List of top Questions asked in MHT CET

If \( \vec{a} = \hat{i} + 5\hat{k}, \, \vec{b} = 2\hat{i} + 3\hat{k}, \, \vec{c} = 4\hat{i} - \hat{j} + 2\hat{k}, \, \vec{d} = \hat{i} - \hat{j} \), then \( (\vec{c} - \vec{a}) \cdot (\vec{b} \times \vec{d}) = \)

If \( f(x) = x^2 - 3x + 4 \) and \( f(x) = f(2x + 1) \), then \( x = \)

The area bounded by the parabola \( y^2 = 16x \) and its latus-rectum in the first quadrant is

20 meters of wire is available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, then the radius of the circle is

If the radius of a circle \( x^2 + y^2 - 4x + 6y - k = 0 \) is 5, then \( k = \)

The equation of the normal to the curve \( 2x^2 + 3y^2 - 5 = 0 \) at \( P(1, 1) \) is

The angle between the lines \( \frac{x - 1}{4} = \frac{y - 3}{1} = \frac{z}{8} \) and \( \frac{x - 2}{2} = \frac{y + 1}{2} = \frac{z - 4}{1} \) is

If the direction cosines of a line are \( \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \), then

If \( \frac{1}{4}, a, b, \frac{1}{19} \) form a harmonic progression (H.P.), then the values of \( a \) and \( b \) are respectively

Evaluate \( \int_0^{\frac{\pi}{2}} \left( e^{\sin x} - e^{\cos x} \right) \, dx \)

The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is

A fair coin is tossed 2 times. A person receives \( X^3 \) if he gets \( X \) number of heads. His expected gain is

If \( x = 3 \sin \theta \), \( y = 3 \cos \theta \cos \phi \), \( z = 3 \cos \theta \sin \phi \), then \( x^2 + y^2 + z^2 = \)

Evaluate \( \int_{-2}^{1} \left[ x + 1 \right] \, dx \), where \( [x] \) is the greatest integer function not greater than \( x \)

If the origin is the centroid of the triangle whose vertices are \( A(2, p, -3) \), \( B(q, -2, 5) \) and \( C(-5, 1, r) \), then

Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink

If \( f(x) = \frac{x^2 + 2{18} \), for \( -2<x<4 \), and 0 otherwise, is the p.d.f. of a random variable \( X \), then the value of \( P(|X|<2) \) is}

If \( a \), \( b \), \( c \) are non-negative distinct numbers and \( ai + aj + ck \), \( i + j + k \), and \( ci + cj + bk \) are coplanar vectors, then

If foci of the ellipse \( \frac{x^2}{16} + \frac{y^2}{b^2} = 1 \) (\( b^2<16 \)) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide, then the value of \( b^2 \) is

The principal value of \( \sin^{-1} \left( -\frac{1}{2} \right) \) is

The separate equations of the lines represented by the equation \( 3x^2 - 2\sqrt{3} xy - 3y^2 = 0 \) are

If \( A = \begin{bmatrix} 1 & 1 \\ 2 & 1 \end{bmatrix}, B = \begin{bmatrix} 4 & 3 \\ 1 & 1 \end{bmatrix} \), then \( (A + B)^{-1x} = \)

The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is

If line \( x + y = 0 \) touches the curve \( ax^2 = 2y^2 - b \) at \( (1, -1) \), then the values of \( a \) and \( b \) are respectively

Evaluate \( \int \frac{dx}{\cos 2x + \sin^2 x} \)