List of top Mathematics Questions

The angle between the line \[ \mathbf{r} = (i + j + k) + \lambda (3i + j + 3k) \] and the plane \[ \mathbf{r} \cdot (i + 2j + 3k) = 8 \] is

If \[ \frac{x}{\sqrt{1 + x^2}} + \frac{y}{\sqrt{1 + y^2}} = 0, \quad x \neq y, \text{ then } (1 + x^2)^2 \frac{dy}{dx} = \]

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

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 \( t = \)

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 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 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 acute angle between the lines given by \( y - \sqrt{3}x + 1 = 0 \) and \( \sqrt{3}y - x + 7 = 0 \) 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

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 \( \int e^{\tan^{-1} x} \left( 1 + \frac{x}{1 + x^2} \right) dx \)

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

The distance of the point \( (2, -1, 0) \) from the plane \( 2x + y + 2z + 8 = 0 \) is

Evaluate the integral \( \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx = \)

If the sum of the slopes of the pair of lines given by \( 4x^2 + 2hxy - 7y^2 = 0 \) is equal to the product of the slopes, then \( h \) is

A line makes angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma \) is equal to

The number of solutions of the equation \( \tan x + \sec x = 2 \cos x \) lying in the interval \( [0, 2\pi] \) is

The solution of the differential equation \( \log \left( \frac{dy}{dx} \right) = 9x - 6y + 6 \) is (given that \( y = 1 \) when \( x = 0 \))

If \( y = e^{\sin(\cosec^{-1}x)} \), then \( \dfrac{dy}{dx} \) is