List of top Questions asked in MHT CET

The acute angle between the lines given by \( y - \sqrt{3}x + 1 = 0 \) and \( \sqrt{3}y - x + 7 = 0 \) is
Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)
The volume of a tetrahedron whose vertices are \( A = (-1, 2, 3) \), \( B = (3, -2, 1) \), \( C = (2, 1, 3) \), and \( D = (-1, -2, 4) \) is
The joint equation of the lines through the origin trisecting angles in the first and third quadrant is
Evaluate \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)
If \( \sin x + \sin^2 x = 1 \), then \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is
The perimeter of the triangle whose vertices have the position vectors \( \hat{i} + \hat{j} + \hat{k} \), \( 5\hat{i} + 3\hat{j} - 3\hat{k} \), and \( 2\hat{i} + 5\hat{j} + 9\hat{k} \) is
Evaluate \( \int_{-4}^{4} \log \left( \frac{8 - x}{8 + x} \right) dx \)
If \( \mathbf{a} = 2\hat{i} - \hat{j} + \hat{k} \), \( \mathbf{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), and \( \mathbf{c} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) are coplanar, then \( \lambda \) is the root of the equation
If the tangent to the curve given by \( x = t^2 - 1 \) and \( y = t^2 - t \) is parallel to the x-axis, then the value of \( t \) is
If \( f \) and \( g \) are differentiable functions satisfying \( g'(a) = 2 \), \( g(a) = b \), and \( f \circ g = 1 \), where 1 is an identity function, then \( f'(b) \) is equal to
If the p.m.f. is given by \( P(X) = k \left( \frac{4}{x} \right) \) for \( x = 0, 1, 2, 3, 4 \) and \( k>0 \), then the value of \( k \) is
If the A.M. and G.M. of the roots of a quadratic equation in \( x \) are \( p \) and \( q \) respectively, then its equation is
If \( A = \left[ \begin{array}{cc} 1 & -1 \\ 7 & 0 \end{array} \right] \), \( |A| = \left| \begin{array}{cc} 1 & 0 \\ 1 & 1 \end{array} \right| \), and \( A^2 = 8A + kI \), then the value of \( k \) is
If \( 2f(x) = f'(x) \) and \( f(0) = 3 \), then the value of \( f(2) \) is
If \( A + B + C = 180^\circ \), then the value of \( \tan \left( \frac{A}{2} \right) \tan \left( \frac{B}{2} \right) + \tan \left( \frac{B}{2} \right) \tan \left( \frac{C}{2} \right) + \tan \left( \frac{C}{2} \right) \tan \left( \frac{A}{2} \right) \) is
The angle between the two lines \( \frac{x-4}{1} = \frac{y+4}{2} = \frac{z+1}{2} \) and \( \frac{x+1}{2} = \frac{y+3}{2} = \frac{z-4}{-1} \) is
Evaluate \( \int e^{\tan^{-1} x} \left( 1 + \frac{x}{1 + x^2} \right) dx \)
The co-ordinates of the mid-point of the chord cut off by the line \( 2x - 5y + 18 = 0 \) by the circle \( x^2 + y^2 - 6x + 2y - 54 = 0 \) are
The differential equation of the family of curves \( y = e^{x} (A \cos x + B \sin x) \), where \( A \) and \( B \) are arbitrary constants, is
The area of the region bounded by the curve \( y = x^2 + 1 \), the lines \( x = 1 \), \( x = 2 \), and the x-axis is
For the probability distribution of \( X \) given below, the variance of \( X \) is
If \( n(X) = 700 \), \( n(A) = 200 \), \( n(B) = 300 \), \( n(A \cap B) = 100 \), where \( X \) is the universal set and \( A \) and \( B \) are subsets of \( X \), then \( n(A' \cap B') = \)
Evaluate \( \int 7^{7^{7x}} 7^{7x} dx = \)
The optimal solution of the L.P.P. \( Z = 8x + 3y \) subject to the constraints \( x + y \leq 3 \), \( 4x + y \leq 6 \), \( x \geq 0 \), \( y \geq 0 \) is