List of top Mathematics Questions asked in MHT CET

A metal wire \(108\) meters long is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are

The displacement of a particle at the time \( t \) is given by \[ s = \sqrt{1 + t}, \quad \text{then its acceleration } a \text{ is proportional to} \]

The function \( f(x) = \log x - \frac{2x}{x+2} \) is increasing for all:

If the equation \[ ax^2 + hxy + by^2 = 0, \quad c \neq 0 \text{ represents a pair of coincident lines, then} \]

Evaluate the integral: \[ \int_0^{\frac{\pi}{2}} \frac{dx}{1 + \cos x} \]

If the radius of a circle \( x^2 + y^2 - 4x + 6y - k = 0 \) is 5, then \( k = \)

If the plane \[ 2x + 3y + 5z = 1 \] intersects the coordinate axes at the points A, B, C, then the centroid of \( \triangle ABC \) is

The direction cosines of a line which lies in the \( ZOX \) plane and makes an angle of \( 30^\circ \) with the \( Z \)-axis are

The equation of the line passing through the point \( (2, 3, -4) \) and perpendicular to the XOZ plane is

If \[ \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} \neq 0, \quad \text{then} \quad \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} = \]

If \( \frac{1-\tan\theta}{1+\tan\theta} = \frac{1}{\sqrt{3}}, \) where \( \theta \in \left(0,\frac{\pi}{2}\right) \), then \( \theta = \)

If \[ |3x - 2| \leq \frac{1}{2}, \] then \( x \in \)

If \( A(-1,2,3) \), \( B(3,-2,1) \), \( C(2,1,3) \) and \( D(-1,-2,4) \) are the vertices of a tetrahedron, then its volume is

If $A$ and $B$ are two angles such that $A,B\in(0,\pi)$ and they are not supplementary angles such that $\sin A-\sin B=0$, then

The co-ordinates of the mid-point of the chord cut off by the line \( 2x - 5y + 18 = 0 \) by the circle \( x^2 + y^2 - 6x + 2y - 54 = 0 \) are

The rate of decay of mass of a certain substance at time \( t \) is proportional to the mass at that instant. The time during which the original mass of \( m_0 \) gm will be left to \( m_1 \) gm is

Evaluate the integral \[ \int_0^\infty \frac{dx}{(x^2 + 4)(x^2 + 9)} = \]

If the foot of perpendicular drawn from the origin to the plane is \( (3, 2, 1) \), then the equation of the plane is

Simplify \( \cos\left(\dfrac{3\pi}{4}+x\right) - \sin\left(\dfrac{\pi}{4}-x\right) \)

The distance of the point \( (3,4,5) \) from the point of intersection of the line \[ \frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2} \] and the plane \( x+y+z=2 \) is

If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively

If \( n(X) = 700 \), \( n(A) = 200 \), \( n(B) = 300 \), \( n(A \cap B) = 100 \), where \( X \) is the universal set and \( A \) and \( B \) are subsets of \( X \), then \( n(A' \cap B') = \)

The matrix \( A = \begin{bmatrix} a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix} \) is not invertible only if \( a = \)

If the lines given by \( \frac{x-1}{2\lambda} = \frac{y-1}{5} = \frac{z-1}{2} \) and \( \frac{x+2}{\lambda} = \frac{y+3}{\lambda} = \frac{z+5}{1} \) are parallel, then the value of \( \lambda \) is