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In a Young’s double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle α as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11.0 mm. Which of the following statements(s) is/are correct?
A block of mass 2M is attached to a massless spring with spring–constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in the figure. the system is released from rest with the spring in its unstretched state.The maximum extension of the spring is x0. Which of the following option(s) is/are correct?
[g is the acceleration due to gravity. neglect friction]
In the frame of pulley B, the hanging masses have accelerations :
M → (a2 – a1), 2M → (a3 – a1) : downward.
∴ (a2 – a1) = –(a3 – a1) [constant]
Assuming that the extension of the spring is x
We consider the FBD of A :
A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is
released from rest so that it falls by rotating about its contactpoint with the floor without slipping. Which
of the following statement(s) is/are correct, when the rod makes an angle 60° with vertical ?
[g is the acceleration due to gravity]
A small particle of mass m moving inside a heavy,hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is L = L_{0 }the particle speed is v = v_{0}. The piston is moved inward at a very low speed V such that , where dL is the infinitesimal displacement of the piston. which of the following statement(s) is/are correct?
Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3m). If H1, H2 and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:
An electric dipole with dipole moment is held fixed at the origin O in the presence of an uniform electric field of magnitude E0.If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are:
( ∈_{0} is permittivity of free space. R >> dipole size)
A ball is thrown from ground at an angle θ with horizontal and with an initial speed u_{0}. For the resulting
projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for
the first time is V1. After hitting the ground, the ball rebounds at the same angle θ but with a reduced speed
of u0/α. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the
ball for entire duration of motion is 0.8 V1, the value of α is________.
A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1Ω as shown in the figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x * 10^{3} A, where the value of x is ________
[Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given: e^{1} = 0.37, where e
is base of the natural logarithm]
A perfectly reflecting mirror of mass M mounted on a spring constitutes a springmass system of angular frequency Ω such that 4πMΩ/h =10^{24 }m^{2} with h as Planck’s constant. N photons of wavelength λ = 8π * 10^{6} m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 µm. If the value of N is x * 10^{12 }then the value of x is _________. [Consider the spring as massless]
A monochromatic light is incident from air on a refracting surface of prism of angle 75° and refractive index n_{0} = √3 . The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure.
The light suffers total internal reflection at the coated prism surface for an incidence angle of θ ≤ 60°. The value of n2 is _______
When angle of incidence on first face of the prism is 60° the angle of incidence on the other surface of the
prism will be slightly greater than critical angle.
For refraction at first surface of the prism
An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark.The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is_______.
Q. If the tension in each string is T_{0}, the correct match for the highest fundamental frequency in f_{0} units will be, Options
Q. If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PVdiagram with P_{0}V_{0 } =1/3 RT_{0}, the correct match is
Q. If the process on one mole of monatomic ideal gas is as shown in the TVdiagram with P_{0}V_{0} = 1/3 RT_{0}, the correct match is,
Choose the correct option(s) that give(s) an aromatic compound as the major product
Consider the following reactions (unbalanced)
Choose the correct option(s)
Which of the following reactions produce(s) propane as a major product?
The ground state energy of hydrogen atom is – 13.6 eV. Consider an electronic state ψ of He+ whose
energy, azumuthal quantum number and magnetic quantum number are 3.4 eV, 2 and 0, respectively.
Which of the following statement(s) is(are) true for the state ψ ?
The cyanide process of gold extraction involves leaching out gold from its ore with CN^{} in the presence of
Q in water to form R. Subsequently, R is treated with T to obtain Au and Z. Choose the correct option(s)
With reference to aqua regia, choose the correct option(s)
Choose the correct option(s) for the following reaction sequence
Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular
formula C4H8O is_______
The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the
solution is 1.2 g cm3, the molarity of urea solution is______
(Given data: Molar masses of urea and water are 60 g mol1 and 18 g mol1, respectively)\
Total number of cis NMnCl bond angles (that is, Mn – N and Mn – Cl bonds in cis positions) present in a
molecule of cis[Mn(en)2Cl2] complex is______(en = NH2CH2CH2NH2)
The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. HNO3 to a
compound with the highest oxidation state of sulphur is______
(Given data : Molar mass of water = 18 g mol1)
The decomposition reaction is started in a closed cylinder under
isothermal isochoric condition at an initial pressure of 1 atm. After Y × 103 s, the pressure inside the
cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5 × 104 s1, assuming ideal gas
behaviour, the value of Y is_______
Total number of hydroxyl groups present in a molecule of the major product P is_________
Answer the following by appropriately matching the lists based on the information given in the paragraph
Q. Which of the following options has the correct combination considering ListI and ListII?Options
Answer the following by appropriately matching the lists based on the information given in the paragraph
Q. Which of the following options has the correct combination considering ListI and ListII?Options
Answer the following by appropriately matching the lists based on the information given in the paragraph
ListI includes starting materials and reagents of selected chemical reactions. ListII gives structures ofcompounds that may be formed as intermediate products and/or final products from the reactions of ListI.
Q. Which of the following options has the correct combination considering ListI and ListII?Options
Answer the following by appropriately matching the lists based on the information given in the paragraph
ListI includes starting materials and reagents of selected chemical reactions. ListII gives structures of
compounds that may be formed as intermediate products and/or final products from the reactions of ListI.
Q. Which of the following options has the correct combination considering ListI and ListII?Options
Three lines
are given. For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R
are collinear?
Q. where denotes the transpose of the matrix P_{k}. Then which of the following options is/are correct?
Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of
the three colours red, blue and green, then the number of ways of distributing the hats such that the persons
seated in adjacent seats get different coloured hats is ______
Let x denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each
element is equally likely to occur. If A and B are independent events associated with S, then the number of
ordered pairs (A, B) such that 1 ≤ B < A, equals _____
Answer the following by appropriately matching the lists based on the information given in the paragraph
Q. Which of the following is the only CORRECT combination?
Answer the following by appropriately matching the lists based on the information given in the paragraph
Q. Which of the following is the only CORRECT combination?
Answer the following by appropriately matching the lists based on the information given in the paragraph
Q. Which of the following is the only CORRECT combination?
Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles C1 : x^{2} + y^{2} = 9 and C2 : (x – 3)^{2} + (y – 4)^{2} = 16, intersect at the points X and Y. Suppose that another circle C3 : (x – h)^{2} + (y – k)^{2} = r^{2} satisfies and following conditions:
(i) centre of C_{3} is collinear with the centres of C_{1} and C_{2}
(ii) C_{1} and C_{2} both lie inside C_{3,} and
(iii) C_{3} touches C_{1} at M and C_{2} at N.
Let the line through X and Y intersect C_{3} at Z and W, and let a common tangent of C_{1} and C_{3} be a tangent to the parabola x^{2} = 8αy.
There are some expressions given in the List–I whose values are given in List–II below:
Q. Which of the following is the only INCORRECT combination?
Centre of C_{3} will lie on line MN : 3x = 4y at a
distance of 3 units from origin in first quadrant
Equation of ZW : C1 – C2 = 0
⇒ 6x + 8y – 18 = 0 or 3x + 4y = 9
perpendicular distance from centre of C3 to
Common tangent of C_{1}C_{3} : C_{1} – C_{3} = 0 (as they touch each other)
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