List of top Questions asked in MHT CET

The domain of the function \( f(x) = \sqrt{x} \) is
For every value of \( x \), the function \( f(x) = \frac{1}{a^x}, a>0 \) is
If \( f(x) = \sin^{-1} \left( \sqrt{\frac{1 - x}{2}} \right) \), then \[ f'(x) = \]
Evaluate \[ \int_0^1 \frac{x^2 - 2}{x^2 + 1} \, dx \]
If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is
If \( a = \sin 175^\circ + \cos 175^\circ \), then
The rational form of the number \( 1.41 \overline{41} \) is
The order and degree of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^3 \right]^{\frac{3}{2}} = 7 \frac{d^2y}{dx^2} \] are respectively
The negation of the statement 'He is poor but happy' is
If the line \[ \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \quad \text{is parallel to the plane} \quad \vec{r} \cdot (3i - 2j + mk) = 10, \] then the value of \( m \) is
If the equation \[ ax^2 + 2hxy + by^2 + 2gx + 2fy = 0 \] has one line as the bisector of the angle between the co-ordinate axes, then \[ (a + b)^2 = 4(h^2 + g^2) \]
If the volume of the parallelepiped whose coterminous edges are along the vectors \[ \vec{a}, \vec{b}, \vec{c} \] is 12, then the volume of the tetrahedron whose coterminous edges are \[ \vec{a} + \vec{b}, \, \vec{b} + \vec{c}, \, \vec{c} + \vec{a} \] is
If the plane \[ 2x + 3y + 5z = 1 \] intersects the coordinate axes at the points A, B, C, then the centroid of \( \triangle ABC \) is
The angle between the lines \[ \frac{x - 1}{4} = \frac{y - 3}{8} = \frac{z - 2}{2} \quad \text{and} \quad \frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 4}{2} \] is
The p.d.f. of a continuous r.v. \( X \) is given by \[ f(x) = \frac{x}{8}, \quad 0<x<4 \quad \text{and} \quad f(x) = 0, \text{ otherwise,} \] then \( P(X \leq 2) \) is
Evaluate \[ \int \frac{\log x - 1}{1 + (\log x)^2} \, dx \]
If a die is thrown at random, then the expectation of the number on it is
The function \[ f(x) = \frac{x + 1}{9x + x^3} \] is
Evaluate \[ \tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = \]
The particular solution of the differential equation \[ y \frac{dx}{dy} = x \log x \quad \text{at} \quad x = e \text{ and } y = 1 \] is
The odds in favour of drawing a king from a pack of 52 playing cards is
The eccentricity of the ellipse \[ y^2 + 4x^2 - 12x + 6y + 14 = 0 \] is
Evaluate the integral \[ \int \frac{dx}{\cos 2x - \cos^2 x} \]
The straight lines represented by the equation \( 9x^2 - 12xy + 4y^2 = 0 \) are
The length of the latus rectum of the parabola \( x^2 + 2y = 8x - 7 \) is