List of top Mathematics Questions asked in MHT CET

If the foot of perpendicular drawn from the origin to the plane is \( (3, 2, 1) \), then the equation of the plane is
The letters of the word 'LOGARITHM' are arranged at random. The probability that the arrangement starts with a vowel and ends with a consonant 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 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 \( \tan 2A + \tan 2B + \tan 2C = \)
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
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
Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)
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
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
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 \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)
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
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 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 \( 2f(x) = f'(x) \) and \( f(0) = 3 \), then the value of \( f(2) \) 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 \( A = \left[ \begin{array}{cc} 1 & -1 \\ 7 & 0 \end{array} \right] \), \( |A| = \left| \begin{array}{cc} 1 & 0 \\ 1 & 1 \end{array} \right| \), and \( A^2 = 8A + kI \), then the value of \( k \) is
If 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