Which of the following combinations has the dimension of electrical resistance ($$\varepsilon_0$$ is the permittivity of vacuum and $$\mu_0$$ is the permeability of vacuum)?
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Which of the following combinations has the dimension of electrical resistance ($$\varepsilon_0$$ is the permittivity of vacuum and $$\mu_0$$ is the permeability of vacuum)?
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The trajectory of a projectile near the surface of the earth is given as $$y = 2x - 9x^2$$. If it were launched at an angle $$\theta_0$$ with speed $$v_0$$ then g = 10 m s$$^{-2}$$:
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A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t$$_1$$ and t$$_2$$ are the values of the time taken by it to hit the target in two possible ways, the product t$$_1$$t$$_2$$ is:
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A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s$$^{-1}$$ with respect to the man. The speed of the man with respect to the surface is:
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A person of mass M is sitting on a swing of length L and swinging with an angular amplitude $$\theta_0$$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $$l$$ ($$l << L$$), is close to:
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A uniform rod of length $$l$$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\frac{\sigma_0}{r}$$, then the radius of gyration of the disc about its axis passing through the center is
At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m. The value of M is close to:
(Coefficient of linear expansion of brass are $$10^{-5}$$/°C and Young's modulus of brass is $$10^{11}$$ N/m$$^2$$, respectively; g = 10 m s$$^{-2}$$)
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When M$$_1$$ gram of ice at -10°C (specific heat = 0.5 cal g$$^{-1}$$ °C$$^{-1}$$) is added to M$$_2$$ gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g$$^{-1}$$ is:
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A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:
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Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? R = 8.3 J/mol K
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A submarine A travelling at 18 km hr$$^{-1}$$ is being chased along the line of its velocity by another submarine B travelling at 27 km hr$$^{-1}$$. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency v. The value of v is close to (Speed of sound in water 1500 m s$$^{-1}$$)
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A progressive wave travelling along the positive x-direction is represented by $$y(x, t) = A\sin(kx - \omega t + \phi)$$. Its snapshot at t = 0 is given in the figure.
For this wave, the phase $$\phi$$ is:
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Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre a dipole $$\vec{p}$$ is placed as shown then:
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A Point dipole $$\vec{p} = -p_0\hat{x}$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Taken V = 0 at infinity)
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Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K$$_1$$, K$$_2$$ and K$$_3$$. The first capacitor is filled as shown in figure I, and the second one is filled as shown in figure II.
If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E$$_1$$ refers to capacitor I and E$$_2$$ to capacitor II):
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To verify Ohm's law, a student connects the voltmeter across the battery as shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained.
If V$$_0$$ is almost zero, identify the correct statement:
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A galvanometer of resistance 100 Ω has 50 divisions on its scale and has sensitivity of 20 μA/division. It is to be converted to voltmeter with three ranges, of 0 - 2 V, 0 - 10 V and 0 - 20 V. The appropriate circuit to do so is:
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The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:
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A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45° and 40 times per minute where the dip is 30°. If B$$_1$$ and B$$_2$$ are the net magnetic fields due to the earth at the two places respectively, then the ratio B$$_1$$/B$$_2$$ is approximately equal to
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A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $$40\pi$$ rad s$$^{-1}$$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $$3.8 \times 10^{-9}$$ T, then the charge carried by the ring is close to $$\mu_0 = 4\pi \times 10^{-7}$$ N/A$$^2$$.
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The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards the right with a constant speed of 1 cm s$$^{-1}$$. At some instant, a part of L is in a uniform magnetic field of 1T perpendicular to the plane of the loop. If the resistance of L is 1.7 Ω, the current in the loop at that instant will be close to:
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An electromagnetic wave is represented by the electric field $$\vec{E} = E_0\hat{n}\sin(\omega t + 6y - 8z)$$. Taking unit vectors in x, y and z directions to be $$\hat{i}, \hat{j}, \hat{k}$$, the direction of propagation $$\hat{s}$$, is:
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A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33)
The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength 5000 Å is used, the minimum separation between two points, to be seen as distinct, will be:
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In a double slit experiment, when a thin film of thickness t having refractive index μ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($$\lambda$$ is the wavelength of the light used):
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The stopping potential V$$_0$$ (in volt) as a function of frequency ($$\nu$$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be:
(Given: Planck's constant h = $$6.63 \times 10^{-34}$$ J s, electron charge (e) = $$1.6 \times 10^{-19}$$ C)
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An excited He$$^+$$ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm in making a transition to the ground state. The quantum number n, corresponding to its initial excited state is
(for a photon of wavelength $$\lambda$$, energy E = $$\frac{1240 \text{ eV}}{\lambda(\text{in nm})}$$)
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The truth table for the circuit given in the figure is:
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The transfer characteristic curve of a transistor, having input and output resistance 100 Ω and 100 kΩ respectively, is shown in the figure. The voltage and power gain, are respectively:
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5 moles of AB$$_2$$ weigh $$125 \times 10^{-3}$$ kg and 10 moles of A$$_2$$B$$_2$$ weigh $$300 \times 10^{-3}$$ kg. The molar mass of A (M$$_A$$) in kg mol$$^{-1}$$ are:
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The electrons are more likely to be found:
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The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are:
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The correct statement among the following is:
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An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:
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Enthalpy of sublimation of iodine is 24 cal g$$^{-1}$$ at 200°C. If specific heat of I$$_2$$(s) and I$$_2$$(vap) are 0.055 and 0.031 cal g$$^{-1}$$ K$$^{-1}$$ respectively, then enthalpy of sublimation of iodine at 250°C in cal g$$^{-1}$$ is:
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What is the molar solubility of Al(OH)$$_3$$ in 0.2 M NaOH solution? Given that, solubility product of Al(OH)$$_3$$ = $$2.4 \times 10^{-24}$$:
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An example of a disproportionation reaction is
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Given:
Co$$^{3+}$$ + e$$^-$$ $$\to$$ Co$$^{2+}$$; E° = +1.81V
Pb$$^{3+}$$ + 2e$$^-$$ $$\to$$ Pb$$^{2+}$$; E° = +1.67V
Ce$$^{4+}$$ + e$$^-$$ $$\to$$ Ce$$^{3+}$$; E° = +1.61V
Bi$$^{3+}$$ + 3e$$^-$$ $$\to$$ Bi; E° = +0.20V
Oxidizing power of the species will increase in the order:
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The correct sequence of thermal stability of the following carbonates is:
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The basic structural unit of feldspar, zeolites, mica, and asbestos is:
The increasing order of the pK$$_b$$ of the following compound is:
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The major product(s) obtained in the following reaction is/are:
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The major product of the following addition reaction is
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But-2-ene on reaction with alkaline KMnO$$_4$$ at elevated temperature followed by acidification will give:
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The correct set of species responsible for the photochemical smog is:
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An element has a face-centered cubic fcc structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is
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The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol kg$$^{-1}$$) of the aqueous solution is:
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In the following reaction; xA $$\to$$ yB
$$\log_{10}\left(-\frac{dA}{dt}\right) = \log_{10}\left(-\frac{dB}{dt}\right) + 0.3010$$
'A' and 'B' respectively can be:
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Peptization is a:
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The idea of froth flotation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:
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The metal that gives hydrogen gas upon treatment with both the acid as well as the base is
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The complex ion that will lose its crystal field stabilization energy upon oxidation of metal to +3 state is:
(Phen = phenanthroline, ignore pairing energy)
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Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).
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The major products of the following reaction are:
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The major product of the following reaction:
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Which of the following is a thermosetting polymer?
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An organic compound 'A' is oxidized with Na$$_2$$O$$_2$$ followed by boiling with HNO$$_3$$. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is:
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Glucose and Galactose are having identical configuration in all the positions except position.
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Which of the following statements is not true about RNA?
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If $$\alpha$$ and $$\beta$$ are the roots of the equation $$375x^2 - 25x - 2 = 0$$, then $$\lim_{n \to \infty} \sum_{r=1}^{n} \alpha^r + \lim_{n \to \infty} \sum_{r=1}^{n} \beta^r$$ is equal to:
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The equation $$|z - i| = |z - 1|$$, $$i = \sqrt{-1}$$, represents:
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The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:
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If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:
Let S$$_n$$ denote the sum of the first n terms of an A.P. If S$$_4$$ = 16 and S$$_6$$ = -48, then S$$_{10}$$ is equal to:
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The coefficient of $$x^{18}$$ in the product $$(1 + x)(1 - x)^{10}(1 + x + x^2)^9$$ is
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The equation $$y=\sin x\sin\left(x+2\right)-\sin^2(x+1)$$ represents a straight line lying in:
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The number of solutions of the equation $$1 + \sin^4 x = \cos^2 3x$$, $$x \in \left[-\frac{5\pi}{2}, \frac{5\pi}{2}\right]$$ is:
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If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is:
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If the normal to the ellipse $$3x^2 + 4y^2 = 12$$ at a point P on it is parallel to the line, $$2x + y = 4$$ and the tangent to the ellipse at P passes through Q(4, 4) then PQ is equal to:
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Let P be the point of intersection of the common tangents to the parabola $$y^2 = 12x$$ and the hyperbola $$8x^2 - y^2 = 8$$. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio:
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If the truth value of the statement $$p \to (\sim q \vee r)$$ is false F, then the truth values of the statements p, q, r are respectively
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If the data $$x_1, x_2, \ldots, x_{10}$$ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2000, then the standard deviation of this data is:
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If $$B = \begin{pmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{pmatrix}$$ is the inverse of a 3$$\times$$3 matrix A, then the sum of all values of $$\alpha$$ for which det(A) + 1 = 0, is:
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If A is a symmetric matrix and B is skew-symmetric matrix such that $$A + B = \begin{pmatrix} 2 & 3 \\ 5 & -1 \end{pmatrix}$$, then AB is equal to:
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The value of $$\sin^{-1}\frac{12}{13} - \sin^{-1}\frac{3}{5}$$ is equal to:
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For $$x \in R$$, Let [x] denotes the greatest integer $$\leq x$$, then the sum of the series $$\left[-\frac{1}{3}\right] + \left[-\frac{1}{3} - \frac{1}{100}\right] + \left[-\frac{1}{3} - \frac{2}{100}\right] + \ldots + \left[-\frac{1}{3} - \frac{99}{100}\right]$$ is
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For $$x \in \left(0, \frac{3}{2}\right)$$, let $$f(x) = \sqrt{x}$$, $$g(x) = \tan x$$ and $$h(x) = \frac{1 - x^2}{1 + x^2}$$. If $$\phi(x) = ((h \circ f) \circ g)(x)$$, then $$\phi\left(\frac{\pi}{3}\right)$$ is equal to:
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If $$e^y + xy = e$$, the ordered pair $$\left(\frac{dy}{dx}, \frac{d^2y}{dx^2}\right)$$ at x = 0 is equal to
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A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is:
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If m is the minimum value of k for which the function $$f(x) = x\sqrt{kx - x^2}$$ is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to:
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The integral $$\int \frac{2x^3 - 1}{x^4 + x} dx$$, is equal to
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Let $$f: R \to R$$ be a continuous and differentiable function such that $$f(2) = 6$$ and $$f'(2) = \frac{1}{48}$$. If $$\int_6^{f(x)}4t^3dt=\left(x-2\right)g(x)$$, then $$\lim_{x \to 2} g(x)$$ is equal to
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If $$\int_0^{\pi/2} \frac{\cot x}{\cot x + \text{cosec} x} dx = m(\pi + n)$$, then mn is equal to
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If the area (in sq. units) of the region $$\{(x, y): y^2 \leq 4x, x + y \leq 1, x \geq 0, y \geq 0\}$$ is $$a\sqrt{2} + b$$, then a - b is
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Consider the differential equation, $$y^2 dx + \left(x - \frac{1}{y}\right) dy = 0$$. If value of y is 1 when x = 1, then the value of x for which y = 2, is
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If the volume of parallelepiped formed by the vectors $$\hat{i} + \lambda\hat{j} + \hat{k}$$, $$\hat{j} + \lambda\hat{k}$$ and $$\lambda\hat{i} + \hat{k}$$ is minimum, then $$\lambda$$ is
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Let $$\vec{a} = 3\hat{i} + 2\hat{j} + 2\hat{k}$$ and $$\vec{b} = \hat{i} + 2\hat{j} - 2\hat{k}$$ be two vectors. If a vector perpendicular to both the vectors $$\vec{a} + \vec{b}$$ and $$\vec{a} - \vec{b}$$ has the magnitude 12 then one such vector is:
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If the line $$\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$$ intersects the plane $$2x + 3y - z + 13 = 0$$ at a point P and the plane $$3x + y + 4z = 16$$ at a point Q, then PQ is equal to
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Let a random variable X has a binomial distribution with mean 8 and variance 4. If $$P(X \leq 2) = \frac{k}{2^{16}}$$, then the value of k is equal to
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