PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

The angle of intersection of the curves xy = a² and x² − y² = 2a² is ______________ .

If the curve ay + x² = 7 and x³ = y cut orthogonally at (1, 1), then a is equal to _____________ .

If the line y = x touches the curve y = x² + bx + c at a point (1, 1) then _____________ .

The slope of the tangent to the curve x = 3t² + 1, y = t³ −1 at x = 1 is ___________ .

The curves y = ae^x and y = be^−x cut orthogonally, if ___________ .

The equation of the normal to the curve x = a cos³ θ, y = a sin³ θ at the point θ = π/4 is __________ .

If the curves y = 2 e^x and y = ae^−x intersect orthogonally, then a = _____________ .

The point on the curve y = 6x − x² at which the tangent to the curve is inclined at π/4 to the line x + y= 0 is __________ .

The angle of intersection of the parabolas y² = 4 ax and x² = 4ay at the origin is ____________ .

The angle of intersection of the curves y = 2 sin² x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .

Any tangent to the curve y = 2x⁷ + 3x + 5 __________________ .

The point on the curve 9y² = x³, where the normal to the curve makes equal intercepts with the axes is

(a) \[\left( 4, \frac{8}{3} \right)\]

(b) \[\left( - 4, \frac{8}{3} \right)\]

(c) \[\left( 4, - \frac{8}{3} \right)\]

(d) none of these

The slope of the tangent to the curve x = t² + 3t − 8, y = 2t² − 2t − 5 at the point (2, −1) is _____________ .

The line y = mx + 1 is a tangent to the curve y² = 4x, if the value of m is ________________ .

The normal at the point (1, 1) on the curve 2y + x² = 3 is _____________ .

The normal to the curve x² = 4y passing through (1, 2) is _____________ .

Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`