List of top Questions asked in MHT CET

In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is

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 \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}

The difference between the maximum value and minimum value of objective function \( z = 3x + 5y \) subject to \( x + 3y \le 60, x + y \ge 10, x - y \ge 0, x, y \ge 0 \) is

If \( ^{15}C_4 + ^{15}C_5 + ^{16}C_6 + ^{17}C_7 + ^{18}C_8 = ^{19}C_r \), then the value of \( r \) is equal to}

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

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

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

The combined equation of the tangent and normal to the curve \( xy = 15 \) at the point (5, 3) is

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

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

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

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

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

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

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

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 \( p + q + r = \)}

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

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

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

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

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

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

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

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

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