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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 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.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.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

Q86.Let β†’a = 4Λ†i + 3Λ†j andβ†’b = 3Λ†i βˆ’4Λ†j + 5Λ†k andβ†’cis a vector such that β†’cβ‹…(β†’a β†’ b) + 25 = 0,β†’cβ‹…(Λ†i Λ†k) β†’ and projection of β†’con β†’a is 1 , then the projection of β†’con b equals: (1) 5 (2) 1 √2 5 (3) 1 (4) 3 √2 √2

202329 Jan Shift 2Vectors
MathsMedium

Q86.Let β†’a = 6Λ†i + 9Λ†j + 12Λ†k, b = Ξ±Λ†i + 11Λ†j βˆ’2Λ†k and β†’cbe vectors such that β†’aΓ—β†’c=β†’aΓ— b If β†’aβ‹…β†’c= βˆ’12, and β†’cβ‹…(Λ†i βˆ’2Λ†j + Λ†k) = 5 then β†’cβ‹…(Λ†i + Λ†j + Λ†k) is equal to _______

202308 Apr Shift 1Vectors
MathsMedium

Q86.Let β†’a = 3Λ†i +Λ†j βˆ’Λ†k and β†’c= 2Λ†i βˆ’3Λ†j + 3Λ†k. If b is a vector such that β†’a = b Γ—β†’c and b = 50, then β†’ 2 72 βˆ’ b +β†’c is equal to __________.

202313 Apr Shift 1Vectors
MathsMedium

Q86.Let the plane x + 3y βˆ’2z + 6 = 0 meet the co-ordinate axes at the points A, B, C . If the orthocenter of the triangle ABC is (Ξ±, Ξ², 76 ), then 98(Ξ± + Ξ²)2 is equal to __________.

202312 Apr Shift 13D Geometry
MathsMedium

Q86.The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper

202313 Apr Shift 2Number Theory (not in taxonomy, closest is Binomial Theorem - but actually Discrete Math/Modular Arithmetic)
MathsMedium

Q86.Let a tangent to the curve 9π‘₯2 + 16𝑦2 = 144 intersect the coordinate axes at the points 𝐴 and 𝐡. Then, the minimum length of the line segment 𝐴𝐡 is ______

202324 Jan Shift 1Ellipse
MathsMedium

Q86.Let β†’aandβ†’b be two vectors. Let β†’a = 1, β†’b = 4 and β†’aβ‹…β†’b = 2 . If β†’c= (2β†’a β†’b) (1) βˆ’24 (2) βˆ’48 (3) βˆ’84 (4) βˆ’60

202330 Jan Shift 2Vectors
MathsMedium

Q86.Let A = {1, 2, 3, 4} and R be a relation on the set A Γ— A defined by R = {((a, b), (c, d)) : 2a + 3b = 4c + 5d} . Then the number of elements in R is _________. Ξ±, Ξ² > 0 , then Ξ±2 + Ξ²2 is dx , |x| <

202315 Apr Shift 1Sets Relations Functions
MathsMedium

Q86.If the variance of the frequency distribution π‘₯𝑖 2 3 4 5 6 7 8 Frequency 𝑓i 3 6 16 𝛼 9 5 6 is 3, then 𝛼 is equal to

202331 Jan Shift 1Statistics
MathsMedium

Q86.Let β†’a, b and β†’cbe three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D βˆ’βˆ’βˆ’β†’ β†’ β†’ β†’ β†’ β†’ β†’ be β†’aβˆ’ b +β†’c, Ξ»β†’aβˆ’3 b + 4β†’c, βˆ’β†’a+ 2 b βˆ’3β†’cand 2β†’aβˆ’4 b + 6β†’crespectively. If AB , AC and AD are coplanar, then Ξ» is : JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper

202329 Jan Shift 1Vectors
MathsMedium

Q86.Let 𝐻𝑛: π‘₯2 𝑦2 1, π‘›βˆˆβ„•. Let π‘˜ be the smallest even value of 𝑛 such that the eccentricity of π»π‘˜ is a 1 + 𝑛- 3 + 𝑛= rational number. If 𝑙 is the length of the latus rectum of π»π‘˜, then 21𝑙 is equal to

202311 Apr Shift 1Parabola
MathsMedium

Q86.The sum of all values of Ξ±, for which the points whose position vectors are Λ†i βˆ’2Λ†j + 3Λ†k, 2Λ†i βˆ’3Λ†j + 4Λ†k, (Ξ± + 1)Λ†i + 2Λ†k and 9Λ†i + (Ξ± βˆ’8)Λ†j + 6Λ†k are coplanar, is equal to (1) βˆ’2 (2) 2 (3) 6 (4) 4

202306 Apr Shift 2Vectors
MathsMedium

Q86.The area of the quadrilateral ABCD with vertices A(2, 1, 1), B(1, 2, 5), C(βˆ’2, βˆ’3, 5) and D(1, βˆ’6, βˆ’7) is equal to (1) 48 (2) 8√38 (3) 54 (4) 9√38

202308 Apr Shift 2Vectors
MathsMedium

Q86.Let 𝑓1π‘₯= 3π‘₯+ 2 π‘₯βˆˆπ‘…- - 3 For 𝑛β‰₯2, define 𝑓𝑛π‘₯= 𝑓1π‘œπ‘“π‘›- 1π‘₯. If 𝑓5π‘₯= π‘Žπ‘₯+ 𝑏 gcdπ‘Ž, 𝑏= 1, then π‘Ž+ 𝑏 is 2π‘₯+ 3, 2. 𝑏π‘₯+ π‘Ž, equal to ________

202330 Jan Shift 1Sets Relations Functions
MathsMedium

Q86.Let β†’a,β†’b,β†’cbe three vectors such that β†’a = √31, 4 β†’b = β†’c = 2 and 2(β†’a β†’b) β†’ 2 2Ο€ β†’aΓ—β†’c , then is equal to _____ . between b and β†’cis β†’ 3 b ) ( β†’aβ‹…

202331 Jan Shift 2Vectors
MathsMedium

Q86.The shortest distance between the lines x + 1 = 2 y = βˆ’12z and x = y + 2 = 6z βˆ’6 is (1) 2 (2) 3 (3) 5 (4) 3 2 2

202325 Jan Shift 23D Geometry
MathsMedium

Q87.The distance of the point P(4, 6, βˆ’2) from the line passing through the point (βˆ’3, 2, 3) and parallel to a line with direction ratios 3, 3, βˆ’1 is equal to: (1) 3 (2) √6 (3) 2√3 (4) √14

202325 Jan Shift 13D Geometry
MathsMedium

Q87.Let the plane P pass through the intersection of the planes 2x + 3y βˆ’z = 2 and x + 2y + 3z = 6, and be perpendicular to the plane 2x + y βˆ’z + 1 = 0. If d is the distance of P from the point (βˆ’7, 1, 1), then d2 is equal to : (1) 250 (2) 15 83 53 (3) 25 (4) 250 83 82

202301 Feb Shift 23D Geometry
MathsMedium

Q87.The number of ordered triplets of the truth values of 𝑝, π‘ž and π‘Ÿ such that the truth value of the statement π‘βˆ¨π‘žβˆ§π‘βˆ¨π‘Ÿβ‡’π‘žβˆ¨π‘Ÿ is True, is equal to Q88. 0 1 2 Let 𝐴= π‘Ž0 3 , where π‘Ž, π‘βˆˆπ‘…. If 𝐴3 = 𝐴 and the positive value of π‘Ž belongs to the interval ( 𝑛- 1, 𝑛], 1 𝑐 0 where π‘›βˆˆβ„•, then 𝑛 is equal to ____. 2

202311 Apr Shift 1Mathematical Reasoning
MathsMedium

Q87.Let P be the plane passing through the points (5, 3, 0), (13, 3, βˆ’2) and (1, 6, 2). For Ξ± ∈N, if the distance of the points A(3, 4, Ξ±) and B(2, Ξ±, a) from the plane P are 2 and 3 respectively, then the positive value of a is (1) 6 (2) 3 (3) 5 (4) 4

202311 Apr Shift 23D Geometry
MathsMedium

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