List of top Mathematics Questions

Equation of the circle with centre $(-3, 2)$ and radius 4 is

In a $\Delta ABC$, $\sum a^2 \cos(B - C) =$

Principle value of $\cot^{-1}(-1)$ is

$(-1 + 2i) + \left(\frac{1}{2} - i\right) =$

In a $\Delta ABC$, if $a=13, b=14$ and $c=15$ then the value of $\tan \left(\frac{A}{2}\right)$ is

The value of $\sin 45^\circ$ is

If $2 \cos \theta = x + \frac{1}{x}$ then $2 \cos 3\theta =$

$\sin 15^\circ =$

In a triangle $\Delta ABC$, the value of $\cos \left(\frac{B+C}{2}\right)$ in terms of angle $A$.

In any $\Delta ABC$, $\tan \frac{B+C}{2} =$

If $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ then $(A^{-1}) =$

If $-1 \leq x \leq 1$, then $\cos^{-1} x + \sin^{-1} x =$

If $\tan A = \frac{4}{3}$ then the value of $\cos 2A$ is

If $\frac{3x}{x^2+x-2} = \frac{A}{x+2} + \frac{B}{x-1}$, then the ordered pair $(A, B)$ is

If $\deg f(x) \geq \deg g(x)$, then the rational fraction $\frac{f(x)}{g(x)}$ is called

If two rows (or columns) of a determinant of order 3 are identical then the value of determinant is

The Matrix $\begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$ is

Co-factor of -4 in $\begin{vmatrix} 1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9 \end{vmatrix}$ is

Order of the matrix $\begin{bmatrix} 1 & 6 \\ 2 & 0 \\ 7 & -1 \end{bmatrix}$ is

The length of the altitude through the point \( D \) of the tetrahedron where the vertices of the tetrahedron are
\[ A(2, 3, 1), B(4, 1, -2), C(6, 3, 7), D(-5, -4, 8), \] is

The volume of the tetrahedron whose coterminous edges are represented by
\[ \mathbf{a} = -12\hat{i} + p\hat{k}, \quad \mathbf{b} = -3\hat{j} - \hat{k}, \quad \mathbf{c} = -2\hat{i} + \hat{j} - 15\hat{k}, \] is 570 cu. units, then \( p = \)

The direction ratios of the line of intersection of the planes \( x - y + z - 5 = 0 \) and \( x - 3y - 6 = 0 \), are:

In a culture, the bacteria count is 1,00,000 initially. The number increases by 10% in the first 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

If \( y = ax^r - bx^{r-1} \), then \[ \frac{d^2y}{dx^2} = ? \]

The points \( (1, 3) \) and \( (5, 1) \) are two opposite vertices of a rectangle. The other two vertices lie on the line \[ y = 2x + c, \quad \text{where} \quad c \text{ is the constant}, \quad \text{then the co-ordinates of the other two vertices are} \]