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

202301 Feb Shift 1Binomial Theorem
MathsMedium

Q84.If the four points, whose position vectors are 3Λ†i βˆ’4Λ†j + 2Λ†k,Λ†i + 2Λ†j βˆ’Λ†k, βˆ’2Λ†i βˆ’Λ†j + 3Λ†k and 5Λ†i βˆ’2Ξ±Λ†j + 4Λ†k are coplanar, then Ξ± is equal to (1) 7317 (2) βˆ’10717 (3) βˆ’7317 (4) 10717 β†’ β†’ β†’

202325 Jan Shift 2Vectors
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.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 = 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.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 a, b, c be three distinct real numbers, none equal to one. If the vectors aΛ†i + Λ†j + Λ†k, Λ†i + bΛ†j + Λ†k and Λ†i + Λ†j + cΛ†k are coplanar, then 1βˆ’a1 + 1βˆ’b1 + 1βˆ’c1 is equal to (1) 2 (2) βˆ’1 (3) βˆ’2 (4) 1 β†’

202312 Apr Shift 1Vectors
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.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

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

Q85.Let Ξ± = 4Λ†i + 3Λ†j + 5Λ†k and Ξ² = Λ†i + 2Λ†j βˆ’4Λ†k. Let Ξ²1 be parallel to Ξ± and Ξ²2 be perpendicular to Ξ±. If β†’ β†’ β†’ β†’ + Ξ² = Ξ²1 + Ξ²2 , then the value of 5 Ξ²2 β‹…(Λ†i +Λ†j Λ†k) is (1) 6 (2) 11 (3) 7 (4) 9 β†’ β†’ β†’ β†’ b + 43 = 0 , β†’aΓ—β†’c= b Γ—β†’c, then β†’aβ‹… b is equal to

202324 Jan Shift 2Vectors
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.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» ∈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

Q85.If the points with position vectors Ξ±Λ†i + 10Λ†j + 13Λ†k, 6Λ†i + 11Λ†j + 11Λ†k, 92Λ†i + Ξ²Λ†j βˆ’8Λ†k are collinear, then (19Ξ± βˆ’6Ξ²)2 is equal to (1) 36 (2) 25 (3) 49 (4) 16 β†’ β†’

202308 Apr 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 + 2Λ†j + 3Λ†k, b = Λ†i βˆ’Λ†j + 2Λ†k and β†’c= 5Λ†i βˆ’3Λ†j + 3Λ†k, be there(three) vector. If β†’ris a vector such that, β†’rΓ—β†’b =β†’cΓ—β†’b and β†’rβ‹…β†’a = 0, then 25β†’r 2 is equal to (1) 560 (2) 339 (3) 449 (4) 336 . If the angle Γ— = 3(β†’cΓ—β†’a)

202331 Jan Shift 2Vectors
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 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.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.The coefficient of π‘₯7 in 1 - π‘₯+ 2π‘₯310 is __________ .

202310 Apr Shift 1Binomial Theorem
MathsMedium

Q85.If β†’a = Λ†i + 2Λ†k, β†’b= Λ†i + Λ†j + Λ†k, β†’c= 7Λ†i βˆ’3Λ†j + 4Λ†k, β†’rΓ—β†’b+β†’bΓ—β†’c=β†’0 and β†’rβ‹…β†’a = 0 then β†’r.β†’cis equal to: (1) 34 (2) 12 (3) 36 (4) 30 + Λ†j + Γ— = 4

202329 Jan 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.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.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

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