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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 an ellipse with centre (1, 0) and latus rectum of length 21 have its major axis along x-axis. If its minor axis subtends an angle 60∘ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to _______.

202315 Apr Shift 1Ellipse
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 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.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

Q85.Let β†’a = βˆ’Λ†i βˆ’Λ†j + Λ†k,β†’aβ‹… b = 1 and β†’aΓ— b = Λ†i βˆ’Λ†j. Then β†’aβˆ’6 b is equal to (1) 3(Λ†i βˆ’Λ†j βˆ’Λ†k) (2) 3(Λ†i + Λ†j + Λ†k) + (3) 3(Λ†i βˆ’Λ†j Λ†k) (4) 3(Λ†i + Λ†j βˆ’Λ†k)

202325 Jan Shift 2Vectors
MathsHard

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

202310 Apr Shift 1Binomial Theorem
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.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 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.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 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.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.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.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 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.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

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