List of top Questions asked in MHT CET

If \( x = \sin \theta, y = \sin^3 \theta \), then \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{6} \) is

If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}

The sum of two nonzero numbers is 4. The minimum value of the sum of their reciprocals is

The rates of change of the perimeter and area of a rectangle respectively when length $x=5$ cm and breadth $y=2$ cm, if $dx/dt = -5$ cm/min and $dy/dt = 3$ cm/min, are

The angle between the line \( x = \frac{y-1}{2} = \frac{z-3}{\lambda} \) and the plane \( x + 2y + 3z = 6 \) is \( \cos^{-1} \sqrt{\frac{5}{14}} \), then the value of \( \lambda \) is

\( \int \sqrt{x^2 + 3x} dx = \)}

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

In a triangle ABC with usual notations if \( b \sin C (b \cos C + c \cos B) = 42 \), then area of triangle ABC =}

If \( 0 \le \cos^{-1} x \le \pi \) and \( -\frac{\pi}{2} \le \sin^{-1} x \le \frac{\pi}{2} \), then at \( x = \frac{1}{5} \) the value of \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) is

Let the plane passing through point (2, 1, -1) containing line joining the points (1, 3, 2) and (1, 2, 1) makes intercepts \( p, q, r \) on co-ordinate axes, then \( p + q + r = \)}

\( \int \frac{x}{1+x^4} dx = \)}

\( \int \frac{(5 \sin \theta - 2) \cos \theta}{(5 - \cos^2 \theta - 4 \sin \theta)} d\theta = \)}

\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^2 + \log (\frac{\pi - x}{\pi + x}) \cdot \cos x) dx = \)}

The area bounded by the curve \( y = x^2 + 3, y = x, x = 3 \) and \( y \)-axis is

Number of switches in alternative equivalent simple circuit for the circuit is (are)

\( \int_{0}^{1} \log (\frac{1}{x} - 1) dx = \)}

If the foot of the perpendicular drawn from the origin to a plane is \( P(2, -1, 4) \), then the equation of the plane is

Solution of \( (2y - x) \frac{dy}{dx} = 1 \) is

The integrating factor of \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \) is

The angle between the lines \( x = y, z = 0 \) and \( y = 0, z = 0 \) is

The line passing through the points \( (a, 1, 6) \) and \( (3, 4, b) \) crosses the \( yz \)-plane at \( (0, \frac{17}{2}, -\frac{13}{2}) \), then the value of \( (3a + 4b) \) is

The differential equation whose solution is \( Ax^2 + By^2 = 1 \), where A and B are arbitrary constants is of}

Let \( \bar{a}, \bar{b}, \bar{c} \) be three vectors such that \( \bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 3, |\bar{b}| = 4, |\bar{c}| = 5 \), then \( \bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a} = \)}

If \( (\cos^{-1} x)^2 - (\sin^{-1} x)^2>0 \), then}

The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm, after 2 minutes its radius becomes 9 cm, then radius of balloon after 4 minutes is