List of top Mathematics Questions asked in MHT CET

If $\vec{a} = 2\hat{\text{i}} + 3\hat{\text{j}} - \hat{\text{k}}$, $\vec{b} = -\hat{\text{i}} + 2\hat{\text{j}} - 4\hat{\text{k}}$ and $\vec{c} = \hat{\text{i}} + \hat{\text{j}} - 2\hat{\text{k}}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c}) =$

The differential equation obtained by eliminating A and B from $y = A \cos \omega t + B \sin \omega t$ is

If $y = x \tan y$, then $\frac{dy}{dx} =$

The distance between the parallel lines $3x + 4y = 9$ and $6x + 8y = 15$ is

The Cartesian equation of a plane which passes through the points $\text{A}(2, 2, 2)$ and making equal nonzero intercepts on the co-ordinate axes is

The value of the definite integral $\int_{0}^{\pi} \frac{1}{4 + 3 \cos x} \, dx$ is

If $A = \left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]$, then cofactors of all elements of second row are respectively

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is 6. Then the probability that it is actually 6 is

Radium decomposes at the rate proportional to the amount present at any time. If $P\%$ of amount disappears in one year, then amount of radium left after 2 years is

The minimum value of the objective function $z = 4x + 6y$ subject to $x + 2y \ge 80$, $3x + y \ge 75$, $x, y \ge 0$ is

The joint equation of pair of lines through the origin and having slopes $(1+\sqrt{2})$ and $\frac{1}{(1+\sqrt{2})}$ is

If $4ab = 3h^2$, then the ratio of slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is

The vectors $\overrightarrow{\text{AB}} = 3\hat{\text{i}} + 4\hat{\text{k}}$ and $\overrightarrow{\text{AC}} = 5\hat{\text{i}} - 2\hat{\text{j}} + 4\hat{\text{k}}$ are the sides of a triangle ABC. The length of the median through A is

The principal solutions of $\cot x = \sqrt{3}$ are

The area of the region included between the parabolas $y^2 = 8x$ and $x^2 = 8y$ is

"If two triangles are congruent, then their areas are equal." is the given statement, then the contrapositive of the inverse of the given statement is

The common region of the solutions of the inequations $x + 2y \ge 4$, $2x - y \le 6$ and $x, y > 0$ is

If $\int \frac{\cos x - \sin x}{8 - \sin 2x} \, dx = \frac{1}{p} \log \left[ \frac{3 + \sin x + \cos x}{3 - \sin x - \cos x} \right] + c$, then $p = $

For a $3 \times 3$ matrix $A$, if $A(\operatorname{adj}A) = \begin{bmatrix} -10 & 0 & 0 \\ 0 & -10 & 0 \\ 0 & 0 & -10 \end{bmatrix}$, then the value of the determinant of $A$ is

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7 \end{bmatrix}$ and $B = \begin{bmatrix} 13 & 2 & b \\ -3 & -1 & 2 \\ -2 & 0 & 1 \end{bmatrix}$ where matrix $B$ is the inverse of matrix $A$, then the values of $a$ and $b$ are

A die is thrown four times. The probability of getting a perfect square in at least one throw is

The differential equation of the family of parabolas with focus at the origin and the $X$-axis as its axis, is

In any $\triangle ABC$, with usual notations, $c(a \cos B - b \cos A) = $

If in a $\triangle ABC$, with usual notations, $a^2$, $b^2$, $c^2$ are in A.P., then $\frac{\sin 3B}{\sin B} = $

If $A = (-2, 2, 3)$, $B = (3, 2, 2)$, $C = (4, -3, 5)$, and $D = (7, -5, -1)$, then the projection of $\vec{AB}$ on $\vec{CD}$ is