Q24.Let y = f(x) be the solution of the differential equation dydx + x2−1xy = √1−x2x6+4x f(0) = 0. If 6 ∫1/2−1/2 f(x)dx = 2π −α then α2 is equal to _______ .
What This Question Tests
This question tests the ability to solve a first-order linear differential equation, apply initial conditions, and then evaluate a definite integral of the solution, requiring multiple steps.
Concepts Tested
Formulas Used
dy/dx + P(x)y = Q(x)
Integrating Factor = e^∫P(x)dx
y * IF = ∫(Q(x) * IF)dx
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
📋 Question Details
- Chapter
- Differential Equations
- Topic
- Linear Differential Equations
- Year
- 2025
- Shift
- 22 Jan Shift 2
- Q Number
- Q24
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 9: Differential Equations
More from this Chapter
Q98.The solution of the differential equation dx dy = x+yx satisfying the condition y(1) = 1 is (1) y = ln x + x (2) y = x ln x + x2 (3) y = xe(x−1) (4) y = x ln x + x
Q99.The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is (1) (x −2)y′2 = 25 −(y −2)2 (2) (y −2)y′2 = 25 −(y −2)2 (3) (y −2)2y′2 = 25 −(y −2)2 (4) (x −2)2y′2 = 25 −(y −2)2 Q100.The non-zero verctors →a,→b and →c are related by →a = 8→b and →c = −7→b. Then the angle between →a and→cis (1) 0 (2) π/4 (3) π/2 (4) π Q101.The vector →a = α^i + 2^j + β^k lies in the plane of the vectors →b = ^i + ^j and →c = ^j + ^k and bisects the angle between →b and →c. Then which one of the following gives possible values of α and β ? (1) α = 2, β = 2 (2) α = 1, β = 2 (3) α = 2, β = 1 (4) α = 1, β = 1 Q102.The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz− plane at the point (0, 172 , −132 ). Then JEE Main 2008 JEE Main Previous Year Paper (1) a = 2, b = 8 (2) a = 4, b = 6 (3) a = 6, b = 4 (4) a = 8, b = 2 Q103.If the straight lines x−1 k = y−22 = z−33 and x−23 = y−3k = z−12 intersect at a point, then the integer k is equal to (1) −5 (2) 5 (3) 2 (4) −2 Q104.It is given that the events A and B are such that P(A) = 41 , P ( BA ) = 12 and P ( BA ) = 32 . Then P(B) is (1) 1 (2) 1 6 3 (3) 2 (4) 1 3 2 Q105.A die is thrown. Let A be the event that the number obtained is greater than 3 . Let B be the event that the number obtained is less than 5 . Then P(A ∪B) is (1) 3 (2) 0 5 (3) 1 (4) 2 5 JEE Main 2008 JEE Main Previous Year Paper
Q86.If →u, →v, ¯w are non-coplanar vectors and p, q are real numbers, then the equality [ 3→u p→v p→w ] −[ p→v →w q→u ] −[ 2→w q→v q→u ] = 0 holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)
Q84.Solution of the differential equation cos xdy = y(sin x −y)dx, 0 < x < π2 is (1) y sec x = tan x + c (2) y tan x = sec x + c (3) tan x = (sec x + c)y (4) sec x = (tan x + c)y