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Q82.If Ο•(x) 1 Ο€ βˆ’3Ο•β€²(t))dt, 4 (4√2 (1) 4 (2) 8 6+βˆšΟ€ 6+βˆšΟ€ (3) 8 (4) 4 βˆšΟ€ 6βˆ’βˆšΟ€

202331 Jan Shift 2Calculus
MathsHard

Q82.Let f(x) = x , x ∈R βˆ’{βˆ’1}, n ∈N, n > 2 . If f n(x) = (fofof. . . . upto n times) (x), then (1+xn) 1n lim 0 xnβˆ’2(f n(x))dx is equal to nβ†’βˆžβˆ«1

202306 Apr Shift 2Limits & Continuity
MathsHard

Q82.If βˆ«Ο€0 5cos x(1+cos x cos 3x+cos21+5cos xx+cos3 x cos 3x)dx = JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper

202301 Feb Shift 2Definite Integration & Area
MathsHard

Q83.Let y = y(x), y > 0, be a solution curve of the differential equation (1 + x2)dy = y(x βˆ’y)dx. If y(0) = 1 = Ξ², then and y(2√2) = + + 2√2) (2) e3Ξ²βˆ’1 e(5 √2) (1) e3Ξ²βˆ’1 = e(3 = + + 2√2) (4) eΞ²βˆ’1 eβˆ’2(5 √2) (3) eΞ²βˆ’1 = eβˆ’2(3

202312 Apr Shift 1Differential Equations
MathsHard

Q83.Let A be the area of the region {(x, y) : y β‰₯x2, y β‰₯(1 βˆ’x)2, y ≀2x(1 βˆ’x)}. Then 540A is equal to y(1) = 0 is

202330 Jan Shift 2Definite Integration & Area
MathsHard

Q83.Let the area enclosed by the lines x + y = 2, y = 0 , x = 0 and the curve f(x) = min{x2 + 43 , 1 + [x]} where [x] denotes the greatest integer ≀x, be A . Then the value of 12A is

202308 Apr Shift 2Definite Integration & Area
MathsHard

Q83.A circle passing through the point 𝑃𝛼, 𝛽 in the first quadrant touches the two coordinate axes at the points 𝐴 and 𝐡. The point 𝑃 is above the line 𝐴𝐡. The point 𝑄 on the line segment 𝐴𝐡 is the foot of perpendicular from 𝑃 on 𝐴𝐡. If 𝑃𝑄 is equal to 11 units, then the value of 𝛼𝛽 is _______

202306 Apr Shift 1Circles
MathsHard

Q83.Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is ________.

202310 Apr Shift 1Permutation & Combination
MathsHard

Q83.Consider the triangles with vertices A(2, 1), B(0, 0) and C(t, 4), t = [0, 4]. If the maximum and the minimum perimeters of such triangles are obtained at t = Ξ± and t = Ξ² respectively, then 6Ξ± + 21Ξ² is equal to ___________.

202315 Apr Shift 1Coordinate Geometry
MathsHard

Q83.Let Ξ” be the area of the region {(x, y) ∈R2 : x2 + y2 ≀21, y2 ≀4x, x β‰₯1}. Then 21 (Ξ” √7 equal to (1) 2√3 βˆ’13 (2) √3 βˆ’23 (3) 2√3 βˆ’23 (4) √3 βˆ’43

202329 Jan Shift 1Definite Integration & Area
MathsHard

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 Ξ±x = exp(xΞ²yΞ³) be the solution of the differential equation 2x2ydy βˆ’(1 βˆ’xy2)dx = 0 , x > 0, y(2) = √loge 2 . Then Ξ± + Ξ² βˆ’Ξ³ equals : (1) 1 (2) βˆ’1 (3) 0 (4) 3 β†’

202301 Feb Shift 2Differential Equations
MathsHard

Q84.Let the point 𝑝, 𝑝+ 1 lie inside the region 𝐸= π‘₯, 𝑦: 3 - π‘₯β‰€π‘¦β‰€βˆš9 - π‘₯2 , 0 ≀π‘₯≀3 . If the set of all values of 𝑝 is the interval π‘Ž, 𝑏, then 𝑏2 + 𝑏- π‘Ž2 is equal to ________ .

202306 Apr Shift 1Applications of Derivatives
MathsHard

Q84.The remainder, when 7103 is divided by 17, is

202313 Apr Shift 2Sequences & Series
MathsHard

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 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 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.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

Q86.Let β†’a = 2Λ†i βˆ’7Λ†j + 5Λ†k , b = Λ†i + Λ†k andβ†’c= Λ†i + 2Λ†j βˆ’3Λ†k be three given vectors. Ifβ†’ris a vector such that β†’rΓ—β†’a =β†’cΓ—β†’a andβ†’rβ‹…β†’b = 0 , then β†’r is equal to: (1) 11 7 √2 (2) 117 (3) 11 5 √2 (4) √9147

202301 Feb Shift 2Vectors
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.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.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.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 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

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