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Which of the following statements is false?

A) In a balanced Wheatstone bridge, if the cell and the galvanometer are exchanged, the null point is disturbed

B) A rheostat can be used as a potential divider

C) Kirchhoff 's second law represents energy conservation

D) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.

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

A) 7.8 nm

B) 9.75 nm

C) 15.6 nm

D) 1.56 nm

An external pressure P is applied on a cube at 0° C . so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

A) $\frac{P}{\alpha K}$

B) $\frac{3\alpha}{P K}$

C) $3PK\alpha$

D) $\frac{P}{3\alpha K}$

The temperature of an open room of volume 30 m³ increases from 17° C to 27° C due to the sunshine . The atmosphere pressure in the room remains 1× 10⁵ 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

A) $1.38\times 10^{23}$

B) $2.5\times 10^{25}$

C) $-2.5\times 10^{25}$

D) $-1.61\times 10^{23}$

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that this density remains the same, the stress in the leg will change by a factor of

A) $\frac{1}{9}$

B) 81

C) $\frac{1}{81}$

D) 9

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.

A) 1 and 4

B) 2 and 4

C) 1 and 3

D) 2 and 3

A water sample has ppm level concentration of following anions $F^{-} =10 $: $SO_{4}^{2-} =100 $ : $NO_{3}^{-}=50$ the anion /anions that, make/makes the water sample unsuitable for drinking is/are

A) Only $NO_{3}^{-}$

B) Both $SO_{4}^{2-} and NO_{3}^{-}$

C) only $F^{-} $

D) Only $SO_{4}^{2-} $

1 g of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01186 mole of CO₂ . The molar mass M₂CO₃ in g mol^-1 is

A) 1186

B) 84.3

C) 118.6

D) 11.86

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

A) Cr

B) $Mn^{2+}$

C) $Cr^{3+}$

D) $Cl^{-}$

If 20 m of wire is available for fencing off a flower -bed in the form of a circular sector, then the maximum area ( in sq m) of the flower-bed is

A) 12.5

B) 10

C) 25

D) 30

The area ( in sq units) of the region {(x,y):x ≥ 0, x +y ≤ 3, x² ≤ 4y and y ≤ 1+√x } is

A) $ \frac{59}{12}$

B) $ \frac{3}{2}$

C) $ \frac{7}{3}$

D) $ \frac{5}{2}$

If $(2+sin x)\frac{\text{d}y}{\text{d}x}+(y+1)\cos x=0$ and y(0)=1, then $y(\frac{\pi}{2})$ is equal to

A) $\frac{1}{3}$

B) $-\frac{2}{3}$

C) $-\frac{1}{3}$

D) $\frac{4}{3}$

If a hyperbola passes through the point $P(\sqrt{2},\sqrt{3})$ and has foci at (± 2,0), then the tangent to this hyperbola at P also passes through the point

A) $(3\sqrt{2},2\sqrt{3})$

B) $(2\sqrt{2},3\sqrt{3})$

C) $(-\sqrt{3},\sqrt{2})$

D) $(-\sqrt{2},-\sqrt{3})$

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

A) invertible

B) injective but not surjective

C) surjective but not injective

D) neither injective nor surjective

The value of $(^{21}C_{1}-^{10}C_{1})+(^{21}C_{2}-^{10}C_{2})+(^{21}C_{3}-^{10}C_{3})+.....+(^{21}C_{10}-^{10}C_{10})$ is

A) $2^{21}-2^{11}$

B) $2^{21}-2^{10}$

C) $2^{20}-2^{9}$

D) $2^{20}-2^{10}$

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