List of top Mathematics Questions asked in MHT CET

If the lines given by \( \frac{x-1}{2\lambda} = \frac{y-1}{5} = \frac{z-1}{2} \) and \( \frac{x+2}{\lambda} = \frac{y+3}{\lambda} = \frac{z+5}{1} \) are parallel, then the value of \( \lambda \) is
In a triangle \( ABC \) with usual notations, if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \), then the area of triangle \( ABC \) with \( a = \sqrt{6} \) is
In a quadrilateral \( ABCD \), \( M \) and \( N \) are the mid-points of the sides \( AB \) and \( CD \) respectively. If \( AD + BC = t \cdot MN \), then \( t = \)
If a point \( P \) on the line segment joining the points \( (3, 5, -1) \) and \( (6, 3, -2) \) has its \( y \)-coordinate 2, then its \( z \)-coordinate is
The growth of population is proportional to the number present. If the population of a colony doubles in 50 years, then the population will become triple in
If rectangles are inscribed in a circle of radius \( r \) units, then the dimensions of the rectangle which has maximum area are
If \( A, B, C \) are angles of a triangle ABC, then \( \tan 2A + \tan 2B + \tan 2C = \)
The entries in the last column of the truth table for \( \neg (p \wedge q) \) are
The acute angle between the lines given by \( y - \sqrt{3}x + 1 = 0 \) and \( \sqrt{3}y - x + 7 = 0 \) is
The distance of the point \( (7, 5, 2) \) from the plane \( 3x + 4y + 2z - 8 = 0 \) measured parallel to the line \( \frac{x - 1}{3} = \frac{y - 2}{6} = \frac{z + 1}{2} \) is
Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)
If a fair coin is tossed 8 times, then the probability that it shows heads more than tails is
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 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
If \( \sin x + \sin^2 x = 1 \), then \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is
Evaluate \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)
The joint equation of the lines through the origin trisecting angles in the first and third quadrant 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 \( 2f(x) = f'(x) \) and \( f(0) = 3 \), then the value of \( f(2) \) is
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 \( f \) 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 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