77. Answer () The given function can be written as f() = ( 6 + 5) 5 = ( 6 + 5) Hence, f() is continuous everywhere. 78. Answer (3) Clearly, y = sin 8 d y d = 8 sin8 = 8 sin 8k k = 8 k + 8 = 79. Answer (3) The equation can be written as f() f() 5 ( f ) f() f( ) f( ) f() = f() = Hence, f() is constant. Hence, it is even function. 8. Answer () log = + [log ] As [log ] is an integer, hence log is also an integer by the given equation. [log ] = log Hence, the given equation can be written as (log ) log = (log )(log + ) = log = = = And log 8. Answer (3) () Number of functions from A to B = 9. () Number of surjective function from B to C is. (3) Number of surjective functions from C to B = 3 3 C (3 ) + 3 C (3 ) = 36. () Number of one-one function = 3 P = 6 8. Answer () If {a + } > [a + ] [a + ] =,,... but [a + ] > {b + } [a + ] =,, 3,... Hence no value of a and b eists. Hence R is null relation. 83. Answer () Using AM GM for, 3 3 Also, /3 is minimum at =. y ( ) y ma also at = Hence, the minimum value of f() = 3 =. 8. Answer (3) f(g()) = g(f()) = f(g()) g()= g(f()) f() = g( ) g() f( g( )) f( g()) But g() is the value of at which f() = = + sin = g() = g() f () Again, f() = + sin f() = + cos f() = 9 Sum 6/7 g()

7 85. Answer () Differentiating the equation with respect to, 3 ( ) f f 5 At =, f() + 3f() = 5 f() = 86. Answer () Statement : Number of refleive relation = =. Statement : If, then [] = k. log k sin Also, Hence, Statement- and Statement- both are true, but Statement- is not the correct eplanation of Statement Answer () Statement : The given it can be written as sin cos (Using L-H rule) sin Statement : The it can be written as tan tan e tan tan e Hence statement- and statement- both are true but statement- does not eplain statement Answer () Statement-: 33 6 = + 6 = 5 Hence statement- is false. Statement-: = cos sin sin cos Hence statement- is true. 89. Answer (3) Satement-: at =, f() = ( ) f Hence statement- is true. Statement- f() is countinuous at = Hence statement- is false 9. Answer (3) Statement-: Hence statement- is true. 3 Statement- is clearly false as k = e. 7/7