List of top Mathematics Questions on Relations and Functions asked in MHT CET

If \( \bar{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}) \) and \( \bar{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k}) \), then the value of \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}

If the line \( ax + by + c = 0 \) is normal to the curve \( xy = 1 \), then}

The number of values of \( x \) in the interval \( [0, 3\pi] \) satisfying the equation \( 2 \sin^2 x + 5 \sin x - 3 = 0 \) is

Argument of the complex number z = \( \frac{13-5i}{4-9i} \), i = \( \sqrt{-1} \) is

In a triangle $ABC$, with usual notations, if $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$ Then $\cos \text{A} : \cos \text{B} : \cos \text{C}$ is

An ellipse has OB as semi-minor axis, S and S' are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is

If a random variable $X$ has the p.d.f. $f(x) = \begin{cases} \frac{k}{x^2+1} & , \text{if } 0<x<\infty \\ 0 & , \text{otherwise} \end{cases}$ then c.d.f. of X is

A plane passes through $(1, -2, 1)$ and is perpendicular to the planes $2x - 2y + z = 0$ and $x - y + 2z = 4$. The distance of the point $(1, 2, 2)$ from this plane is ________ units.

The general solution of the differential equation $\frac{\text{d}y}{\text{d}x} + \sin \left( \frac{x+y}{2} \right) = \sin \left( \frac{x-y}{2} \right)$ is

$\int \sec^{\frac{2}{3}} x \cdot \csc^{\frac{4}{3}} x dx =$

$\lim_{x \to 1} (\log_3 3x)^{\log_x 8} = .......$

Considering only the principal values of the inverse trigonometric function, the value of $\tan \left( \cos^{-1} \frac{1}{5\sqrt{2}} - \sin^{-1} \frac{4}{\sqrt{17}} \right)$ is