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Match List I with List II
| List I | List II | ||
|---|---|---|---|
| A. | Torque | I. | $$M L^{-2} T^{-2}$$ |
| B. | Stress | II. | $$M L^2 T^{-2}$$ |
| C. | Pressure gradient | III. | $$M L^{-1} T^{-1}$$ |
| D. | Coefficient of viscosity | IV. | $$M L^{-1} T^{-2}$$ |
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Given below are two statements:
Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given statements, choose the correct answer from the options given below.
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The trajectory of projectile, projected from the ground is given by $$y = x - \frac{x^2}{20}$$. Where $$x$$ and $$y$$ are measured in meter. The maximum height attained by the projectile will be.
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A bullet of mass 0.1 kg moving horizontally with speed 400 m s$$^{-1}$$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is
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The orbital angular momentum of a satellite is $$\mathbf{L}$$, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
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The acceleration due to gravity at height $$h$$ above the earth if $$h \ll R$$ (Radius of earth) is given by
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A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying load is 250 cm$$^2$$. The maximum pressure the smaller piston would have to bear is [Assume $$g = 10$$ m s$$^{-2}$$]
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Work done by a Carnot engine operating between temperatures 127$$^\circ$$C and 27$$^\circ$$C is 2 kJ. The amount of heat transferred to the engine by the reservoir is:
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The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27$$^\circ$$C is
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For particle $$P$$ revolving round the centre $$O$$ with radius of circular path $$r$$ and regular velocity $$\omega$$, as shown in below figure, the projection of $$OP$$ on the $$x$$-axis at time $$t$$ is
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Electric potential at a point $$P$$ due to a point charge of $$5 \times 10^{-9}$$ C is 50 V. The distance of $$P$$ from the point charge is:
(Assume, $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$)
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The equivalent resistance between A and B as shown in figure is:
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Electromagnets are made of soft iron.
Reason R: Soft iron has high permeability and low retentivity.
In the light of above statements, choose the most appropriate answer from the options given below.
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An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T, when move with a velocity of:
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The waves emitted when a metal target is bombarded with high energy electrons are
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The width of fringe is 2 mm on the screen in a double slit experiment for the light of wavelength of 400 nm. The width of the fringe for the light of wavelength 600 nm will be:
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In photoelectric effect
A. The photocurrent is proportional to the intensity of the incident radiation.
B. Maximum kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
C. Max K.E. with which photoelectrons are emitted depends on the frequency of incident light.
D. The emission of photoelectrons require a minimum threshold intensity of incident radiation.
E. Max K.E. of the photoelectrons is independent of the frequency of the incident light.
Choose the correct option from the options given below:
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A radio active material is reduced to $$\frac{1}{8}$$ of its original amount in 3 days. If $$8 \times 10^{-3}$$ kg of the material is left after 5 days the initial amount of the material is
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For a given transistor amplifier circuit in CE configuration $$V_{CC} = 1$$ V, $$R_C = 1$$ k$$\Omega$$, $$R_b = 100$$ k$$\Omega$$ and $$\beta = 100$$. Value of base current $$I_b$$ is
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The power radiated from a linear antenna of length $$l$$ is proportional to (Given, $$\lambda$$ = Wavelength of wave):
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A body of mass 5 kg is moving with a momentum of 10 kg m s$$^{-1}$$. Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _______ J.
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A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m s$$^{-1}$$ (as shown in figure). Maximum height with respect to the initial position covered by it will be _______ cm.
(take, $$g = 10$$ m s$$^{-2}$$)
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A steel rod of length 1 m and cross-sectional area $$10^{-4}$$ m$$^2$$ is heated from 0$$^\circ$$C to 200$$^\circ$$C without being allowed to extend or bend. The compressive tension produced in the rod is _______ $$\times 10^4$$ N. (Given Young's modulus of steel $$= 2 \times 10^{11}$$ N m$$^{-2}$$, coefficient of linear expansion $$= 10^{-5}$$ K$$^{-1}$$)
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A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental of 180 Hz will be _______ cm.
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A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is _______ $$\mu$$J.
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The number density of free electrons in copper is nearly $$8 \times 10^{28}$$ m$$^{-3}$$. A copper wire has its area of cross-section $$= 2 \times 10^{-6}$$ m$$^2$$ and is carrying a current of 3.2 A. The drift speed of the electrons is _______ $$\times 10^{-6}$$ m s$$^{-1}$$.
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The ratio of magnetic field at the centre of a current carrying coil of radius $$r$$ to the magnetic field at distance $$r$$ from the centre of coil on its axis is $$\sqrt{x}$$ : 1. The value of $$x$$ is _____.
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A series combination of resistor of resistance 100 $$\Omega$$, inductor of inductance 1 H and capacitor of capacitance 6.25 $$\mu$$F is connected to an ac source. The quality factor of the circuit will be _____.
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Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is _______ cm.
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The ratio of wavelength of spectral lines $$H_\alpha$$ and $$H_\beta$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _____.
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Which of the following have same number of significant figures?
(A) 0.00253
(B) 1.0003
(C) 15.0
(D) 163
Choose the correct answer from the options given below
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Henry Moseley studied characteristic X-ray spectra of elements. The graph which represents his observation correctly is
Given $$\nu$$ = Frequency of X-ray emitted, $$Z$$ = Atomic number
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The number of atomic orbitals from the following having 5 radial nodes is
7s, 7p, 6s, 8p, 8d
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The number of species from the following carrying a single lone pair on central atom Xenon is
$$XeF_5^+$$, $$XeO_3$$, $$XeO_2F_2$$, $$XeF_5^-$$, $$XeO_3F_2$$, $$XeOF_4$$, $$XeF_4$$
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Arrange the following gases in increasing order of van der Waals constant 'a'
(A) Ar
(B) CH$$_4$$
(C) H$$_2$$O
(D) C$$_6$$H$$_6$$
Choose the correct option from the following.
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The incorrect statements from the following is:
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. $$E^\circ_{cell}$$ is dependent on the pressure.
C. $$\frac{dE_{cell}}{dT} = \frac{\Delta_r S}{nF}$$
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.
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Given below are two statements:
Statement-I: Methyl orange is a weak acid.
Statement-II: The benzenoid form of methyl orange is more intense/deeply coloured than the quinonoid form.
In the light of the above statement, choose the most appropriate answer from the options given below:
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Given below are two statements:
Statement I: In redox titration, the indicators used are sensitive to change in pH of the solution.
Statement II: In acid-base titration, the indicators used are sensitive to change in oxidation potential.
In the light of the above statements, choose the most appropriate answer from the options given below
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Which of the following can reduce decomposition of H$$_2$$O$$_2$$ on exposure to light
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For a good quality cement, the ratio of lime to the total of the oxides of Si, Al and Fe should be as close as to
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Sodium is about 30 times as abundant as potassium in the oceans.
Reason R: Potassium is bigger in size than sodium.
In the light of the above statements, choose the correct answer from the options given below
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The descending order of acidity for the following carboxylic acid is-
(A) CH$$_3$$COOH
(B) F$$_3$$C-COOH
(C) ClCH$$_2$$-COOH
(D) FCH$$_2$$-COOH
(E) BrCH$$_2$$-COOH
Choose the correct answer from the options given below:
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The correct IUPAC nomenclature for the following compound is:
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Which of these reactions is not a part of breakdown of ozone in stratosphere?
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The correct reaction profile diagram for a positive catalyst reaction.
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The statement/s which are true about antagonists from the following is/are:
A. They bind to the receptor site.
B. Get transferred inside the cell for their action.
C. Inhibit the natural communication of the body.
D. Mimic the natural messenger.
Choose the correct option from the options given below:
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In Hall-Heroult process, the following is used for reducing Al$$_2$$O$$_3$$:-
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Match List-I with List-II
| LIST-I Coordination Complex | LIST-II Number of unpaired electrons | ||
|---|---|---|---|
| A. | $$[Cr(CN)_6]^{3-}$$ | I. | 0 |
| B. | $$[Fe(H_2O)_6]^{2+}$$ | II. | 3 |
| C. | $$[Co(NH_3)_6]^{3+}$$ | III. | 2 |
| D. | $$[Ni(NH_3)_6]^{2+}$$ | IV. | 4 |
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The correct order of reactivity of following haloarenes towards nucleophilic substitution with aqueous NaOH is:
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A compound 'X' when treated with phthalic anhydride in presence of concentrated H$$_2$$SO$$_4$$ yields 'Y'. 'Y' is used as an acid/base indicator. 'X' and 'Y' are respectively
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For complete combustion of ethene,
$$C_2H_4(g) + 3O_2(g) \to 2CO_2(g) + 2H_2O(l)$$
the amount of heat produced as measured in bomb calorimeter is 1406 kJ mol$$^{-1}$$ at 300 K. The minimum value of T$$\Delta$$S needed to reach equilibrium is ($$-$$) kJ. (Nearest integer)
Given: R = 8.3 J K$$^{-1}$$ mol$$^{-1}$$
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The solubility product of BaSO$$_4$$ is $$1 \times 10^{-10}$$ at 298 K. The solubility of BaSO$$_4$$ in 0.1 M K$$_2$$SO$$_4$$(aq) solution is _______ $$\times 10^{-9}$$ g L$$^{-1}$$ (nearest integer).
Given: Molar mass of BaSO$$_4$$ is 233 g mol$$^{-1}$$
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If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio 2:1 and their enthalpy of vaporizations are in the ratio 1:2, then the boiling point elevation constant of X is m times the boiling point elevation constant of Y. The value of m is (nearest integer).
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Coagulating value of the electrolytes AlCl$$_3$$ and NaCl for As$$_2$$S$$_3$$ are 0.09 and 50.04 respectively. The coagulating power of AlCl$$_3$$ is x times the coagulating power of NaCl. The value of x is _____.
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The ratio of sigma and $$\pi$$ bonds present in pyrophosphoric acid is _____.
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The observed magnetic moment of the complex $$[Mn(NCS)_6]^{x-}$$ is 6.06 BM. The numerical value of x is _____.
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The sum of oxidation state of the metals in Fe(CO)$$_5$$, VO$$^{2+}$$ and WO$$_3$$ is _____.
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Major product 'P' formed in the following reaction is:
The product (P) formed from the following multistep reaction is:
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Match List I with List II
| List I Natural amino acid | List II One Letter Code | ||
|---|---|---|---|
| (A) | Glutamic acid | (I) | Q |
| (B) | Glutamine | (II) | W |
| (C) | Tyrosine | (III) | E |
| (D) | Tryptophan | (IV) | Y |
Choose the correct answer from the options given below:
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Let $$m$$ and $$n$$ be the numbers of real roots of the quadratic equations $$x^2 - 12x + [x] + 31 = 0$$ and $$x^2 - 5|x + 2| - 4 = 0$$ respectively, where $$[x]$$ denotes the greatest integer $$\leq x$$. Then $$m^2 + mn + n^2$$ is equal to
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Let $$A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}$$. Then the sum of the elements in $$A$$ is
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If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is $$(6!)k$$ then $$k$$ is equal to
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Let $$a_n$$ be $$n^{th}$$ term of the series $$5 + 8 + 14 + 23 + 35 + 50 + \ldots$$ and $$S_n = \sum_{k=1}^{n} a_k$$. Then $$S_{30} - a_{40}$$ is equal to
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The absolute difference of the coefficients of $$x^{10}$$ and $$x^7$$ in the expansion of $$\left(2x^2 + \frac{1}{2x}\right)^{11}$$ is equal to
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$$25^{190} - 19^{190} - 8^{190} + 2^{190}$$ is divisible by
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The value of $$36(4\cos^2 9^\circ - 1)(4\cos^2 27^\circ - 1)(4\cos^2 81^\circ - 1)(4\cos^2 243^\circ - 1)$$ is
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Let $$A(0, 1)$$, $$B(1, 1)$$ and $$C(1, 0)$$ be the mid-points of the sides of a triangle with incentre at the point $$D$$. If the focus of the parabola $$y^2 = 4ax$$ passing through $$D$$ is $$\left(\alpha + \beta\sqrt{2}, 0\right)$$, where $$\alpha$$ and $$\beta$$ are rational numbers, then $$\frac{\alpha}{\beta^2}$$ is equal to
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Let $$O$$ be the origin and $$OP$$ and $$OQ$$ be the tangents to the circle $$x^2 + y^2 - 6x + 4y + 8 = 0$$ at the points $$P$$ and $$Q$$ on it. If the circumcircle of the triangle $$OPQ$$ passes through the point $$\left(\alpha, \frac{1}{2}\right)$$, then a value of $$\alpha$$ is
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If $$\alpha > \beta > 0$$ are the roots of the equation $$ax^2 + bx + 1 = 0$$, and
$$\lim_{x \to \frac{1}{\alpha}} \left(\frac{1 - \cos(x^2 + bx + a)}{2(1 - \alpha x)^2}\right)^{\frac{1}{2}} = \frac{1}{k}\left(\frac{1}{\beta} - \frac{1}{\alpha}\right)$$, then $$k$$ is equal to
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The negation of $$(p \wedge (-q)) \vee (-p)$$ is equivalent to
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Let the mean and variance of 12 observations be $$\frac{9}{2}$$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $$\frac{m}{n}$$, where $$m$$ and $$n$$ are coprime, then $$m + n$$ is equal to
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Let $$A = \{1, 2, 3, 4, 5, 6, 7\}$$. Then the relation $$R = \{(x, y) \in A \times A : x + y = 7\}$$ is
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If $$A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}$$, $$A^{-1} = \alpha A + \beta I$$ and $$\alpha + \beta = -2$$, then $$4\alpha^2 + \beta^2 + \lambda^2$$ is equal to:
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Let $$S$$ be the set of all values of $$\theta \in [-\pi, \pi]$$ for which the system of linear equations
$$x + y + \sqrt{3}z = 0$$
$$-x + (\tan\theta)y + \sqrt{7}z = 0$$
$$x + y + (\tan\theta)z = 0$$
has non-trivial solution. Then $$\frac{120}{\pi}\sum_{\theta \in S} \theta$$ is equal to
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If domain of the function $$\log_e\left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right)$$ is $$(\alpha, \beta) \cup (\gamma, \delta)$$, then $$18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2)$$ is equal to
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The integral $$\int\left(\left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x\right) \log_2 x \, dx$$ is equal to
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Let the vectors $$\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}$$, $$\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k}$$, and $$\vec{u}_3 = c\hat{i} + \hat{j} + \hat{k}$$ be coplanar. If the vectors $$\vec{v}_1 = (a+b)\hat{i} + c\hat{j} + c\hat{k}$$, $$\vec{v}_2 = a\hat{i} + (b+c)\hat{j} + a\hat{k}$$ and $$\vec{v}_3 = b\hat{i} + b\hat{j} + (c+a)\hat{k}$$ are also coplanar, then $$6(a + b + c)$$ is equal to
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Let $$P$$ be the plane passing through the line $$\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$$ and the point $$(2, 4, -3)$$. If the image of the point $$(-1, 3, 4)$$ in the plane $$P$$ is $$(\alpha, \beta, \gamma)$$, then $$\alpha + \beta + \gamma$$ is equal to
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If the probability that the random variable $$X$$ takes values $$x$$ is given by $$P(X = x) = k(x + 1)3^{-x}$$, $$x = 0, 1, 2, 3, \ldots$$, where $$k$$ is a constant, then $$P(X \geq 2)$$ is equal to
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Let $$0 < z < y < x$$ be three real numbers such that $$\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$$ are in an arithmetic progression and $$x, \sqrt{2}y, z$$ are in a geometric progression. If $$xy + yz + zx = \frac{3}{\sqrt{2}}xyz$$, then $$3(x + y + z)^2$$ is equal to _____.
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The ordinates of the points $$P$$ and $$Q$$ on the parabola with focus $$(3, 0)$$ and directrix $$x = -3$$ are in the ratio 3 : 1. If $$R(\alpha, \beta)$$ is the point of intersection of the tangents to the parabola at $$P$$ and $$Q$$, then $$\frac{\beta^2}{\alpha}$$ is equal to _____.
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Let $$R = \{a, b, c, d, e\}$$ and $$S = \{1, 2, 3, 4\}$$. Total number of onto functions $$f : R \to S$$ such that $$f(a) \neq 1$$, is equal to _____.
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Let k and m be positive real numbers such that the function $$f(x) = \begin{cases} 3x^2 + k\sqrt{x + 1}, & 0 < x < 1 \\ mx^2 + k^2, & x \geq 1 \end{cases}$$ is differentiable for all $$x > 0$$. Then $$\frac{8f'(8)}{f'(\frac{1}{8})}$$ is equal to _____.
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Let $$[t]$$ denote the greatest integer function. If $$\int_0^{2.4} [x^2] dx = \alpha + \beta\sqrt{2} + \gamma\sqrt{3} + \delta\sqrt{5}$$, then $$\alpha + \beta + \gamma + \delta$$ is equal to _____.
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Let the area enclosed by the lines $$x + y = 2$$, $$y = 0$$, $$x = 0$$ and the curve $$f(x) = \min\left\{x^2 + \frac{3}{4}, 1 + [x]\right\}$$ where $$[x]$$ denotes the greatest integer $$\leq x$$, be $$A$$. Then the value of $$12A$$ is _____.
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Let the solution curve $$x = x(y)$$, $$0 < y < \frac{\pi}{2}$$, of the differential equation $$(\log_e(\cos y))^2 \cos y \, dx - (1 + 3x \log_e(\cos y)) \sin y \, dy = 0$$ satisfy $$x\left(\frac{\pi}{3}\right) = \frac{1}{2\log_e 2}$$. If $$x\left(\frac{\pi}{6}\right) = \frac{1}{\log_e m - \log_e n}$$, where $$m$$ and $$n$$ are coprime, then $$mn$$ is equal to _____.
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The area of the quadrilateral $$ABCD$$ with vertices $$A(2, 1, 1)$$, $$B(1, 2, 5)$$, $$C(-2, -3, 5)$$ and $$D(1, -6, -7)$$ is equal to _____.
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For $$a, b \in \mathbb{Z}$$ and $$|a - b| \leq 10$$, let the angle between the plane $$P: ax + y - z = b$$ and the line $$L: x - 1 = a - y = z + 1$$ be $$\cos^{-1}\left(\frac{1}{3}\right)$$. If the distance of the point $$(6, -6, 4)$$ from the plane $$P$$ is $$3\sqrt{6}$$, then $$a^4 + b^2$$ is equal to _____.
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Let $$P_1$$ be the plane $$3x - y - 7z = 11$$ and $$P_2$$ be the plane passing through the points $$(2, -1, 0)$$, $$(2, 0, -1)$$, and $$(5, 1, 1)$$. If the foot of the perpendicular drawn from the point $$(7, 4, -1)$$ on the line of intersection of the planes $$P_1$$ and $$P_2$$ is $$(\alpha, \beta, \gamma)$$, then $$\alpha + \beta + \gamma$$ is equal to _____.
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