List of top Mathematics Questions asked in MHT CET

The line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x + 3y - \alpha z + \beta = 0$, then value of $\alpha \beta$ is

Given $p$ : A man is a judge, $q$ : A man is honest.
If $S_1$ : If a man is a judge, then he is honest
$S_2$ : If a man is a judge, then he is not honest
$S_3$ : A man is not a judge or he is honest
$S_4$ : A man is a judge and he is honest
Then

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

$$\lim_{x \to 2} (x - 1)^{\frac{1}{3x - 6}} =$$

If the vectors $2\hat{i} - \hat{j} - \hat{k}$, $\hat{i} + 2\hat{j} - 3\hat{k}$ and $3\hat{i} + \lambda\hat{j} + 5\hat{k}$ are coplanar, then the value of $\lambda$ is

If $2 \tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$, then the value of $x$ is

A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is $3\text{ mm}$ and $1\text{ hour}$ later has been reduced to $2\text{ mm}$, then the expression of radius $r$ of the raindrop at any time $t$ is (where $0 \le t \lt 3$)

$$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\csc x \cdot \cot x}{1 + \csc^2 x} \, dx =$$

The function $f(x) = \frac{\lambda \sin x + 6 \cos x}{2 \sin x + 3 \cos x}$ is increasing, if

For an invertible matrix $A$, if $A(\text{adj } A) = \begin{bmatrix} 20 & 0 \\ 0 & 20 \end{bmatrix}$, then $|A| =$

The area bounded by the parabola $y^2 = x$ and the line $x + y = 2$ in the first quadrant is

If $2 \cos \theta = x + \frac{1}{x}$, then $2 \cos 3\theta =$

If $f(x) = x^2 + ax + b$ has minima at $x = 3$ whose value is $5$, then the values of $a$ and $b$ are respectively

Two circles centred at $(2,3)$ and $(4,5)$ intersect each other. If their radii are equal, then the equation of the common chord is

The degree of the differential equation whose solution is $y^2 = 8a(x+a)$, is

In $\Delta ABC$, with usual notations $\frac{b\sin B - c\sin C}{\sin(B-C)} =$

If $G(4,3,3)$ is the centroid of the triangle $ABC$ whose vertices are $A(a,3,1)$, $B(4,5,b)$ and $C(6,c,5)$, then the values of $a$, $b$, $c$ are

If the sum of slopes of lines represented by $ax^2+8xy+5y^2=0$ is twice their product, then $a =$

The d.r.s. of the normal to the plane passing through the origin and the line of intersection of the planes $x+2y+3z=4$ and $4x+3y+2z=1$ are

The numbers can be formed using the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy odd places in ways.

If $y = \tan^{-1}\left(\sqrt{\frac{1+\cos x}{1-\cos x}}\right)$, then $\frac{dy}{dx} =$

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \text{adj } A = A \cdot A^T$, then $5a + b =$

The area of triangle with vertices $(1,2,0)$, $(1,0,a)$ and $(0,3,1)$ is $\sqrt{6}$ sq. units, then the values of '$a$' are

Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students in a class. Then subject shows the highest variability in marks. Choose the correct subject from the options below:

Let $$f(x) = \begin{array}{cc} x + a\sqrt{2}\sin x & , 0 \le x \lt \frac{\pi}{4} \\ 2x\cot x + b & , \frac{\pi}{4} \le x \lt \frac{\pi}{2} \\ a\cos 2x - b\sin x & , \frac{\pi}{2} \le x \le \pi \end{array}$$ If $f(x)$ is continuous for $0 \le x \le \pi$, then