RankLab

Practice Questions

3,523 questions across 23 years of JEE Main β€” find and practise any topic!

Search & Filter

Subject

PhysicsChemistryMaths

Difficulty

😊 Easy PeasyπŸ€” TrickyπŸ”₯ Hard

Type

MCQNumerical

Year

βœ• Clear all filters

Found 3,523 results

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.The area of the region enclosed by the curve f(x) = max{sin x, cos x}, βˆ’Ο€ ≀x ≀π and the xβˆ’axis is + (1) 2√2(√2 1) (2) 4 + 1) (3) 4(√2) (4) 2(√2

202313 Apr Shift 1Definite Integration & Area
MathsMedium

Q83.The area of the region given by {(x, y) : xy ≀8, 1 ≀y ≀x2} is : (1) 8 loge 2 βˆ’133 (2) 16 loge 2 βˆ’143 (3) 8 loge 2 + 76 (4) 16 loge 2 + 37

202301 Feb Shift 2Definite Integration & Area
MathsMedium

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

Q83.Let y = y(t) be a solution of the differential equation dydt + Ξ±y = Ξ³eβˆ’Ξ²t Where, Ξ± > 0, Ξ² > 0 and Ξ³ > 0 . Then Limtβ†’βˆž y(t) (1) is 0 (2) does not exist (3) is 1 (4) is βˆ’1

202325 Jan Shift 2Differential Equations
MathsMedium

Q83.The area bounded by the curves y = |x βˆ’1| + |x βˆ’2| and y = 3 is equal to (1) 4 (2) 6 (3) 3 (4) 5

202306 Apr Shift 2Definite Integration & Area
MathsMedium

Q83.The area of the region A = {(x, y) : |cos x βˆ’sin x| ≀y ≀sin x, 0 ≀x ≀π2 } (1) 1 βˆ’ 3 + 4 (2) √5 + 2√2 βˆ’4. 5 √2 √5 (3) 3 βˆ’ 3 + 1 (4) √5 βˆ’2√2 + 1 √5 √2 > y(2) = 2,

202329 Jan Shift 2Definite Integration & Area
MathsMedium

Q83.The area of the region {(x, y) : x2 ≀y ≀8 βˆ’x2, y ≀7} is (1) 27 (2) 18 (3) 20 (4) 21

202308 Apr Shift 1Definite Integration & Area
MathsMedium

Q84.Let y = y(x) be the solution of the differential equation x loge x dxdy + y = x2 loge x, (x 1). If then y(e) is equal to (1) 4+e2 (2) 1+e2 4 4 (3) 2+e2 (4) 1+e2 2 2

202329 Jan Shift 2Differential Equations
MathsMedium

Q84.Let y = y(x) be the solution of the differential equation (x2– 3y2)dx + 3 xy dy = 0, y(1) = 1 . Then 6y2(e) is equal to (1) 3e2 (2) e2 (3) 2e2 (4) 3e22 β†’ β†’ β†’ β†’ β†’ β†’

202324 Jan Shift 2Differential Equations
MathsMedium

Q84.Let y = y(x) be the solution curve of the differential equation dxdy = xy (1 + x2(1 + loge x)), x > 0, y(1) = 3. y2(x) Then is equal to : 9 (1) x2 (2) x2 5βˆ’2x3(2+loge x3) 2x3(2+loge x3)βˆ’3 (3) x2 (4) x2 3x3(1+loge x2)βˆ’2 7βˆ’3x3(2+loge x2) JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper be a vector such that = 2 . If β†’d

202325 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

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 a, b, c be three distinct real numbers, none equal to one. If the vectors aΛ†i + Λ†j + Λ†k, Λ†i + bΛ†j + Λ†k and Λ†i + Λ†j + cΛ†k are coplanar, then 1βˆ’a1 + 1βˆ’b1 + 1βˆ’c1 is equal to (1) 2 (2) βˆ’1 (3) βˆ’2 (4) 1 β†’

202312 Apr Shift 1Vectors
MathsMedium

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 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.Let y = y(x) be the solution of the differential equation (3y2 βˆ’5x2)ydx + 2x(x2 βˆ’y2)dy = 0 such that y(1) = 1. Then (y(2))3 βˆ’12y(2) is equal to : (1) 64 (2) 32√2 (3) 32 (4) 16√2 β†’

202331 Jan Shift 2Differential Equations
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.If the solution curve f(x, y) = 0 of the differential equation (1 + loge x) dxdy βˆ’x loge x = ey, x > 0, passes through the points (1, 0) and (a, 2), then aa is equal to (1) e2e2 (2) ee2 (3) e√2e2 (4) e2e√2 β†’

202306 Apr Shift 2Differential Equations
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.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 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 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.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

Showing 926–950 of 3,523

← Prev3637383940Next β†’