List of top Mathematics Questions on Three Dimensional Geometry asked in MHT CET

Find the direction cosines of a line that makes equal angles with the coordinate axes.

If \( x = \sin \theta, y = \sin^3 \theta \), then \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{6} \) is

\( \int \frac{(5 \sin \theta - 2) \cos \theta}{(5 - \cos^2 \theta - 4 \sin \theta)} d\theta = \)}

If the foot of the perpendicular drawn from the origin to a plane is \( P(2, -1, 4) \), then the equation of the plane is

\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^2 + \log (\frac{\pi - x}{\pi + x}) \cdot \cos x) dx = \)}

The angle between the lines \( x = y, z = 0 \) and \( y = 0, z = 0 \) is

The foci of the conic \( 25x^2 + 16y^2 - 150x = 175 \) are

If $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$, $\beta \in R$ where I is the identity matrix of order 2, then $4(\alpha + \beta) =$}

The value of $\int_{-3}^{3} \sin^7 x \cos^{16} x \, dx$ is

The value of \( \int_{1/3}^{1} \frac{(x - x^3)^{\frac{1{3}}}{x^4} dx \) is

If \( x^{\frac{2}{5}} + y^{\frac{2}{5}} = \text{a}^{\frac{2}{5}} \) then \( \frac{dy}{dx} = \)

If \( X \sim B(n, p) \) then \( \frac{P(X=k){P(X=k-1)} = \)}

A line L is passing through points A(1, 3, 2) and B(2, 2, 1). If mirror image of point P(1, 1, -1) in the line L is (x, y, z) then $x + y + z =$

The co-ordinates of the point in which line joining $(1, 1, 1)$ and $(2, 2, 2)$ intersects the plane $x + y + z = 9$ are

If the plane $\frac{x}{3} + \frac{y}{2} - \frac{z}{4} = 1$ cuts the co-ordinate axes at points A, B and C, then the area of the triangle ABC is

The angle between the curves $xy = 6$ and $x^2y = 12$ is

$f(x) = (\cos x + \text{i}\sin x) \cdot (\cos 3x + \text{i}\sin 3x) \cdots [\cos(2\text{n} - 1)x + \text{i}\sin(2\text{n} - 1)x] \text{n} \in \mathbb{N}$ Then $f''(x) = $ ________, (Where $\text{i} = \sqrt{-1}$ )

If the angle $\theta$ between the line $\frac{x+1}{1} = \frac{y-1}{2} = \frac{z-2}{2}$ and the plane $2x - y + \sqrt{\lambda}z + 4 = 0$ is such that $\sin \theta = \frac{1}{3}$, then $\lambda + 1 =$

The ratios of sides in a triangle ABC are $5 : 12 : 13$ and its area is 270 . Then sides of the triangle are

The sum to infinite terms of the series $\tan^{-1} \left(\frac{1}{3}\right) + \tan^{-1} \left(\frac{2}{9}\right) + ..................... + \tan^{-1} \left(\frac{2^{n-1}}{1+2^{2n-1}}\right) + ..............$ is

The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x = 8, x = 10, y = 11$ and $y = 12$ is

Let the line \(\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}\) lie in the plane \(x + 3y - \alpha z + \beta = 0\), then the value of \((\beta - \alpha)\) is equal to

The perimeter of a square whose two sides have equations \(\frac{x-1}{2} = \frac{y+2}{3} = \frac{z-3}{4}\) and \(\frac{x}{2} = \frac{y-1}{3} = \frac{z+1}{4}\) is

A line L is passing through points A(1, 3, 2) and B(2, 2, 1). If mirror image of point P(1, 1, -1) in the line L is (x, y, z) then $x + y + z =$

The co-ordinates of the point in which line joining $(1, 1, 1)$ and $(2, 2, 2)$ intersects the plane $x + y + z = 9$ are