List of top Mathematics Questions asked in MHT CET

If \[ A=\begin{bmatrix} 1 & 2 & i\\ 1 & 1 & 1\\ 1 & 1 & 0 \end{bmatrix}, \] then \( [\operatorname{adj}(\operatorname{adj}A)]^{-1} \) is

If \( \mu \) and \( \sigma^2 \) are mean and variance of a random variable \( X \) whose p.m.f. is given by \[ P(X = x) = \binom{6}{x} \left( \frac{1}{4} \right)^x \left( \frac{3}{4} \right)^{6 - x}, \quad x = 0, 1, 2, 3, 4, 5, 6, \text{ then the value of } 2\mu + 12\sigma^2 = \]

In a triangle \(ABC\) with usual notations, \[ \frac{\cos A - \cos C}{a - c} + \frac{\cos B}{b} = \]

Simplify the expression \( \sin \left( \frac{\pi}{3} + x \right) - \cos \left( \frac{\pi}{6} + x \right) \)

The area of the region bounded by the parabola $x^2=16y$, the lines $y=1$, $y=4$ and the $y$-axis lying in the first quadrant is

If the direction cosines of a line are \( \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \), then

For the probability distribution of \( X \) given below, the variance of \( X \) is

The area of the region bounded by the parabola \[ y^2 = 8x \quad \text{and its latus rectum is} \]

The integral \[ \int_0^a \frac{x}{\sqrt{a - x}} \, dx = \]

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

If \( P(A) = \frac{2}{5}, \, P(B) = \frac{1}{4}, \, P(A \cup B) = \frac{1}{2}, \) then \( P(A' \cup B') = \)

If the line \( \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \) is parallel to the plane \( \vec{r} = (3i - 2j - mk) = 5 \), then the value of \( m \) is

Evaluate \[ \int_{-\pi/2}^{\pi/2} \sin^2 x\,dx \]

If the origin is the centroid of the triangle whose vertices are \( A(2, p, -3) \), \( B(q, -2, 5) \) and \( C(-5, 1, r) \), then

Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin^{\frac{2}{3}} x}{\sin^{\frac{2}{3}} x + \cos^{\frac{2}{3}} x}\, dx \]

The eccentricity of the ellipse \[ y^2 + 4x^2 - 12x + 6y + 14 = 0 \] is

In a certain culture of bacteria, the rate of increase is proportional to the number present. It is found that the number doubles in 4 hours. Then the number of times the bacteria are increased in 12 hours is

Evaluate \( \int \frac{\cos \sqrt{x}}{\sqrt{x}} \, dx \)

The displacement of a particle at time \(t\) is \[ s = t^3 - 4t^2 - 5t \] Then the velocity of the particle at \(t = 2\) sec 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:

The separate equations of the lines represented by the equation \( 3x^2 - 2\sqrt{3} xy - 3y^2 = 0 \) are

If the points $A(2,1,-1)$, $B(0,-1,0)$, $C(4,0,4)$ and $D(2,0,x)$ are coplanar, then $x=$

If \( A = \begin{bmatrix} 1 & 1 \\ 2 & 1 \end{bmatrix}, B = \begin{bmatrix} 4 & 3 \\ 1 & 1 \end{bmatrix} \), then \( (A + B)^{-1x} = \)

If the Cartesian equation of the line is \[ x - 1 = 2y + 3 = 3 - z, \] then its vector equation is

If one of the lines given by the equation \( x^2 + kxy + 2y^2 = 0 \) is \( x + 2y = 0 \), then the value of \( k \) is