#imp
- The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is Correct option is (d) y=x+2 Explaination:: tangents to the curve y²=8x is y=mx+2/m , so it must satisfy xy=-1 x(mx+2/m)=-1 mx²+2/mx+1=0 , si... 1
- The general solution of the differential equation (y^2 – x^3 )dx – xydy = 0 (x ≠ 0) is : The correct option is 2) y²+2x³+cx²=0 Detailed explaination 1
- Let a ∈ (0,π/2) be fixed. If the integral ∫ tan x + tan α/tan x - tan α dx = A(x) cos 2α + B(x) sin 2α + C, where C is a Correct option is (4) x – α and log_e|sin(x – α)| Detailed Explaination: ∫ tan x + tan α/tan x - tan α dx = ∫ sin x /cos x+ sin α/cos α/sin... 1
- A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate Correct solution is option A ) 2aα B Explaination: "a" at any time "t" , the side of the square a= (a₀-α_t) , where α₀ side at t=0 . at this... 1
- Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, axis of rotation B) option is correct answer Detailed solution: Moment of inertia of the rod about an axis passing through its centre and perpendicular to th... 1
- Solve the following equations by Cramer’s method i. 7x + 3y = 15; 12y - 5x = 39 Solving the folllowing equation with crammers method or rule solution of 1 Given: 7x+3y=15 ....(1) 12y-5x=39 ........(2) Equation (1) and (2... 2