List of top Mathematics Questions asked in MHT CET

If the points \(\mathrm{A}(1,1,2), \mathrm{B}(2,1, \mathrm{p}), \mathrm{C}(1,0,3)\) and \(D(2,2,0)\) are coplanar then the value of \(p\) is

\[ \int \frac{\mathrm{e}^{\tan ^{-1} 2 x}}{1+4 x^2}= \]

In a triangle ABC with usual notations if \(|\overline{\mathrm{BC}}|=8,|\overline{\mathrm{CA}}|=7,|\overline{\mathrm{AB}}|=10\) then the projection of \(\overline{\mathrm{AB}}\) on \(\overline{\mathrm{AC}}\) is

If \(\bar{a}=\hat{i}+\hat{j}, \bar{b}=2 \hat{i}-\hat{k}\) then the point of intersection of the lines \(\overline{\mathrm{r}} \times \overline{\mathrm{a}}=\overline{\mathrm{b}} \times \overline{\mathrm{a}}\) and \(\overline{\mathrm{r}} \times \overline{\mathrm{b}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) is

A scholarship amount is given by \(\mathrm{z}=550 x+300 y\) and is to be distributed among \(x\) boys and \(y\) girls. From the graph given below the maximum amount of scholarship is __________

Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]
If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + \text{C} = 0$, then C =}
Given the vectors: \[ \mathbf{a} = i + 3j - k, \quad \mathbf{b} = 3i - j + 2k, \quad \mathbf{c} = i + 2j - 2k \] and the following information: \[ \frac{\mathbf{a} \cdot \mathbf{c}}{|\mathbf{c}|} = \frac{10}{3} \] Find the value of \( \alpha + \beta \) and the projection of \( \mathbf{a} \) on \( \mathbf{c} \).
If $y = \tan^{-1} \left[ \frac{12x - 64x^3}{1 - 48x^2} \right]$, then $dy/dx = \dots$
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
If $ f(x) = 3x^2 + 5x - 7 $, find $ f(2) $.
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
From the following options, the nearest line to the origin is ....
The slopes of the lines represented by $6x^2 + 2hxy + y^2 = 0$ are in the ratio 2 : 3, then $h = \dots$
The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}
A particle P starts from $Z_0 = 1 + 2i$. It moves horizontally away from origin by 5 units, then vertically up by 3 units to $Z_1$. From $Z_1$ it moves $\sqrt{2}$ units in direction $\hat{i} + \hat{j}$, then moves through $\pi/2$ anticlockwise on a circle with centre at origin to reach $Z_2$. Then $Z_2 = \dots$
The length of the perpendicular drawn from the origin on the normal to the curve $x^2 + 2xy - 3y^2 = 0$ at the point $(2, 2)$ is ______.
The area bounded by the curve $y = 4x - x^2$ and X-axis in square units, is \dots
If $x = \sin t$ and $y = \sin pt$, then the value of $(1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + p^2 y = \dots$
The general solution of differential equation $(y^2 - x^2)dx = xy dy$ ($x \neq 0$) is ______.
There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is ______.
Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?
A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.