$A$ train moving at a speed of $220\, ms^{-1}$ towards a stationary object,emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is .... $Hz$ (speed of sound in air is $330\, ms^{-1}$)

The transformed equation of $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle of $45^{\circ}$,is

The slope of the tangent to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

The electron affinity of sulfur is........

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer function,then the range of $f$ is: