List of top Mathematics Questions

If \( z = x+iy \), \( x^2+y^2 = 1 \) and \( z_1 = e^{i\theta} \), then the expression \( \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} \) simplifies to:
Let \( A, B, C, D, \) and \( E \) be \( n \times n \) matrices, each with non-zero determinant. If \( ABCDE = I \), then \( C^{-1} \) is:
If \(2.4^{2n+1} + 3^{3n+1}\) is divisible by \(k\) for all \(n \in \mathbb{N}\), then \(k\) is:
The square root of \( 7 + 24i \) is:
Angles of a triangle are in ratio 1 : 5 : 12, the biggest angle of this triangle is:
If the side of the cube is 6 cm, then the diagonal of the cube is:
The quadratic equation, whose roots are \( \frac{4 + \sqrt{7}}{2} \) and \( \frac{4 - \sqrt{7}}{2} \), is:
A train passes a telegraph post in 40 seconds moving at a rate of 36 km/h. Then the length of the train is:
If \((\alpha + \beta)\) is not a multiple of \(\frac{\pi}{2}\) and \(3 \sin(\alpha - \beta) = 5 \cos(\alpha + \beta)\), then \[ \tan\left(\frac{\pi}{4} + \alpha\right) + 4\tan\left(\frac{\pi}{4} + \beta\right) = \]
The factor of \( a^4 b^4 - 16c^4 \) is:
If \([x]\) is the greatest integer function, then evaluate the integral \( \int_{0}^{5} [x] \, dx \):
If \( L_1 \) and \( L_2 \) are two lines which pass through origin and have direction ratios \( (3, 1, -5) \) and \( (2, 3, -1) \) respectively, then the equation of the plane containing \( L_1 \) and \( L_2 \) is:
The largest among the distances from the point \(P(15,9)\) to the points on the circle \(x^2 + y^2 - 6x - 8y - 11 = 0\) is:
If \( \vec{f} = i + j + k \) and \( \vec{g} = 2i - j + 3k \), then the projection vector of \( \vec{f} \) on \( \vec{g} \) is:
Let \( \mathbf{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} \), \( \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} \). The projection of the sum of the vectors \( \mathbf{a}, \mathbf{b} \) on the vector perpendicular to the plane of \( \mathbf{a}, \mathbf{b} \) is:
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
The length of the latus rectum of \( 16x^2 + 25y^2 = 400 \) is:
If a function $f(x)$ is defined as: $$ f(x) = \begin{cases} \frac{\tan(4x) + \tan 2x}{x} & \text{if } x> 0 \\ \beta & \text{if } x = 0 \\ \frac{\sin 3x - \tan 3x}{x^2} & \text{if } x < 0 \end{cases} $$ and is continuous at $x = 0$, then find $|\alpha| + |\beta|$.
If the coefficients of the \( (2r + 6)^{th \) and \( (r - 1)^{th} \) terms in the expansion of \( (1 + x)^{21} \) are equal, then the value of \( r \) is:}
The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:
The orthogonal projection vector of \( \bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k} \) on \( \bar{b} = \bar{i} - 2\bar{j} + \bar{k} \) is:
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
Let \( \mathbf{a}, \mathbf{b} \) be two unit vectors. If \( \mathbf{c} = \mathbf{a} + 2\mathbf{b} \) and \( \mathbf{d} = 5\mathbf{a} - 4\mathbf{b} \) are perpendicular to each other, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
If the vectors \(a\bar{i} + \bar{j} + \bar{k}\), \(\bar{i} + b\bar{j} + \bar{k}\), \(\bar{i} + \bar{j} + c\bar{k}\) (\(a \ne b \ne c \ne 1\)) are coplanar, then \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)