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sete pmeee ote teens oo em me wrens ee ww ome cone coe we cere owas ees ©, , MATHEMATICS MAX.MARKS: 100, SECTION -1, (SINGLE CORRECT ANSWER TYPE), This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its, answer, out of which ONLY ONE option can be correct., Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct., , 61. The line x =5 divides the triangle with vertices (0,0),(1,1)and(9,1) into two regions. If the, area of the two regions is the same, then c is equal to, 1) 30 2)6 32 4) 15, , 62. The distance of the y-axis from the center of the circle which lies in the first quadrant, (see figure) and tangent to the lines y=a% y = 4and the x-axis is, , , , 1) 4425 units 2) 4-5 unis 3) 2+ 8 nits 4) 4-25 units, , 63. A tangent is drawn to the parabola y* =8x at P(2,4)to intersect the x-axis at Q, from, , which another tangent is drawn to the parabola to touch it at R. if the normal at R, intersects the parabola again at S, then the coordinates of S are, , 1) (6,4) 2) (18,12) 3) (8,8) 4) (8,6), , 64. The tangent at the extremities of the latus rectum of the ellipse 3x° +4y* =12 forma, rhombus PQRS. Area (in sq. units) of the rhombus PQRS outside the ellipse is equal to, , 1) 8-23 2) 12-243 3) 14-f 4) 16-23

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ewer yur te uo ee ek, , , , 65., , 67., , Consider the function f(x) = min {|x° ~4],|x* -1)} , then the number of points where f(x) is, non-differentiable is/are, 10 2)7 3)6 4)4, , If f:A— Bdefined as f(x) =2sin.x—2cos x+3¥2 is an invertible function, then the correct, , statement can be, , » a-|£ 5) [as] 2 a-|~ 7 | 0-[vi.si], , 3) A -|L 2) 9-8] 4) a-|t.¥).a-[ 2.508], The average weight of students in a class of 32 students is 40 kg. If the weight of the, , teacher be included, the average rises by hg , then the weight of the teacher is, , 1) 40.5 kg 2) 50 kg 3) 41 kg 4) 5ikg, , An observer finds that the angular elevation of a tower is , , On advancing 3m towards, the tower, the elevation is 45° and on advancing 2m further more towards the tower, the, elevation is 90°-, . The height of the tower is (assume the height of observer is, , negligible and observer lies on the same level as the foot of the tower), , 1) 2m 2)4m 3) 6m 4) 8m, , 8, ", 2, i, ~, +, R,, ms, , =i+}-4k and non-zero vector care such that (axb)xe=ax(bxe), then, , 1) 43-2} +64 2) 4in2j+68 3) 74.j-E 4) i-aj+k

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Norsyane ui Accoemy Pyverst_ 20) OY 2u_ JEE-mN_oim- ren, , 70. Leta, b and c are the roots of the equation x’ —7x° +9x~—13=Oand A and B are two, abe be~a -b ab-c, matrices given by A=|b ¢ aland B=|ca-b* ab-c* be—a’ |, then the value of, cab ab-c? be-a" ca-b*, |4l|B|is equal to, 1) -154 2) -(154)" 3) -22 4) -(22)", 71. The plane /has the equation 41~2y+2:=3and », Parte -22=7. If the, , angle between es, , , , 72. Let a-|? i 2, then, , 73. Thei, 8, 74. If both —mx¢+, 1) ms-2 3) -Ism,s3 4) O<m<=, , NARAYANA .OU I, , 75. The number of solutions of the equation sin’ xcos.x+sin* xcos* x+cos’ xsinx+1=Oin the, interval [0,2f Jis equal to, , 10 2)2 3)4 4)8

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76. The solution of the differential equation 2,2. aS (|s|< iis, , Wy =-FO) c(1-x'), where {4}=3and C is an arbitrary constant. Then, the value of, , (4), , 3 3 1 3, 1) eS 2) 3 3) a "a 2, a) . - n ., 77. The limit L=lim Ya psatisfies, f r £, I) 7>6 2) ae 3) rae 4) 7<!, , 78. If the integral = fzaodeak +1 (x'-2)+C, (where, Cis the constant of, integration), thenthe value of 9K is equal to, 14 2)2 3)6 4) 10, , 79. The function f(x) =2x’—3(a+b)x° +6abxhas a local maximum at x=a, if, l) a>b 2) a<b 3)a>0 4) a<0, , 80. If A={z:x=3 -2n-Lne N} and B= {x:x=4(n-1),ne N}, then, , 1) AcB 2) BcA 3) AUB=A 4) ANB=B, SECTION-II, (Numerical Value Answer Type), , This section contains 10 questions. The answer to each question is a Numerical value. If the numerical value has, more than two decimal places, Truncate /Round-off the value of Two decimal ploces. Have to Answer, any 5 only out of 10 questions and question will be evaluated according to the following marking scheme:, Marking scheme: +4 for correct answer, 0 in all other cases., , 81. If the area bounded by the curves x’ + y’ <4,.+y22, and y2lis at Ely units,, , then the value of K is equal to

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82. The second term of an infinite geometric Gagan is 2 and its sum to infimity i is $8. “The, first term is, , 83. The probability of a bomb hitting a bridge is :. Two direct hits are needed to destroy, the bridge. The minimum number of bombs required such that the probability of bridge, , being destroyed is greater than “ is, , 91n(2—cos 25x) ., 84. The val f tim “Vis s equal to, ‘eee © Sin’ (sin 3x +1), , 85. The number of distinct complex number(s) z, such that |z|=1and ='is purely imaginary,, is/are equal to, 86. Let AB is the focal chord of a parabola and D and C be the foot of the perpendiculars, , from A and B on its directrix respectively. If CD=6 units and area of trapezium ABCD is, 36 square units, then the length (in units) of the chord AB is, , 87. A total of 6 boys are 6 girls are to sit alternatively in a row and in a circle. Let m be the, number of arrangements in the row and n be the number of arrangements in the circle., , =, ift=—— . then the value of k is, 88. Let @=7+2]+3k,6 =i-j+2k and 2 =(x-2)i-(x-3)j-&. If é lines in the plane of a and, b then ~ is equal to, 89. nie) ; +C (where, C is the constant of integration) and (1) =~- 2, then, the value of |r(W3) is, , 90. Number of integral terms in the expansion of (v5+97)" is