In a series $LCR$ circuit,$R=300 \Omega, L=0.9 \text{ H}, C=2.0 \mu\text{F}$ and $\omega=1000 \text{ rad/s}$,then the impedance of the circuit is: (in $\Omega$)

In order to double the frequency of the fundamental note emitted by a stretched string,the length is reduced to $\frac{3}{4}$ of the original length and the tension is changed. The factor by which the tension is to be changed is

The highest stable $Mn$ fluoride is $MnF_4$,whereas the highest $Mn$ oxide is $Mn_2O_7$. This is due to $-$

In a binomial distribution, the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then, its mean is

Two closed organ pipes of length $100\,cm$ and $101\,cm$ long give $16$ beats in $20\,sec$ when each pipe is sounded in fundamental mode. Calculate the velocity of sound in $m/s$.

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is: