List of top Mathematics Questions on coordinates of a point in space asked in BITSAT

If \[ \left[ \begin{array}{cc} 1 & -\tan(\theta) \\ \tan(\theta) & 1 \end{array} \right] \left[ \begin{array}{cc} 1 & \tan(\theta) \\ -\tan(\theta) & 1 \end{array} \right]^{-1} = \left[ \begin{array}{cc} a & -b \\ b & a \end{array} \right], \] then:

If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:
Given \[ \frac{dy}{dx} \tan x = y \sec^2 x + \sin x, \quad {find the general solution:} \]
The area of the region bounded by the parabola \( (y - 2)^2 = (x - 1) \), the tangent to the parabola at the point \( (2, 3) \), and the X-axis is:
For each parabola \( y = x^2 + px + q \), meeting the coordinate axes at three distinct points, if circles are drawn through these points, then the family of circles must pass through:
The image of the point $(3, 2, 1)$ in the plane $2x-y+3z = 7$ is