List of top Mathematics Questions asked in MHT CET

If $AX = B$, where $A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4 \end{bmatrix}$, $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $B = \begin{bmatrix} 12 \\ 15 \\ 13 \end{bmatrix}$, then $x^2 + y^2 + z^2 =$

The dual of the statement `Mangoes are delicious but expensive' is

The angle between the lines $\vec r = (2\hat i + \hat j - 3\hat k) + \lambda(\hat i - \hat j + \hat k)$ and $\dfrac{x-1}{1} = \dfrac{y+2}{3} = \dfrac{z-3}{2}$ is

If $Z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$, $x \ge 0$, $y \ge 0$, then $Z$ is maximum at the point

A problem in statistics is given to three students $P$, $Q$ and $R$. Their chances of solving the problem are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently, then the probability that the problem is solved is

The vector equation of the line \[ \frac{x+3}{2}=\frac{2y-3}{5}, \quad z=-1 \] is

If \(\tan A = \dfrac{5}{6}\), \(\tan B = \dfrac{1}{11}\), then find \(A + B\).

Evaluate \[ \int_{2}^{3} \frac{dx}{x^2 + x} \]

If \(A, B, C\) are the angles of \(\triangle ABC\), then with usual notations, \[ \frac{c^2 - a^2 + b^2}{a^2 - b^2 + c^2} = \]

If \(A(3,-2,2)\), \(B(2,\lambda+1,5)\) are the end points of the diameter of a circle and if the point \((5,6,-1)\) lies on the circle, then \(\lambda =\)

The parametric equations of the line passing through \( A(3, 4, -7) \), \( B(1, -1, 6) \) are

Evaluate the integral: \[ \int \frac{dx}{\cos x \sqrt{\cos 2x}}. \]

The auxiliary equation of the lines passing through the origin and having slopes \[ \sqrt{3} + 1 \quad \text{and} \quad \sqrt{3} - 1 \quad \text{is} \]

The equation of a plane containing the point \( (1, -1, 1) \) and parallel to the plane \[ 2x + 3y - 4z = 17 \text{ is} \]

The angle between the line \[ \frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2} \] and the plane \[ \mathbf{r} \cdot (6\hat{i} - 2\hat{j} - 3\hat{k}) = 5 \] is

If \[ \frac{\sin(A + B)}{\sin(A - B)} = \frac{\cos(C + D)}{\cos(C - D)}, \] then \( \tan A \cot B = \)

If \[ f(x) = |x - 2|, \quad x \in [0, 4], \quad \text{then the Rolle's theorem cannot be applied to the function because} \]

The particular solution of the differential equation \[ \sin^2 y \frac{dx}{dy} + x = \cot y \quad \text{when} \quad x = 0 \quad \text{and} \quad y = \frac{3\pi}{4} \text{ is} \]

If \[ y = 3e^{5x} + 5e^{3x}, \quad \text{then} \quad \frac{d^2 y}{dx^2} - 8 \frac{dy}{dx} = \]

If \[ | \mathbf{a} \times \mathbf{b} \times \mathbf{c} | = 4, \] then the volume of the parallelepiped with coterminous edges \[ \mathbf{a} + 2\mathbf{b}, \quad \mathbf{b} + 2\mathbf{c}, \quad \mathbf{c} + 2\mathbf{a} \] is

If \( \theta \) is a parameter, then the parametric equations of the circle \[ x^2 + y^2 - 6x + 4y - 3 = 0 \] are given by

If \[ \mathbf{a} = \frac{1}{\sqrt{10}} (3i + k), \quad \mathbf{b} = \frac{1}{7} (2i + 3j - 6k), \quad \text{then the value of} \] \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

If \( \cos 2\theta = \sin \alpha \), then \( \theta = \)

The maximum value of the function \[ y = e^{5 + \sqrt{3} \sin x + \cos x} \]