List of top Questions asked in MET- 2010

Choose the alternative which best expresses the meaning of the word given in capital letters.
MOSQUERADE

The angle of minimum deviation \( \delta_m \) for an equilateral glass prism is \( 30^\circ \). The refractive index of the prism is

1 \( \text{cm}^3 \) of water at its boiling point absorbs 540 cal of heat to become steam with a volume of 1671 \( \text{cm}^3 \). If the atmospheric pressure \( = 1.013 \times 10^5 \, \text{N/m}^2 \) and the mechanical equivalent of heat \( = 4.19 \, \text{J/cal} \), the energy spent in this process in overcoming intermolecular forces is

In the reaction \( {}_7N^{14} + \alpha \longrightarrow {}_8X^{17} + {}_1p^1 \), identify \( X \).

In Young's double slit experiment, slit separation is 0.6 mm and the separation between slit and screen is 1.2 m. The angular width is (the wavelength of light used is 4800 \( \dot{A} \))

X-ray of wavelength \( \lambda = 2 \, \dot{A} \) is emitted from the metal target. The potential difference applied across the cathode and the metal target is

The standard emf of a cell involving one electron change is found to be 0.591 V at \( 25^\circ C \). The equilibrium constant of the reaction is ________. (\( F = 96,500 \, \text{C/mol} \))

On igniting \( Fe_2O_3 \) at \( 1400^\circ C \), the product obtained is ________.

\( C_6H_6 \xrightarrow{350 \, K, \, H_2SO_4} A \xrightarrow{\text{Alkali Fusion}} B \xrightarrow{\text{Br}_2/\text{H}_2O} C \). In the above sequence, C is ________.

The domain of the function \( f(x) = \frac{\sqrt{9 - x^2}}{\sin^{-1}(3 - x)} \) is ________.

The term independent of \( x \) in the expansion of \( \left[ \sqrt{\frac{x}{3}} + \sqrt{\frac{3}{2}} x^2 \right]^{10} \) is ________.

In a \( \Delta ABC \), \( \angle B = 90^\circ \), then \( \tan^2\left(\frac{A}{2}\right) \) is

In a trapezoid of the vector \( \vec{BC} = \lambda \vec{AD} \). We will, then find that \( \vec{P} = \vec{AC} + \vec{BD} \) is collinear with \( \vec{AD} \). If \( \vec{P} = \mu \vec{AD} \), then

If \( P(\vec{p}) \), \( Q(\vec{q}) \), \( R(\vec{r}) \), and \( S(\vec{s}) \) are four points such that \( 3\vec{p} + 8\vec{q} = 6\vec{r} + 5\vec{s} \), then the lines PQ and RS are

Let \( \vec{a} = 2\hat{i} + \hat{j} - 2\hat{k} \) and \( \vec{b} = \hat{i} + \hat{j} \), if \( \vec{c} \) is a vector such that \( \vec{a} \cdot \vec{c} = |\vec{c}| \), \( |\vec{c} - \vec{a}| = 2\sqrt{2} \), and the angle between \( \vec{a} \times \vec{b} \) and \( \vec{c} \) is \( 30^\circ \), then \( |(\vec{a} \times \vec{b}) \times \vec{c}| \) is equal to

Consider a tetrahedron with faces \( F_1, F_2, F_3, F_4 \). Let \( \vec{v_1}, \vec{v_2}, \vec{v_3}, \vec{v_4} \) be area vectors perpendicular to these faces in the outward direction, then \( |\vec{v_1} + \vec{v_2} + \vec{v_3} + \vec{v_4}| \) equals

If \( V \) is the volume of the parallelepiped with edges \( \vec{a}, \vec{b}, \vec{c} \), then the volume of the parallelepiped with edges \( \vec{\alpha}, \vec{\beta}, \vec{\gamma} \) (defined by dot products) is

Define the length of \( a\hat{i} + b\hat{j} + c\hat{k} \) as \( |a| + |b| + |c| \). This definition coincides with the usual definition if and only if

If \( \vec{u} = \hat{i} + \hat{j}, \vec{v} = \hat{i} - \hat{j}, \vec{w} = \hat{i} + 2\hat{j} + 3\hat{k} \) and \( \hat{n} \) is a unit vector such that \( \vec{u} \cdot \hat{n} = 0 \) and \( \vec{v} \cdot \hat{n} = 0 \), then \( |\vec{w} \cdot \hat{n}| \) is

\( \lim_{x \to 0} \frac{\sqrt{1 - \cos(2x)}}{\sqrt{2} \cdot x} \) is

Radius of the circle \( \vec{r}^2 + \vec{r} \cdot (2\hat{i} - 2\hat{j} - 4\hat{k}) - 19 = 0, \vec{r} \cdot (\hat{i} - 2\hat{j} + 2\hat{k}) + 8 = 0 \) is

If \( x^y = e^{x - y} \), then \( \frac{dy}{dx} \) is equal to