List of top Mathematics Questions

The angle between the lines \[ \mathbf{r_1} = (i + 2j + 3k) + \lambda (i + j + 2k) \quad \text{and} \quad \mathbf{r_2} = (3i + k) + \lambda' (2i + j - k), \quad \lambda, \lambda' \in \mathbb{R} \] is

The sum of the cofactors of the elements of the second row of the matrix \[ \begin{pmatrix} 1 & 3 & 3 & 2 \\ -2 & 0 & 4 & 1 \\ 5 & 2 & 1 & 1 \end{pmatrix} \] is

If \( (a, -2a), \, a>0 \) is the midpoint of a line segment intercepted between the co-ordinate axes, then the equation of the line is

The p.d.f. of a continuous random variable \( X \) is given by \[ f(x) = \frac{x + 2}{18}, \quad \text{if} \, -2<x<4, \quad f(x) = 0, \, \text{otherwise}. \] Then \( P[ |x|<1 ] = \)

The direction cosines of a line which is perpendicular to lines whose direction ratios are \( 3, -2, 4 \) and \( 1, 3, -2 \) are

The area of the region bounded by the curve \( y = 4x^3 - 6x^2 + 4x + 1 \) and the lines \( x = 1, x = 5 \) and the X axis is

The differential equation obtained from the function \( y = a(x - a)^2 \) is

If \( f(x) = \log(\sin x) \), \( x \in \left[ \frac{\pi}{6}, \frac{5\pi}{6} \right] \), then the value of \( c \) by applying L.M.V.T. is

The polar co-ordinates of the point whose cartesian co-ordinates are \( (-2, -2) \), are given by

If \[ \int \frac{\sin \theta}{\sin^3 \theta} \, d\theta = \frac{1}{2k} \log \left| \frac{k + \tan \theta}{k - \tan \theta} \right| + c, \text{ then } k = \]

If the foot of perpendicular drawn from the origin to the plane is \( (3, 2, 1) \), then the equation of the plane is

The symbolic form of the following circuit is (where \( p, q \) represents switches \( s_1 \) and \( s_2 \) closed respectively)

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

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

The value of \( \int_{2}^{3} \frac{x}{x^2 - 1} \, dx \) 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 \( t = \)

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

The entries in the last column of the truth table for \( \neg (p \wedge q) \) are

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

If \( A, B, C \) are angles of a triangle ABC, then \( \tan 2A + \tan 2B + \tan 2C = \)

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 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