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Q84.Let y = y(x) be the solution of the differential equation x loge x dxdy + y = x2 loge x, (x 1). If then y(e) is equal to (1) 4+e2 (2) 1+e2 4 4 (3) 2+e2 (4) 1+e2 2 2

202329 Jan Shift 2Differential Equations
MathsMedium

Q84.Let y = y(x) be the solution curve of the differential equation dxdy = xy (1 + x2(1 + loge x)), x > 0, y(1) = 3. y2(x) Then is equal to : 9 (1) x2 (2) x2 5βˆ’2x3(2+loge x3) 2x3(2+loge x3)βˆ’3 (3) x2 (4) x2 3x3(1+loge x2)βˆ’2 7βˆ’3x3(2+loge x2) JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper be a vector such that = 2 . If β†’d

202325 Jan Shift 1Differential Equations
MathsMedium

Q84.Let y = y(x) be the solution of the differential equation (3y2 βˆ’5x2)ydx + 2x(x2 βˆ’y2)dy = 0 such that y(1) = 1. Then (y(2))3 βˆ’12y(2) is equal to : (1) 64 (2) 32√2 (3) 32 (4) 16√2 β†’

202331 Jan Shift 2Differential Equations
MathsMedium

Q84.If the solution curve f(x, y) = 0 of the differential equation (1 + loge x) dxdy βˆ’x loge x = ey, x > 0, passes through the points (1, 0) and (a, 2), then aa is equal to (1) e2e2 (2) ee2 (3) e√2e2 (4) e2e√2 β†’

202306 Apr Shift 2Differential Equations
MathsMedium

Q84.Let y = y(x) be the solution of the differential equation (x2– 3y2)dx + 3 xy dy = 0, y(1) = 1 . Then 6y2(e) is equal to (1) 3e2 (2) e2 (3) 2e2 (4) 3e22 β†’ β†’ β†’ β†’ β†’ β†’

202324 Jan Shift 2Differential Equations
MathsMedium

Q84.The number of integral terms in the expansion of 3 2 + 5

202311 Apr Shift 1Binomial Theorem
MathsMedium

Q84.Let 𝛼> 0, be the smallest number such that the expansion of π‘₯ 3 + 2 has a term 𝛽π‘₯-𝛼, π›½βˆˆπ‘. Then 𝛼 is π‘₯3 equal to _____ .

202331 Jan Shift 1Binomial Theorem
MathsMedium

Q84.The remainder when 19200 + 23200 is divided by 49, is _____ .

202301 Feb Shift 1Binomial Theorem
MathsMedium

Q84.Let y = y(x) be the solution of the differential equation dxdy + x(x5+1)5 y(2) is equal to (1) 637 (2) 679 128 128 (3) 693 (4) 697 128 128 is equal to

202311 Apr Shift 2Differential Equations
MathsMedium

Q84.If the solution curve of the differential equation (y βˆ’2 loge x)dx + (x loge x2)dy = 0, x > 1 passes through the points (e, 34 ) and (e4, Ξ±) , then Ξ± is equal to _______

202308 Apr Shift 1Differential Equations
MathsMedium

Q84.Let y = f(x) be the solution of the differential equation y(x + 1)dx βˆ’x2dy = 0, y(1) = e. Then lim xβ†’0+ f(x) is equal to (1) 0 (2) 1e (3) e2 (4) 1 e2 β†’

202329 Jan Shift 1Differential Equations
MathsMedium

Q84.Let y = y1(x) and y = y2(x) be the solution curves the differential equation dxdy = y + 7 with initial conditions y1(0) = 0 and y2(0) = 1 respectively. Then the curves y = y1(x) and y = y2(x) intersect at (1) no point (2) two points (3) one point (4) infinite number of points β†’ β†’ β†’ β†’ β†’ β†’

202313 Apr Shift 1Differential Equations
MathsMedium

Q84.The 4th term of GP is 500 and its common ratio is π‘šβˆˆπ‘. Let 𝑆𝑛 denote the sum of the first 𝑛 terms of π‘š, π‘š is ______ this GP. If 𝑆6 > 𝑆5 + 1 and 𝑆7 < 𝑆6 + 12, then the number of possible values of

202324 Jan Shift 1Sequences & Series
MathsMedium

Q84.The solution of the differential equation dxdy = βˆ’( x2+3y23x2+y2 ), (1) loge|x + y| βˆ’ xy = 0 (2) loge|x + y| + xy = 0 (x+y)2 (x+y)2 (3) loge|x + y| + (x+y)2 2xy = 0 (4) loge|x + y| βˆ’ (x+y)22xy = 0 + Γ— Γ— Γ— βˆ’ = 8Λ†i βˆ’40Λ†j βˆ’24Λ†k then

202330 Jan Shift 2Differential Equations
MathsMedium

Q85.If the domain of the function 𝑓π‘₯= sec-1 is [𝛼, 𝛽) βˆͺ( 𝛾, 𝛿], then 3𝛼+ 10𝛽+ 𝛾+ 21𝛿 is equal to 5π‘₯+ 3 __________ is the largest, = 4AB. If the area of βˆ†CAB is 2√3 - 3 unit2, when ΞΈ2

202310 Apr Shift 2Inverse Trigonometric Functions
MathsMedium

Q85.If the vectors β†’a = Ξ»Λ†i + ΞΌΛ†j + 4Λ†k, b = βˆ’2Λ†i + 4Λ†j βˆ’2Λ†k and β†’c= 2Λ†i + 3Λ†j + Λ†k are coplanar and the projection of β†’a β†’ on the vector b is √54 units, then the sum of all possible values of Ξ» + ΞΌ is equal to (1) 0 (2) 6 (3) 24 (4) 18 β†’

202329 Jan Shift 1Vectors
MathsMedium

Q85.Let the vectors u1β†’ = Λ†i + Λ†j + aΛ†k, u2β†’ = Λ†i + bΛ†j + Λ†k, and u3β†’ = cΛ†i + Λ†j + Λ†k be coplanar. If the vectors βˆ’βˆ’β†’ β†’ v1 = (a + b)Λ†i + cΛ†j + cΛ†k, v2 = aΛ†i + (b + c)Λ†j + aΛ†k and β†’v3 = bΛ†i + bΛ†j + (c + a)Λ†k are also coplanar, then 6(a + b + c) is equal to (1) 0 (2) 4 (3) 12 (4) 6

202308 Apr Shift 2Vectors
MathsMedium

Q85.Let β†’a = Λ†i + 4Λ†j + 2Λ†k, b = 3Λ†i βˆ’2Λ†j + 7Λ†k and β†’c= 2Λ†i βˆ’Λ†j + 4Λ†k. If a vector d satisfies d Γ— b =β†’cΓ— b and d β‹…β†’a = 24, β†’2 then d is equal to (1) 323 (2) 423 (3) 313 (4) 413 β†’ β†’ β†’ 2

202313 Apr Shift 1Vectors
MathsMedium

Q85.If four distinct points with position vectors →a,→b,→cand →d are coplanar, then [→a→b→c] + + + + (1) [→d →b →a] [→a →c →d ] [→d→b →c] (2) [→a →d →b] [→d →c →a] [→d →b →c] (3) [→d →c →a] + [→b →d →a] + [→c →d →b ] (4) [→b →c →d ] + [→d →a →c] + [→d →b →a] → → → = 27 and b ⋅→c=

202311 Apr Shift 2Vectors
MathsMedium

Q85.Let 𝐴= 1, 2, 3, 4, . . . . . . . . . . 10 and 𝐡= 0, 1, 2, 3, 4 . The number of elements in the relation 𝑅= (π‘Ž, 𝑏) βˆˆπ΄Γ— 𝐴: 2π‘Ž- 𝑏2 + 3π‘Ž- π‘βˆˆπ΅ is __________ .

202306 Apr Shift 1Sets Relations Functions
MathsMedium

Q85.Let β†’a = 5Λ†i βˆ’Λ†j βˆ’3Λ†k and b = Λ†i + 3Λ†j + 5Λ†k be two vectors. Then which one of the following statements is TRUE? β†’ β†’ (1) βˆ’13 (2) βˆ’17 Projection of β†’a on b is and the direction Projection of β†’a on b is and the direction of √35 √35 of the projection vector is opposite to the the projection vector is opposite to the direction β†’ β†’ direction of b of b β†’ β†’ (3) 17 (4) 13 Projection of β†’a on b is and the direction of Projection of β†’a on b is and the direction of √35 √35 the projection vector is opposite to the direction the projection vector is opposite to the direction β†’ of b of β†’a β†’

202301 Feb Shift 2Vectors
MathsMedium

Q85.Let Ξ» ∈R,β†’a = Ξ»Λ†i + 2Λ†j βˆ’3Λ†k,β†’b = Λ†i βˆ’Ξ»Λ†j + 2Λ†k, If ((β†’a β†’b) (β†’a β†’b)) (β†’a β†’b) β†’ β†’ + Γ— βˆ’ 2 is equal to Ξ»(β†’a b) (β†’a b) (1) 140 (2) 132 (3) 144 (4) 136 β†’ β†’ b, then the value of Γ— βˆ’3 b β‹…β†’cis

202330 Jan Shift 2Vectors
MathsMedium

Q85.The coefficient of π‘₯7 in 1 - π‘₯+ 2π‘₯310 is __________ .

202310 Apr Shift 1Binomial Theorem
MathsMedium

Q85.If 𝑓π‘₯= π‘₯2 + 𝑔'1π‘₯+ 𝑔"2 and 𝑔π‘₯= 𝑓1π‘₯2 + π‘₯𝑓'π‘₯+ 𝑓"π‘₯, then the value of 𝑓4 - 𝑔4 is equal to _____ .

202301 Feb Shift 1Differentiation
MathsMedium

Q85.Let Ξ» ∈Z, β†’a = Ξ»Λ†i + Λ†j βˆ’Λ†k and b = 3Λ†i βˆ’Λ†j + 2Λ†k. Let β†’c be a vector such that + b = 0, β†’aβ‹…β†’c= βˆ’17 and b β‹…β†’c= βˆ’20. Then β†’cΓ— (Ξ»Λ†i + Λ†j + Λ†k) is equal to (β†’a β†’ β†’ β†’ 2 +β†’c) Γ—β†’c (1) 46 (2) 53 (3) 62 (4) 49 JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper

202312 Apr Shift 1Vectors
MathsMedium

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