List of practice Questions

Impedance of the circuit shown below is

If z is a complex number then $|z+1|=\sqrt3|z-1|$ represents

Imagine a system of units in which the unit of mass is $10\, kg$, length is $1 \,km$ and time is $1 \,min$. Then 1 joule in this system is equal to

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength $\lambda$ (given in terms of Rydberg constant R for the hydrogen atom) equal to

If $z_{1}$, $z_{2}$, $z_{3}$ are any three complex numbers such that $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1$, then find the value of $\left|z_{1}+z_{2}+z_{3}\right|$.

If $Z=\frac{A^{4}\,B^{1/3}}{CD^{3/2}}$. and $\Delta A$, $\Delta B$, $\Delta C$, and $\Delta D$ are their absolute errors in $A$, $B$, $C$ and $D$ respectively. The relative error in $Z$ is

If $z$ is a complex number such that $|z|\geq\,2$, then the minimum value of $ |z + (1/2) | $

If Young's modulus of iron be $2 \times 10^{11}N/m^{-2}$ and interatomic distance be $3 \times10^{-10}m^{-2}$, the interatomic force constant will be

If $z_1=2\sqrt2(1+i)$ and $z_2=1+i\sqrt3$ , then $z_1^2\,\,z_2^3$ is equal to

If $z_1$ and $z_2$ are any two complex numbers, then $|z_1+\sqrt {z_1^2-z_2^2}|+ |z_1+\sqrt {z_1^2-z_2^2}| $ is equal to

If $z_1,z_2$ are two complex numbers and such that $\left|\frac{z_1-z_2}{z_1+z_2}\right|=1$ and $iz_1=Kz_2$ where $K\,\in\,R$, then the angle between $z_1-z_2$ and $z_1+z_2$ is

If $y=\left(tanx\right)^{sinx}$, then $\frac{dy}{dx}$ is equal to

If $y = x^x , x > 0 $ , then $\frac{dy}{dx}$ is

If you touch concentrated $ {HNO_3}$ with your finger and immediately wash it with water, then the skin at the place where it came into contact with $ {HNO_3}$ becomes yellow. This is because of :

If $y = \tan^{-1} \frac{x-\sqrt{1-x^{2}}}{x+\sqrt{1-x^{2}}} , $ then $ \frac{dy}{dx} $ is equal to

If $y=sin^{-1}\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)+sec^{-1}\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)$, $x > 0$, then $\frac{dy}{dx}$ is equal to

If $y=\frac{sin\left(x+9\right)}{cos\,x}$, then $\frac{dy}{dx}$ at $x = 0$ is

If $y = \left(\sin x\right)^{\left(\sin x\right)^{\left(\sin x\right)....\infty}} ,$ then $ \frac{dy}{dx} = $

$ If y = sec^{-1} [cosec\, x] + cosec^{-1} [sec\, x] + sin^{-1} [cos x] + cos^{-1} [sin\, x], then \frac{dy}{dx}$is equal to

If $y = \log\, \tan \, \sqrt{x}$ then the value of $\frac{dy}{dx}$ is:

If $y = \log(\sec x + \tan x),$ then $\frac{dy}{dx} = $

If $y =\log_{\sin x } \left(\tan x\right),$ then $\left(dy/dx\right)\pi/{4} = $

If $y = e^{(1 + \log_e \, x)}$, then $\frac{dy}{dx}$ is equal to :

If $y=e^{3x+7}$, then the value of $\frac{dy}{dx} \bigg|_{x=0}$ is

If $y =\log_{e}x \left(x-2\right)^{2}$ for $ x \ne0 , 2 $ then $y' \left(3\right) = $