If the two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect at two distinct points, then

Let \(z=a-\frac{i}{2} ; a \in R\). Then \(|i+z|^2-|i-z|^2\) is equal to

If \(4 \cos x+3 \sin x=5\), then find the value of \(\tan x=\)

If a square matrix \(A\) is such that \(\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right)\) \(=\left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right)=I\), where \(I\) is a unit matrix, then \(A\) is

The number of ways in which \(n\) distinct objects can be put into two different boxes is

If \((2,0)\) is the vertex and \(Y\)-axis is the directrix of a parabola, then its focus is

\(\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}, \mathbf{c}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are three vectors and a vector \(\mathbf{r}\) is perpendicular to both the vectors \(\mathbf{b}\) and \(\mathbf{c}\). If \(\mathbf{r} \cdot \mathbf{a}=9\), then \(\mathbf{r}=\)

If a current of 15 A passes through a solenoid of length 25 cm, radius 2 cm and number of turns 500, then the magnetic moment of the solenoid is

At what temperature (in K ) the rms velocity of \(\mathrm{SO}_2\) molecules is equal to rms velocity of O, molecules at \(27^{\circ} \mathrm{C}\).

The relation between pressure \(p\) and volume \(V\) is given by \(p V^{1 / 4}=\) constant. If the percentage decrease in volume is \(\frac{1}{2}\), then the percentage increase in pressure is

Match the following :


The correct match is
\(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D }\end{array}\)

Observe the following statements :
a. The thermal stability of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
b. Acidic nature of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
c. The reducing nature of \(\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{Se}\) and \(\mathrm{H}_2\) Te follow the order :
\(\mathrm{H}_2 \mathrm{~S} < \mathrm{H}_2 \mathrm{Se} < \mathrm{H}_2 \mathrm{Te}\)
The correct statement are:

The angular momentum of electron in \(\mathrm{H}\) atom in a particular \(n\) state is \(\frac{h}{\pi}\). What is the energy in \(J\) required to excite the electron from this particular \(\mathrm{n}\) state to \((\mathrm{n}+1)\) state?
\(\left(x=+2.18 \times 10^{-18} \mathrm{~J}\right)\)