Part Test - 14 (JEE Advanced)

The empirical formula of a nonelectrolyte is CH₂O. A solution containing 3g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution. The molecular formula of the compound is

The mass of glucose that should be dissolved in 50 g of water in order to produce the same lowering of vapour pressure as is produced by dissolving 1 g of urea in the same quantity of water is

A bat flies at a steady speed of 4 ms^-1 emitting a sound of f = 90 ´ 10³ Hz. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be _____.

(Take velocity of sound in air as 330 ms^-1).

A battery of e.m.f. E has an internal resistance 'r'. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. lf R alone is gradually reduced to zero, which of the following best describes I and V?

A beam of light of wavelength 600 nm from a distant source falls on a single slit 1mm wide and the resulting diffraction pattern is observed on a screen 2m away. The distance between the first dark fringes on either side of the central bright fringe is _______.

A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options describe best the image formed of an object of height 2 cm placed 30 cm from the lens?

A plano-concave lens is made of glass of refractive index 1.5 and the radius of curvature of its curved face is 100 cm. What is the power of the lens?

Current 'I' is flowing in a conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

Two beams of red and violet colours are made to pass separately through a prism of A = 60°. In the minimum deviation position, the angle of refraction inside the prism will be

At distance of 5cm and 10cm outwards from the surface of a uniformly charged solid sphere, the potentials are 100V and 75V respectively. Then     

A conducting rod of length l is moved at constant velocity ‘v₀’ on two parallel, conducting, smooth, fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane of the rails as shown in figure. A resistance R is connected between the two ends of the rail. Then which of the following is are correct : 

A battery of e.m.f. E has an internal resistance 'r'. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. lf R alone is gradually reduced to zero, which of the following best describes I and V?

In the circuit shown, current through the resistance 2 is i₁ and current through the resistance 30 is i₂. Find the ratio  

In the figure shown the switch S₁ remains connected for long time and the switch S₂ remains opened. Now the switch S₂ is closed. Assuming that ε = 10 volt and L = 1H,  the magnitude of  rate of change of current is 2X (in Amp/sec.) in the inductor just after the switch S₂ is closed then find X .

A point source of radiation power P is placed on the axis of completely absorbing disc. The distance between the source and the disc is 2 times the radius of the disc. The force that light exerts on the disc is P/4ac then find a (c = speed of light).

In the figure, a conducting rod of length  l = 1 meter and mass m = 1 kg moves with initial velocity u = 5 m/s. on a fixed horizontal frame containing inductor L = 2 H and resistance R = 1 . PQ and MN are smooth, conducting wires. There is a uniform magnetic field of strength B = 1T. Initially there is no current in the inductor. Find the total charge in coulomb, flown through the inductor by the time velocity of rod becomes v_f = 1 m/s and the rod has travelled a distance x= 3 meter.  

In a YDSE arrangement composite lights of different wavelengths λ₁ = 560 nm and λ₂ = 400 nm are used. If D = 1m, d = 0.1 mm. If the distance between two nearest completely dark regions is  7X mm then X is :

A unknown liquid has vapour pressure of  76 torr at temperature of 27⁰C. If the enthalpy of vaporization of liquid is 5.52 kcal/mole, then the normal boiling point of liquid will be :  [Take ln10 = 2.3 ; R = 2 cal/mole-K]

For a first order reaction, nA → B whose concentration vs time curve is as shown in the figure. If half-life for this reaction is 24 minutes. Find out the value of n.

A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

In the zinc blende structure, zinc ions occupy alternate tetrahedral voids and S^2–  ions exist as ccp the radii of Zn²⁺ and S^2– ions are 0.83 Å and 1.74 Å respectively. The edge length of the ZnS unit cell is :

Which of the following statement(s) is (are) incorrect ? 

A 0.1 M solution of a certain cation will form a precipitate with 0.1 M solution of all these anions ; 
OH^–, CO₃^2–, Cl^– , SO₄^2–. Which cation fits this description ?

Which one of the following statements is incorrect ?

A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio of 

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button one control panel. The lift starts moving upwards with an acceleration 1.0 m/s². If g = 10 ms^–2, the tension in the supporting cable is

If Avogadro number N_A, is changed from 6.022 × 10²³ mol^–1 to 6.022 × 10²⁰ mol^–1, this would change 

Dry air is slowly passed through three solutions of  different concentrations, c₁, c₂ and c₃ ; each containing (non volatile) NaCl as solute and water as solvent, as shown in  the Figure If the vessel - 2 gains weight and the vessel 3 loses weight, then : 

Concentrated aqueous sulphuric acid is 98% H₂SO₄ by mass and has a density of 1.80 g.mL^–1. Volume of acid required to make 1 litre of 0.1 M H₂SO₄ solution is: 

Which of the following statement(s) is (are) correct for the thiosulphate salt ?  

Which of the following statements is/are correct ?     

Which of the following statements is/are correct about the above reaction ? 

The familiar brown ring test for nitrates depends on the ability of Fe²⁺ to reduce nitrates to nitric oxide, which reacts with Fe²⁺ to form a brown coloured complex [Fe(H₂O)₅NO⁺]SO₄. What is the oxidation state of iron in the complex. (Only write the number 1, 2, 3, ......)

Determine the number of unpaired electrons in the Cr³⁺ gaseous ions.

In the following sequence of reactions all stereoisomers of (X) have been taken. 

Find the Total number of products (Z) formed.

Observe the following reaction sequence carefully.

Find  the total number of stereoisomers formed in step (6).

1 g of a monobasic acid dissolved in 200 g of water lowers the freezing point by 0.186ºC. On the other hand when  1 g of the same acid is dissolved in water so as to make the solution 200 mL, this solution requires 125 mL of 0.1 N NaOH for complete neutralization. If α for the acid is x × 10. Find x :

Number of moles of MnO₄^– required to oxidize one mole of ferrous oxalate completely in acidic medium will be

If the change in the value of g at the height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)

 The value of ‘g’ at a particular point is 9.8 m/sec² suppose the earth suddenly shrink uniformly to half its present size without losing any mass. The value of ‘g’ at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will become

      If x + 2 is a factor of x³ – 2ax² + 16, then value of a is

A body weighs 50 grams in air and 40 grams in water. How much would it weigh in a liquid of specific gravity 1.5?

If A class has 175 students . The following data shows the number of students offering one or more subjects. Mathematics 100 ; Physics 70 ; Chemistry 40 ; Mathematics and Physics 30 ; Mathematics and Chemistry 28 ; Physics and Chemistry 23 ; Mathematics , Physics and Chemistry 18 . How many students have offered Mathematics alone ?

If A is a diagonal matrix of order ‘n’ such that A³A^–1 = A, then number of possible values of matrix A, is 

If f(x) = x + e^x, and g(x) is the inverse function of f(x), then g``(A) equals 

If f (x) = x + |x| + cos ([π²] x) and g (x) = sin x then ([.] denotes greatest integer function) :

Two beams of red and violet colours are made to pass separately through a prism of A = 60°. In the minimum deviation position, the angle of refraction inside the prism will be

If one of the factor of x² + x – 20 is (x + 5). Find the other

Three-fourth of the number of girls in a school is equal to half of the number of boys. If the school has 1420 pupils, how many of them are boys ? 

Compare the statements A and B.

Statement A: Synthesis of DNA takes place in the S-phase of interphase.

Statement B: Every chromosome, during metaphase, has two chromatids.

Choose the correct description :

Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.

The position vectors of two points A and C are respectively. The point of
intersection of the lines containing vectors is P. If vector is
perpendicular to and PQ = 15 units, then possible position vectors of Q are  and Find the value of 

Find the smallest positive integer 'p' for which the equation cos (p sinx) = sin (p cosx) has a solution in [0, 2π].

Let image of the line  in the plane 2x – y + z + 3 = 0 be L. A plane 7x + By + Cz + D = 0 is such that it contains the line L and is perpendicular to the plane 2x – y + z + 3 = 0, then find the value of D + 3C.