List of top Mathematics Questions

\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)

If l,m,n and a,b,c are direction cosines of two lines then

If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =

On differentiation if we get f (x,y)dy - g(x,y)dx = 0 from 2x2-3xy+y2+x+2y-8 = 0 then g(2,2)/f(1,1) =

The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =

The locus of z such that  \(\frac{|z-i|}{|z+i|}\)= 2, where z = x+iy. is

In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, then \( \frac{c}{a} \sin 2A + \frac{a}{c} \sin 2C = \):
If \((l_1, m_1, n_1), (l_2, m_2, n_2)\) are the direction cosines of two lines, then \[ (l_2m_1 - l_1m_2)^2 + (m_1n_2 - m_2n_1)^2 + (n_1l_2 - n_2l_1)^2 + (l_1l_2 + m_1m_2 + n_1n_2)^2 = \]
The sum of the global minimum and global maximum values of the function \[ f(x) = \frac{4}{3}x^3 - 4x \quad \text{in } [0, 2] \text{ is} \]
Let \([t]\) represent the greatest integer not more than \(t\). Then the number of discontinuous points of \(f(x) = \left[\frac{1}{x}\right]\) in \((0, \infty)\) is

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).

If \( \overline{\mathbf{a}} = 2\overline{\mathbf{i}} + 3\overline{\mathbf{j}} + 4\overline{\mathbf{k}} \), \( \overline{\mathbf{b}} = 3\overline{\mathbf{i}} + 4\overline{\mathbf{k}} \), and \( \overline{\mathbf{c}} = 5\overline{\mathbf{i}} + 4\overline{\mathbf{k}} \) are three vectors, then a vector which is perpendicular to \( \overline{\mathbf{a}} \) and \( \overline{\mathbf{b}} \times \overline{\mathbf{c}} \) is
If the number of diagonals of a regular polygon of \( n \) sides is 104, then \( n = \)
The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:
The greatest integer \( r \) such that \( 30^r \) divides \( 30! \) is:
If \( -1 \) is a twice repeated root of the equation \( a(x^3 + x^2) + bx + c = 0 \), then the ratio \( a : b : c \) is:
Evaluate the following expression: \[ (1+i)^{2024} + (1-i)^{2024} \]
The combined equation of the lines passing through the point \( (3, 4) \) and each making an angle of 45° with the line \( x + y + 1 = 0 \) is:
The area (in sq. units) of the region bounded by the curves \( y = 4 \cos x \) and \( y = -|\cos x| \) from \( x = -\frac{\pi}{2} \) to \( x = \frac{\pi}{2} \) is:

Let ABCD be a parallelogram and $ 2\bar{i} + \bar{j} $, $ 4\bar{i} + 5\bar{j} + 4\bar{k} $ and $ -\bar{i} - 4\bar{j} - 3\bar{k} $ be the position vectors of the vertices A, B, D respectively. Then the position vector of one of the points of trisection of the diagonal AC is

If \( 2^n \) divides \( 16! \) and \( 2^{n+1} \) does not divide \( 16! \), then \( n = \)
If \[ \frac{-x^2 + 6x + 1}{(x - 1)^2 (x^2 + 2)} = \frac{A}{x - 1} + \frac{B}{(x - 1)^2} + \frac{Cx - 3}{x^2 + 2}, \] then \(A + B + C =\) ?
The maximum value of $ a $ such that the second derivative of $ x^4 + ax^3 + \frac{3x^2}{2} + 1 $ is positive for all real $ x $ is
Assertion (A): The function \( f(x) = \begin{cases} 1 - \cos x, & x<0 \\ \sin x, & x \geq 0 \end{cases} \) is continuous at \(x = 0\). Reason (R): \(\lim_{x \to 0} \sin x = 0\)
Let \( (a, b) \) denote the angle between vectors \( \mathbf{a} \) and \( \mathbf{b} \). If \( \mathbf{a} = 2i + 3j + 6k \), \( |\mathbf{a}| = 4 \), and \( (\mathbf{a}, \mathbf{b}) = \cos^{-1} \left( \frac{4}{21} \right) \), then \( \mathbf{a} + \mathbf{b} = \)