Some energy levels of molecule are shown in the figure. The ratio of the wavelengths r= λ_{1}/λ_{2} is given by

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1

Some energy levels of molecule are shown in the figure. The ratio of the wavelengths r= λ_{1}/λ_{2} is given by

2

A body of mass m = 10^{-2} kg is moving in a medium and experiences a frictional force F= -kv_{2} . Its initial is v_{0} =10 ms^{-1 }. If , after 10 s. its energy is $\frac{1}{8}mv_{0}^{2}$ , the value of k will be

3

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be

4

In Young's double-slit experiment, slits are separated by 0.5 mm and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen . The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is

5

An electric dipole has a fixed dipole moment p, which makes angle θ with respect to X-axis. When subjected to an electric field $E_{1}=E\hat{i}$ , it experiences a torque $T_{1}=\tau\hat{k}$ . When subjected to another electric field $E_{2}=\sqrt{3}E_{1}\hat{j}$ , it experiences a torque T_{2} = -T_{1} . The angle θ is

6

The temperature of an open room of volume 30 m^{3 } increases from 17° C to 27° C due to the sunshine . The atmosphere pressure in the room remains 1× 10^{5} Pa. If n_{i} and n_{f} are the number of molecules in the room before and after heating , then n_{f } -n_{i} will be

7

A time-dependent force F =6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 s will be

8

ΔU is equal to

9

Two reactions R_{1} and R_{2} have identical pre-exponential factors. The activation energy of R_{1} exceeds that of R_{2} by 10 kj mol^{-1} . If k_{1} and k_{2} are rate constants for reactions R_{1} and R2,_{ }respectively at 300 K. then ln $(\frac{k_{2}}{k_{1}})$ is equal to (R=8.314 J mol^{-1} K^{-1})

10

The Tyndall effect is observed only when the following conditions are satisfied

1. The diameter of the dispersed particles is much smaller than the wavelength of the light used.

2. The diameter of the dispersed particle is not much smaller than the wavelength of the light used.

3. The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude.

4. The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.

11

Given ,$E^{0}_{Cl_{2}/Cl^{-}}$=1.36 V

$E^{0}_{Cr^{3+}/Cr}=-0.74 V$

$E^{0}_{Cr_{2}O^{2-}_{7}/Cr^{3+}}=1.33 V$

$E^{0}_{MnO^{-}_{4}/Mn^{2+}}=1.51 V$

Among the following , the strongest reducing agent is

12

Let a vertical tower AB have its end A on the level ground. Let C be the mid-pont of AB and P be a point on the ground such that AP=2AB. If $\angle$ BPC= β , then tanβ is equal to

13

The function $f:R\rightarrow [-\frac{1}{2},\frac{1}{2}]$ defined as $f(x)=\frac{x}{1+x^{2}} is$

14

The normal to the curve y(x-2) (x-3)=x+6 at the point, where the curve intersects the Y-axis passes through the point

15

For a positive integer n, if the quadratic equation, $x(x+1)+(x+1)(x+2)+.....+(x+\overline{n-1}) (x+n)=10n$ has two consecutive integral solutions, then n is equal to

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