2018 JEE Maths Solved paper

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## 2018 JEE Maths Solved paper

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**www.zigya.com**Previous YearPaper Mathematics -2018**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. Multiple ChoiceQuestions For each t ∈R, let [t] be the greatest integer less than or equal to t. Then limx→0+x1x+2x+......+15x does not exist (in R) is equal to0 is equal to 15 is equal to120 Answer If the tangent at (1, 7) to the curve x2 = y – 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of cis 95 195 185 85 Answer If α, β∈ C are the distinct roots, of the equation x2 -x + 1 = 0, then α101 + β107 is equal to 2 -1 1 Answer PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the anglesof elevation of the top of the tower at P, Q and R are respectively 45o, 30o and 30o, then the height of the tower (in m)is 502 100 50 1003 Answer The sum of the coeﬃcients of all odd degree terms in the expansion of x + x3 -15 + x - x3-15, (x>1) is 2 -1 Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. 1 Answer Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of△PTQ is 365 455 543 603 Answer From 6 diﬀerent novels and 3 diﬀerent dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangementsis At least 750 but less than 1000 At least1000 Less then500 At least 500 but less than 750 Answer Two sets A and B are asunder: A = {(a-b)∈ RxR:|a-5|<1 and|b-5|<1} B = {(a,b)∈ Rx R: 4(a-6)2 + 9 (b-5)2 ≤36},then Neither A ⊂ B nor B ⊂ A B ⊂A A⊂ B A ∩B = ϕ(an empty set) Answer Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and Band, ∠CPB = θthen a value of tan θis 4/3 1/2 2 3 Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. Answer The Boolean expression ~ (p v q )v (-p ∧q) is equivalentto ~q ~p p q Answer A straight line through a ﬁxed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of Ris 3x + 2y = 6xy 3x + 2y =6 2x + 3y = xy 3x + 2y =xy Answer Let A be the sum of the ﬁrst 20 terms and B be the sum of the ﬁrst 40 terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 +..... If B – 2A = 100λ, then λis equal to 496 232 248 464 Answer Let a1, a2, a3, ...., a49 be in A.P.such that ∑k = 012ak-1 = 416 and a9 + a43 = 66. if a12 + a22 + ....... + a172 = 140m then m is equal to 33 66 68 34 Answer 14. Let f(x) = x2 + 1x2 and g (x) = x - 1x, x ΕR - {-1,0,1}. if h(x) = f(x)g(x), then the local minimum value of h(x)is: 22 3 -3 Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. -22 Answer 15. If ∑i=19 (xi -5) = 9 and ∑i = 19(xi - 5)2 = 45 then the standard deviation of the 9 items x1, x2, ...., x9is 3 9 4 2 Answer If the system of linear equations x + ky + 3z =0 3x + ky – 2z = 0 2x + 4y – 3z =0 has a non-zero solution (x,y,z), then xz/y2 is equal to 30 -10 10 -30 Answer If x-42x2x2xx-42x2x2xx-4 = (A +Bx)(x-A)2, then the ordered pair (A,B) is equal to (4,5) (-4,-5) (-4,3) (-4,5) Answer Let S = {t ∈R: f(x) = |x-π|.(e|x| - 1) sin |x| is not diﬀerentiable at t}. Then the set S is equalto {0,π} ϕ(an emptyset) {0} {π} Answer let y = y(x) be the solution of the diﬀerential equation sin x dydx + y cos x = 4x, x∈ (0, π). If y = π2 = 0, then yπ6 is equalto: Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. -49π2 493π2 -893π2 -89π2 Answer 20. Let S = { x ∈ R : x ≥ 0 and 2|x-3| + x(x-6) + 6 = 0} Then S: Contains exactly fourelements Is an empty set Contains exactly one element Contains exactly twoelements Answer If the curves y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is 9/2 6 7/2 4 Answer Let u→ be a vector coplanar with the vectors a a→ = 2i^ + 3j^- k^ and b→ = j^ +k^. if u→ is perpendicular to a→ and u→.b→ = 24, then |u→| is equal to: 84 336 315 256 Answer If L1 is the line of intersection of the plane 2x – 2y + 3z – 2 = 0, x – y + z + 1 = 0 and L2 is the lineof intersection of the plane x + 2y – z – 3 = 0, 3x – y + 2z – 1 = 0, then the distance of the origin from the plane containing the lines L1 and L2 is: 12 142 132 122 Answer The value of ∫-π2π2sin2x1+2xdxis: Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. π/4 π/8 π/2 4π Answer Let g(x) = cos x2, f(x) = x and α, β(α < β) be the roots of the quadrtic equation 18x2 - 9πx + π2= 0. Then thearea(insq.units)boundedbythecurvey=(gof)(x)andthelinesx=α,x=βandy=0is 12(2-1) 12(3-1) 12(3+1) 12(3-2) Answer If sum of all the solutions of the equation 8 cos x. cos π6+x.cosπ6-x-12 = 1 in [0,π] is kπ, then k is equal to: 20/9 2/3 13/9 8/9 Answer The Integral∫sin2 x cos2 x (sin5 x + cos3 x sin2 x + sin3 x cos2 x + cos 5x)2dx is equal to (where C is a constant ofintegration) -11+ cot3 x + C 13(1 + tan3 x) +C -13(1 + tan3 x ) +C 11+ cot3 x + C Answer A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at randomfromthebag,thentheprobabilitythatthisdrawnballisred,is: 3/4 3/10 2/5 1/5 Answer Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is thecircumcentre Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com**Mathematics JEE2018**Exam Year 2018 Study, Assignments, Solved Previous Year Papers .Questions and Answers. Free Forever. of this triangle, then the radius of the circle having line segment AC as diameter,is 352 10 210 352 Answer 30. The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7is: 23 23 2/3 1/3 Answer Like. Share. Bookmark. Download. Make Notes. Print - Your Favourite Questions. Joinwww.zigya.com