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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 number of elements in the set {n ∈N : 10 ≀n ≀100 and 3n βˆ’3 is a multiple of 7} is _______. JEE Main 2023 (15 Apr Shift 1) JEE Main Previous Year Paper

202315 Apr Shift 1Sequences & Series
MathsEasy

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 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

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.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.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 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 β†’a = Λ†i + 2Λ†j + 3Λ†k and b = Λ†i + Λ†j βˆ’Λ†k. If β†’cis a vector such that β†’aβ‹…β†’c= 11, b β‹…(β†’aΓ—β†’c) 2 is equal to βˆ’βˆš3β†’b , then β†’aΓ—β†’c

202311 Apr Shift 2Vectors
MathsHard

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

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 π‘Žβˆˆβ„€ and 𝑑 be the greatest integer ≀𝑑, then the number of points, where the function 𝑓π‘₯= π‘Ž+ 13 sinπ‘₯, π‘₯∈0, πœ‹ is not differentiable, is ____________

202306 Apr Shift 1Applications of Derivatives
MathsHard

Q86.If 1 1 / 1 𝑛 π‘₯21 + π‘₯14 + π‘₯72π‘₯14 + 3π‘₯7 + 6 7𝑑π‘₯= where 𝑙, π‘š, π‘›βˆˆπ‘, π‘š and 𝑛 are co-prime then 𝑙+ π‘š+ 𝑛 ∫0 𝑙11π‘š/ is equal to _____ .

202301 Feb Shift 1Definite Integration & Area
MathsHard

Q86.Let a common tangent to the curves 𝑦2 = 4π‘₯ and π‘₯- 42 + 𝑦2 = 16 touch the curves at the points 𝑃 and 𝑄. Then 𝑃𝑄2 is equal to ________.

202310 Apr Shift 1Coordinate Geometry
MathsHard

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.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.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.In the figure, ΞΈ1 + ΞΈ2 = Ο€2 and √3BE ΞΈ1 then the perimeter (in unit) of βˆ†CED is equal to

202310 Apr Shift 2Trigonometric Functions & Equations
MathsHard

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.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.Let β†’a = Λ†i + 2Λ†j + Ξ»Λ†k, b = 3Λ†i βˆ’5Λ†j βˆ’Ξ»Λ†k, β†’aβ‹…β†’c= 7 , 2( β‹…β†’c)

202324 Jan Shift 2Vectors
MathsHard

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.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, 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

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