Mathematics

The required value for x is

If $x = 2t + 1$ and $y = t^2$, then $\frac{dy}{dt}$ is

The value of $(1 - \omega)(1 - \omega^2)$, where $\omega$ is the cube root of a complex number is

Equation of the tangent of the circle $x^2 + y^2 = 13$ at $(2,3)$ is

If $|x| = 2$ then the solution set is

The smallest prime number is

$$\displaystyle \lim_{x \to 2} \frac{x^3 - 2^3}{x - 2} is$$

If A, B and C are non-empty sets and $A \subset B$ then $A \cap B$ is

The point of inflection for the curve $x^3 + 4x$ is

$\lim_{x\to 0} \frac{\tan x - 5x}{x} is$

The solution of $\cos x = \frac{1}{2}$

The given function is continuous at

The magnitude of $2 - 3i$ is

1 and 2 are the roots of

The matrix $A = \begin{pmatrix}1 & 3\\3 & 2\end{pmatrix}$is

Center of the circle $x^2 + y^2 - 2x - 4y + 1 = 0$

If the derivative of $x^2 + 3x$ is 1, the value of $x$ is

The required value of the determinant is

The value of $\tan(\tan^{-1}1)$ is

The curve $y^2 = 4x$ is symmetric about

The angle between the lines $2x^2 + xy - 2y^2 = 0$ is

$$2 \int_{0}^{1} x \, dx \text{ is equal to } 1$$

The length of the perpendicular from $(0,0)$ to the line $x + y + 1 = 0$ is

$\int \cos x \, dx$ is equal to

If $f(x)=\sqrt{4 - x^2}$ then $f(2)$ is

Find the radius of the circle $x^2 + y^2 - 3x + 2y - \frac{3}{4} = 0$ is

The distance between the parallel lines $y-2x=4$ and $6x-3y=5$ is

The $n^{th}$ term of the series: $2 + 4 + 6 + 12 + 20 + \dots$ is

What is the value of $\log_a \sqrt{a^3 \sqrt{a^2}}$ ?

If $z = \cos\theta + i\sin\theta$ then $z^n + \frac{1}{z^n}$ is equal to

Which one of the following is the area enclosed by the curve $y = 3x$, the x-axis and the ordinate $x = 0, x = 4$?

The range of the function $y=\sqrt{a^2 - x^2}, a>0$ is equal to

The function $f(x) = x - \frac{1}{x^2}$, where $x \in \mathbb{R}, x \neq 0$ is

If A and B are any two sets, then A - (A-B) is equal to

$$\displaystyle \lim_{x \to 0} \frac{a^{x} - b^{x}}{x} \text{is equal to}$$

If $A = [-3, 2]$ and $B = [2, 3]$ then $A - B$ is equal to

If $A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$, then $A^{100}$ is equal to

$$\left| \begin{matrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{matrix} \right| \text{Find its value, where w is an imaginary cube root of unity}$$

The absolute value of the complex number $(1+i)^{-1}$ is

The single equation representing the pairs of lines $y = x$ and $y = -x$ is

If $\lim_{x \to 0^-} f(x) \neq \lim_{x \to 0^+} f(x)$, then f(x) is said to be an

The integral $\int \frac{e^x dx}{e^x+1}$ is equal to

The quadratic equation of whose one root is $(2+\sqrt{3})$ is

Solution of $\tan(ax) = \cot(bx)$ is

The derivative of $y = \cos(\cos\sqrt{x})$ is

For what value of k will the equation $5x^2 - kx + 45 = 0$ have equal roots?

If $a^x = b^y = c^z$ then a,b,c are in G.P then x,y,z are in

If $|x| < 1$ and $y = x + x^2 + x^3 + x^4 + \dots + \infty$, then x is equal to

The derivative of $y=5^x$ with respect to x is equal to

$\cos(3 \cos^{-1}(x))$ is equal to