List of top Mathematics Questions asked in MHT CET

If \( AX = B \), where \( A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4 \end{bmatrix} \), \( B = \begin{bmatrix} 1 \\ 2 \end{bmatrix} \) and \( X = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \), then \( x + y + z = \)

Solution of the differential equation \[ \frac{dy}{dx} + 2y = e^{-x} \text{ is:} \]

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

If \( P(\theta) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and \( S \) and \( S' \) are foci of the hyperbola, then \( SP \cdot SP' = \)

If \( \tan \theta + \sin \theta = a \) and \( \tan \theta - \sin \theta = b \), then the values of \( \cot \theta \) and \( \csc \theta \) are respectively:

Evaluate: \[ \frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} \]

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

If \( X \sim B(4, p) \) and \( 2 P(X = 3) = 3 P(X = 2) \), then the value of \( p \) is:

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The particular solution of the differential equation \[ \left( y + x \frac{dy}{dx} \right) \sin y = \cos x \quad \text{at} \quad x = 0 \, \text{is:} \]

The probability distribution of a discrete r.v. \( X \) is: \[ \begin{array}{c|ccccc} X = x & 0 & 1 & 2 & 3 & 4 \\ P(X = x) & k & 2k & 4k & 2k & k \\ \end{array} \] Then, the value of \( P(X \leq 2) \) is:

If one of the lines given by \( kx^2 + xy - y^2 = 0 \) bisects the angle between the co-ordinate axes, then values of \( k \) are:

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

If \( | \vec{a} \, \vec{b} \, \vec{c} | = 3 \), then the volume of the parallelepiped with \( 2\vec{a} + \vec{b} \), \( 2\vec{b} + \vec{c} \), \( 2\vec{c} + \vec{a} \) as coterminous edges is:

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

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 \( m_0 \) gram will be left to \( m_1 \) gram is
\[ k \text{ is constant of proportionality} \]

If the error involved in making a certain measurement is continuous random variable \( X \) with probability density function \( f(x) = k (4 - x^2) \) for \( -2 \leq x \leq 2 \), and \( f(x) = 0 \) otherwise, then \[ P(|-1<X<1|) \]

If \( \frac{x}{x-y} = \log \left( \frac{a}{x-y} \right) \), then \( \frac{dy}{dx} = \)

Evaluate the integral: \[ \int \left[ \frac{1 - \log x}{1 + (\log x)^2} \right]^2 dx \]

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The equation of a circle passing through the origin and making x-intercept 3 and y-intercept -5 is:

Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]

If \(A(3,2,-1)\) and \(B(1,4,3)\), then the equation of the plane which bisects the segment \(AB\) perpendicularly is

ABCD is a parallelogram. \(P\) is the midpoint of \(AB\). If \(R\) is the point of intersection of \(AC\) and \(DP\), then \(R\) divides \(AC\) internally in the ratio