List of top Mathematics Questions asked in MHT CET

If one of the diameters of the circle, given by the equation $x^2+y^2-4 x+6 y-12=0$, is a chord of a circle, ' S ', whose centre is at $(-3,2)$, then the length of radius of ' S ' is _______ units.

The eccentric angle of the point $\mathrm{P}(-6,2)$ of the ellipse $\frac{x^2}{48}+\frac{y^2}{16}=1$ is

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then $\mathrm{E}\left(\mathrm{X}^2\right)=$

The distance of the point $(5,3,-1)$ from the plane passing through points $(2,1,0),(3,-2,4)$ and $(1,-3,3)$ is

The equation of plane passing through $(1,0,0)$ and $(0,1,0)$ and making an angle $45^{\circ}$ with the plane $x+y-3=0$ is

The approximate value of $\frac{1}{(2.002)^2}$ is

Three numbers are chosen at random from numbers 1 to 20 . The probability that they are consecutive is

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

The area of the triangle whose vertices are $( i, \omega, \omega^2 )$ is (Where $\omega$ is a complex cube root of unity other than 1, $i$ is an imaginary number)________ sq.units

The tangent to the ellipse $9x^{2}+16y^{2}=288$ making equal intercepts on the coordinate axes intersects the X-axis and the Y-axis in the points A and B respectively. Then $A(\triangle OAB)=$ (where O is origin)}

P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio

$\bar{a} = \hat{i} - \hat{j}, \bar{b} = \hat{j} - \hat{k}, \bar{c} = \hat{k} - \hat{i}$ then a unit vector $\bar{d}$ such that $\bar{a} \cdot \bar{d} = 0 = [\bar{b} \bar{c} \bar{d}]$ is

If the truth value of the statement pattern $[p \wedge \sim r] \to \sim r \wedge q$ is False, then which of the following has truth value False?

The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at most $2$ components out of $4$ tested, will survive is

If $ y = y(x) $ and \[ \left( \frac{2+\sin x}{y+1} \right)\frac{dy}{dx} = -\cos x, \] with the initial condition $ y(0) = 1 $, then find \[ y\left(\frac{\pi}{2}\right) = \, ? \]

The number of integral values of $p$ for which the vectors $(p + 1)\hat{i} - 3\hat{j} + p\hat{k},\; p\hat{i} + (p + 1)\hat{j} - 3\hat{k}$ and $-3\hat{i} + p\hat{j} + (p + 1)\hat{k}$ are linearly dependent, is ______.

The length of the altitude through the point $ D $ of the tetrahedron where the vertices of the tetrahedron are
\[ A(2, 3, 1), B(4, 1, -2), C(6, 3, 7), D(-5, -4, 8), \] is

The locus of point of intersection of the tangents to the circle $ x^2 + y^2 = 16 $, such that the angle between them is 60°, is

The locus of the points represented by $ |z + 3| - |z - 3| = 6 $, where $ z $ is a complex number, is ....

If $ f(x) = \frac{k \sin x + 2 \cos x}{\sin x + \cos x} $ is strictly increasing for all real values of $ x $, then:

The direction ratios of the line of intersection of the planes $ x - y + z - 5 = 0 $ and $ x - 3y - 6 = 0 $, are:

The line passing through the point $ (5, 1, a) $ and $ (3, b, 1) $ crosses the yz-plane at $ (0, \frac{17}{2}, \frac{-13}{2}) $, then the value of $ 2a + 3b $ is:

The area of the region bounded by the curve $ y = |x - 2| $ between $ x = 1 $ and $ x = 3 $.

If $\bar{a} = 4\hat{i} + 3\hat{j} + \hat{k}, \bar{b} = \hat{i} - 2\hat{j} + 2\hat{k}$ then $\bar{a} \times (\bar{a} \times (\bar{a} \times (\bar{a} \times \bar{b}))) =$}

If the shortest distance between the lines $\frac{x - k}{2} = \frac{y - 4}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{4} = \frac{y - 4}{6} = \frac{z - 7}{8}$ is $\frac{13}{\sqrt{29}}$, then $k =$}