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

Write the angle made by the tangent to the curve x = e^t cos t, y = e^t sin t at \[t = \frac{\pi}{4}\] with the x-axis ?

Write the equation of the normal to the curve y = x + sin x cos x at \[x = \frac{\pi}{2}\] ?

Find the coordinates of the point on the curve y² = 3 − 4x where tangent is parallel to the line 2x + y− 2 = 0 ?

Write the slope of the normal to the curve \[y = \frac{1}{x}\]  at the point \[\left( 3, \frac{1}{3} \right)\] ?

Write the coordinates of the point at which the tangent to the curve y = 2x² − x + 1 is parallel to the line y = 3x + 9 ?

Write the equation of the tangent drawn to the curve \[y = \sin x\] at the point (0,0) ?

The equation to the normal to the curve y = sin x at (0, 0) is ___________ .

The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .

The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .

The point on the curve y² = x where tangent makes 45° angle with x-axis is ______________ .

If the tangent to the curve x = a t², y = 2 at is perpendicular to x-axis, then its point of contact is _____________ .

The point on the curve y = x² − 3x + 2 where tangent is perpendicular to y = x is ________________ .

The point on the curve y² = x where tangent makes 45° angle with x-axis is ____________________ .

The point at the curve y = 12x − x² where the slope of the tangent is zero will be _____________ .

The angle between the curves y² = x and x² = y at (1, 1) is ______________ .

The equation of the normal to the curve 3x² − y² = 8 which is parallel to x + 3y = 8 is ____________ .