List of top Mathematics Questions asked in MHT CET

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

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

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

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

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

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

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

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

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:

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

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

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

If $x = a\left(t - \frac{1}{t}\right)$ and $y = b\left(t + \frac{1}{t}\right)$, then $\frac{dy}{dx} =$

If $y = \log \sqrt{\tan x}$, then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{4}$ is

Equation of planes parallel to the plane $x - 2y + 2z + 4 = 0$ which are at a distance of one unit from the point $(1, 2, 3)$ are

If $f(x) = \csc^{-1} \left[ \frac{10}{6 \sin(2^x) - 8 \cos(2^x)} \right]$, then $f'(x) =$

The area bounded by the parabola $y^2 = 4ax$ and its latus-rectum $x = a$ is

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are

Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is

Given that the total of 16 values is 528 and the sum of the squares of deviation from 33 is 9158. The variance is