One of the following substances having the tendency to move from stronger region to the weaker region of the magnetic field is

If the displacement \(y~(\mathrm{in~} \mathrm{cm})\) of a particle executing simple harmonic motion is given by the equation \(y=5 \sin (3 \pi t)+5 \sqrt{3} \cos (3 \pi t)\), then the amplitude of the particle is

The position of the direct image obtained at $O ,$ , when a monochromatic beam of light is passed through a plane transmission grating at normal incidence is shown in figure. The diffracted images $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ correspond to the first, second and third order diffraction. When the source is replaced by another source of shorter wavelength

The ratio of the strengths of the four fundamental forces in nature, \(\mathrm{F}_{\mathrm{G}}: \mathrm{F}_{\mathrm{N}}: \mathrm{F}_{\mathrm{E}}: \mathrm{F}_{\mathrm{W}}=\)

If water flows with a velocity of \(20 \mathrm{~cm} \mathrm{~s}^{-1}\) in a pipe of radius 2 cm, then the flow is
(The coefficient of viscosity of water is \(10^{-3} \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1}\) and density of water is \(\left.10^3 \mathrm{~kg} \mathrm{~m}^{-3}\right)\).

The speed of a stationary wave represented by the equation \(y=0.7 \sin \left(\frac{7 \pi}{4} x\right) \cos (350 \pi t)\) is
(In the given equation \(x\) and \(y\) are in metre and \(t\) is in second)

Identify the increasing order of the angular velocities of the following
1. earth rotating about its own axis
2. hour's hand of a clock
3. second's hand of a clock
4. flywheel of radius \(2 \mathrm{~m}\) making \(300\mathrm{rpm}\)

Suppose the axes are to be rotated through an angle \(\theta\) so as to remove the \(x y\) form from the equation \(3 x^2+2 \sqrt{3} x y\) \(+y^2=0\). Then in the new coordinate system the equation \(x^2+y^2+2 x y=2\) is transformed to

Match List-I with List-II
\(\begin{array}{|c|l|l|l|}\hline & \text{List-I (Reaction)} & & \text{List-II (Enzyme)} \\ \hline \text{A.} & \begin{array}{l} \text{Hydrolysis of starch to} \\ \text{maltose}\end{array} & \text{I} & \text{Diastase} \\ \hline \text{B.} & \begin{array}{l} \text{Conversion of proteins} \\ \text{to peptides} \end{array} & \text{II} & \text{Pepsin} \\ \hline \text{C.} & \begin{array}{l} \text{Hydrolysis of sucrose} \\ \text{to glucose and fructose}\end{array} & \text{III} & \text{Invertase} \\ \hline \text{D.} & \text{Glucose to ethanol} & \text{IV} & \text{Zymase} \\ \hline\end{array}\)
The correct answer is

The magnetic susceptibility of the material of a rod is 499. Permeability of vaccum is \(4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}\). Absolute permeability of the material of the rod in \(\mathrm{H} / \mathrm{m}\) is:

If \(\int \frac{d x}{(x \tan x+1)^2}=f(x)+c\), then \(\lim _{x \rightarrow \frac{\pi}{2}} f(x)=\)

Intersection of two perpendicular tangents to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) lies on the circle \(x^2+y^2=\ldots \ldots \ldots\)

Which of the following reactions of \(\mathrm{KMnO}_4\) occurs in acidic medium?