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Q84.The sum of all those terms, of the arithmetic progression 3, 8, 13, . . . , 373, which are not divisible by 3, is equal to ________. JEE Main 2023 (10 Apr Shift 1) JEE Main Previous Year Paper

202310 Apr Shift 1Sequences & Series
MathsMedium

Q84.Let 𝑆 be the set of values of Ξ», for which the system of equations 6πœ†π‘₯- 3𝑦+ 3𝑧= 4πœ†2, 2π‘₯+ 6πœ†π‘¦+ 4𝑧= 1 and 3π‘₯+ 2𝑦+ 3πœ†π‘§= πœ† has no solution. Then,12 βˆ‘πœ†βˆˆπ‘†πœ† is equal to _______. 2π‘₯

202310 Apr Shift 2Matrices & Determinants
MathsHard

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 = 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.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

Q85.The foci of a hyperbola are ( Β± 2, 0 ) and its eccentricity is 32. A tangent, perpendicular to the line 2π‘₯+ 3𝑦= 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the π‘₯- and 𝑦-axes are π‘Ž and 𝑏 respectively, then |6π‘Ž| + | 5𝑏| is equal to

202313 Apr Shift 2Differentiation
MathsHard

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 the vectors β†’a, b, β†’crepresent three coterminous edges of a parallelopiped of volume V . Then the volume of β†’ β†’ the parallelopiped, whose coterminous edges are represented by β†’a, b +β†’cand β†’a+ 2 b + 3β†’cis equal to (1) 2V (2) 6V (3) V (4) 3V

202306 Apr Shift 2Vectors
MathsEasy

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 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.The mean of the coefficients of π‘₯, π‘₯2, … … , π‘₯7 in the binomial expression of ( 2 + π‘₯) 9 is _________

202311 Apr 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 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 β†’a,β†’b andβ†’cbe three non zero vectors such that β†’b β‹…β†’c= 0 and β†’aΓ— (β†’b Γ—β†’c) β†’bβˆ’β†’c β†’ β†’ β†’ β†’ β†’ is equal to Γ— Γ— b β‹… d =β†’aβ‹… b, then (β†’a b) β‹…(β†’c d) (1) 3 (2) 1 4 2 (3) βˆ’14 (4) 41

202325 Jan Shift 1Vectors
MathsHard

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 𝑆= {1, 2, 3, 4, 5, 6}. Then the number of oneone functions 𝑓: 𝑆→𝑃( 𝑆) , where 𝑃( 𝑆) denote the power set of 𝑆, such that 𝑓( 𝑛) βŠ‚π‘“( π‘š) where 𝑛< π‘š is

202330 Jan Shift 1Sets Relations Functions
MathsHard

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 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.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.The remainder on dividing 599 by 11 is _____ .

202331 Jan Shift 1Sets Relations Functions
MathsEasy

Q85.Suppose βˆ‘π‘Ÿ=20230 π‘Ÿ2 Β· 2023πΆπ‘Ÿ= 2023 Γ— 𝛼× 22022, then the value of 𝛼 is

202324 Jan Shift 1Binomial Theorem
MathsHard

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 = 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.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

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