Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:
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Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:
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A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):
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Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:
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A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m s$$^{-1}$$ in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m s$$^{-2}$$. Assume there is no rotational motion and loss of energy after the collision is negligible.]
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A uniform rod of length '$$\ell$$' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $$\omega$$ the rod makes an angle $$\theta$$ with it (see figure). To find $$\theta$$ equate the rate of change of angular momentum (direction going into the paper) $$\frac{m\ell^2}{12}\omega^2 \sin\theta$$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces $$F_H$$ and $$F_v$$ about the CM. The value of $$\theta$$ is then such that:
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The mass density of a planet of radius R varies with the distance r from its centre as $$\rho(r) = \rho_0\left(1 - \frac{r^2}{R^2}\right)$$. Then the gravitational field is maximum at:
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A metallic sphere cools from 50°C to 40°C in 300 s. If atmospheric temperature around is 20°C, then the sphere's temperature after the next 5 minutes will be close to:
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A calorimeter of water equivalent 20 g contains 180 g of water at 25°C. 'm' grams of steam at 100°C is mixed in it till the temperature of the mixture is 31°C. The value of 'm' is close to (Latent heat of water = 540 cal g$$^{-1}$$, specific heat of water = 1 cal g$$^{-1}$$°C$$^{-1}$$)
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To raise the temperature of a certain mass of gas by 50°C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?
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A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $$fA$$. The value of $$f$$ is:
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Concentric metallic hollow spheres of radii R and 4R hold charges $$Q_1$$ and $$Q_2$$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) - V(4R) is:
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Two resistors 400 $$\Omega$$ and 800 $$\Omega$$ are connected in series across a 6V battery. The potential difference measured by a voltmeter of 10 k$$\Omega$$ across 400 $$\Omega$$ resistor is close to:
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Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?
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A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $$\vec{B}$$. Then the field inside the paramagnetic substance is:
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A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB/dt = 0.032 Ts$$^{-1}$$. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$\times$$ 10$$^{-8}$$ $$\Omega$$m)
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The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $$\vec{E} = E_0 \hat{j}\cos(\omega t - kx)$$. The magnetic field $$\vec{B}$$, at the moment t = 0 is:
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Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is:
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Two light waves having the same wavelength $$\lambda$$ in vacuum are in phase initially. Then the first wave travels a path $$L_1$$ through a medium of refractive index $$n_1$$ while the second wave travels a path of length $$L_2$$ through a medium of refractive index $$n_2$$. After this the phase difference between the two waves is:
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The radius R of a nucleus of mass number A can be estimated by the formula $$R = (1.3 \times 10^{-15})A^{1/3}$$ m. It follows that the mass density of n nucleus is of the order of: $$(M_{prot} \cong M_{neut} \simeq 1.67 \times 10^{-27}$$ kg)
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If a semiconductor photo diode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy is: Planck's constant h = 6.63 $$\times$$ 10$$^{-34}$$ J.s, Speed of light c = 3 $$\times$$ 10$$^8$$ m s$$^{-1}$$
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A block starts moving up an inclined plane of inclination 30° with an initial velocity of $$v_0$$. It comes back to its initial position with velocity $$\frac{v_0}{2}$$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $$\frac{I}{1000}$$. The nearest integer to I is:
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An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $$\frac{N}{20}ma^2$$ where N is an integer. The value of N is __________.
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If minimum possible work is done by a refrigerator in converting 100 grams of water at 0°C to ice, how much heat (in calories) is released to the surroundings at temperature 27°C (Latent heat of ice = 80 Cal/gram) to the nearest integer?
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A galvanometer coil has 500 turns and each turn has an average area of $$3 \times 10^{-4}$$ m$$^2$$. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5A is flowing through it, the strength of the field (in T) is __________.
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When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cm s$$^{-1}$$, the speed (in cm s$$^{-1}$$) with which image moves at that instant is
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The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity(M) respectively, are: (Take molar mass of hydrogen peroxide as 34 g/mol)
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Consider the hypothetical situation where the azimuthal quantum number, $$\ell$$, takes values 0, 1, 2, ......... n + 1. Where n is the principal quantum number. Then, the element with atomic number:
The five successive ionization enthalpies of an element are 800, 2427, 3658, 35024, 32824 kJ mol$$^{-1}$$. The number of valence electrons in the element is:
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Consider the following molecules and statements related to them:
(a) (B) is more likely to be crystalline than (A)
(b) (B) has higher boiling point than (A)
(c) (B) dissolves more readily than (A) in water
Identify the correct option from below:
A mixture of one mole each of $$H_2$$, He and $$O_2$$ each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of $$H_2$$ is 2 atm, the total pressure of the gases in the cylinder is:
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100 mL of 0.1 M HCl is taken in a beaker and to it 100 mL 0.1 M NaOH of is added in steps of 2 mL and the pH is continuously measured. Which of the following graphs correctly depicts the change in pH?
Among the statements (I - IV), the correct ones are:
(I) Be has smaller atomic radius compared to Mg.
(II) Be has higher ionization enthalpy than Al.
(III) Charge/radius ratio of Be is greater than that of Al.
(IV) Both Be and Al form mainly covalent compounds
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The incorrect statement(s) among (a) - (d) regarding acid rain is (are):
(a) It can corrode water pipes
(b) It can damage structures made up of stone.
(c) It cannot cause respiratory ailments in animals
(d) It is not harmful for trees
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For the reaction $$2A + 3B + \frac{3}{2}C \to 3P$$, which statement is correct?
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The incorrect statement is:
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Complex A has a composition of $$H_{12}O_6Cl_3Cr$$. If the complex on treatment with conc. $$H_2SO_4$$ loses 13.5% of its original mass, the correct molecular formula of A is:
[Given: atomic mass of Cr = 52 amu and Cl = 35 amu]
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The d-electron configuration of $$[Ru(en)_3]Cl_2$$, and $$[Fe(H_2O)_6]Cl_2$$ respectively are:
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The decreasing order of reactivity of the following compounds towards nucleophilic substitution ($$S_N2$$) is:
The major product in the following reaction is:
Consider the following reaction:
The product 'P' gives positive ceric ammonium nitrate test. This is because of the presence of which of these -OH group(s)?
The increasing order of the reactivity of the following compounds in nucleophile addition reaction is:
Propanal, Benzaldehyde, Propanone, Butanone
The compound A in the following reactions is:
$$A \xrightarrow[(ii)Conc. H_{2}SO_{4}/ \Delta]{(i)CH_{3}MgBr/H_{2}O} B \xrightarrow[(ii) Zn/H_{2}O]{(i) O_{3}} C + D$$
Three isomers A, B and C (mol. formula $$C_8H_{11}N$$) give the following results:
A and C $$\xrightarrow{Diazotization}$$ P + Q $$\xrightarrow[(ii) acidation(KMnO_4+H^+)]{(i) Hydrolysis}$$ R (product of A) + S (product of C)
R has lower boiling point than S
B $$\xrightarrow{C_6H_5SO_2Cl}$$ alkali-insoluble product
A, B and C, respectively are:
An ionic micelle is formed on the addition of:
Match the following drugs with their therapeutic actions:
(i) Ranitidine (a) Antidepressant
(ii) Nardil (Phenelzine) (b) Antibiotic
(iii) Chloramphenicol (c) Antihistamine
(iv) Dimetane (Brompheniramine) (d) Antacid
(e) Analgesic
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$$0.023 \times 10^{22}$$ molecules are present in 10g of a substance 'x'. The molarity of a solution containing 5g of substance 'x' in 2 L solution is _________ $$\times 10^{-3}$$
If 250 cm$$^3$$ of an aqueous solution containing 0.73g of a protein A is isotonic with one litre of another aqueous solution containing 1.65g of a protein B, at 298K, the ratio of the molecular masses of A and B is _________ $$\times 10^{-2}$$ (to the nearest integer).
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An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation $$Cr_2O_7^{2-} + 14H^+ + 6e^- \to 2Cr^{3+} + 7H_2O$$
The amount of $$Cr^{3+}$$ obtained was 0.104g. The efficiency of the process (in %) is (Take: F = 960000C, At. mass of chromium = 52)
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The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is __________.
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The number of
groups present in a tripeptide Asp - Glu - Lys is ____
The set of all real values of $$\lambda$$ for which the quadratic equation $$(\lambda^2 + 1)x^2 - 4\lambda x + 2 = 0$$ always have exactly one root in the interval (0, 1) is:
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If $$z_1, z_2$$ are complex numbers such that $$Re(z_1) = |z_1 - 1|$$ and $$Re(z_2) = |z_2 - 1|$$ and $$\arg(z_1 - z_2) = \frac{\pi}{6}$$, then $$Im(z_1 + z_2)$$ is equal to:
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If the sum of the series $$20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5} + \ldots$$ up to $$n^{th}$$ term is 488 and the $$n^{th}$$ term is negative, then:
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If the term independent of $$x$$ in the expansion of $$\left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9$$ is $$k$$, then $$18k$$ is equal to:
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If a $$\triangle ABC$$ has vertices $$A(-1, 7)$$, $$B(-7, 1)$$ and $$C(5, -5)$$, then its orthocentre has coordinates:
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Let the latus rectum of the parabola $$y^2 = 4x$$ be the common chord to the circles $$C_1$$ and $$C_2$$ each of them having radius $$2\sqrt{5}$$. Then, the distance between the centres of the circles $$C_1$$ and $$C_2$$ is:
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Let $$e_1$$ and $$e_2$$ be the eccentricities of the ellipse $$\frac{x^2}{25} + \frac{y^2}{b^2} = 1$$ $$(b < 5)$$ and the hyperbola $$\frac{x^2}{16} - \frac{y^2}{b^2} = 1$$ respectively satisfying $$e_1 e_2 = 1$$. If $$\alpha$$ and $$\beta$$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $$(\alpha, \beta)$$ is equal to:
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$$\lim_{x \to a}\frac{(a+2x)^{\frac{1}{3}} - (3x)^{\frac{1}{3}}}{(3a+x)^{\frac{1}{3}} - (4x)^{\frac{1}{3}}}$$ $$(a \neq 0)$$ is equal to:
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Let $$p$$, $$q$$, $$r$$ be three statements such that the truth value of $$(p \wedge q) \to (\sim q \vee r)$$ is $$F$$. Then the truth values of $$p$$, $$q$$, $$r$$ are respectively:
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Let $$x_i (1 \leq i \leq 10)$$ be ten observations of a random variable X. If $$\sum_{i=1}^{10}(x_i - p) = 3$$ and $$\sum_{i=1}^{10}(x_i - p)^2 = 9$$ where $$0 \neq p \in R$$, then the standard deviation of these observations is:
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Let $$R_1$$ and $$R_2$$ be two relations defined as follows:
$$R_1 = \{(a, b) \in R^2 : a^2 + b^2 \in Q\}$$ and $$R_2 = \{(a, b) \in R^2 : a^2 + b^2 \notin Q\}$$, where Q is the set of all rational numbers, then
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Let A be a $$3 \times 3$$ matrix such that adj $$A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix}$$ and $$B = $$ adj(adjA). If $$|A| = \lambda$$ and $$\left|(B^{-1})^T\right| = \mu$$, then the ordered pair $$(|\lambda|, \mu)$$ is equal to
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Suppose $$f(x)$$ is a polynomial of degree four having critical points at -1, 0, 1. If $$T = \{x \in R | f(x) = f(0)\}$$, then the sum of squares of all the elements of $$T$$ is:
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If the surface area of a cube is increasing at a rate of 3.6 cm$$^2$$/sec, retaining its shape; then the rate of change of its volume (in cm$$^3$$/sec), when the length of a side of the cube is 10 cm, is:
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If $$\int \sin^{-1}\left(\frac{\sqrt{x}}{1+x}\right)dx = A(x)\tan^{-1}(\sqrt{x}) + B(x) + C$$, where C is a constant of integration, then the ordered pair $$(A(x), B(x))$$ can be:
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If the value of the integral $$\int_0^{\frac{1}{2}}\frac{x^2}{(1-x^2)^{\frac{3}{2}}}dx$$ is $$\frac{k}{6}$$, then $$k$$ is equal to:
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If $$x^3 dy + xy \cdot dx = x^2 dy + 2y dx$$; $$y(2) = e$$ and $$x > 1$$, then $$y(4)$$ is equal to:
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Let $$a, b, c \in R$$ be such that $$a^2 + b^2 + c^2 = 1$$. If $$a\cos\theta = b\cos\left(\theta + \frac{2\pi}{3}\right) = c\cos\left(\theta + \frac{4\pi}{3}\right)$$, where $$\theta = \frac{\pi}{9}$$, then the angle between the vectors $$a\hat{i} + b\hat{j} + c\hat{k}$$ and $$b\hat{i} + c\hat{j} + a\hat{k}$$ is:
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The plane which bisects the line joining the points (4, -2, 3) and (2, 4, -1) at right angles also passes through the point:
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The probability that a randomly chosen 5-digit number is made from exactly two digits is:
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The total number of 3-digit numbers whose sum of digits is 10, is ..........
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If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $$4^{th}$$ A.M. is equal to $$2^{nd}$$ G.M., then $$m$$ is equal to:
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Let $$S$$ be the set of all integer solutions $$(x, y, z)$$ of the system of equations
$$x - 2y + 5z = 0$$
$$-2x + 4y + z = 0$$
$$-7x + 14y + 9z = 0$$
such that $$15 \leq x^2 + y^2 + z^2 \leq 150$$. Then, the number of elements in the set $$S$$ is equal to ..........
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If the tangent to the curve $$y = e^x$$ at a point $$(c, e^c)$$ and the normal to the parabola $$y^2 = 4x$$ at the point (1, 2) intersect at the same point on the $$x$$-axis, then the value of $$c$$ is .....
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Let a plane $$P$$ contain two lines $$\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$$, $$\lambda \in R$$ and $$\vec{r} = -\hat{j} + \mu(\hat{j} - \hat{k})$$, $$\mu \in R$$. If $$Q(\alpha, \beta, \gamma)$$ is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then $$3(\alpha + \beta + \gamma)$$ equals .......
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