1. A block of √3 kg is attached a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angles of 30º  with the wall. The tension T is

(Given g = 10 ms^-2)

2. The equivalent resistance between A and B is ____________.

3. Given below are two statements: One is labelled as assertion A and other is labelled as reason R.

Assertion (A): Efficiency of a reversible heat engine will be highest at -273º C temperature of cold reservoir

Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as η =  (1 - T_2 / T_1).

In the light of the above statements, choose the correct answer from the options given below.

4. An electron accelerated through a potential difference V_1 has a de-Broglie wavelength of λ. When the potential is changed to V_2, its de-Broglie wavelength increases by 50%. The value of (V_1 /V_2) is equal to

5. Match List I with List II.

Choose the correct answer from the options given below.

6. In the given circuit, rms value of current (I_rms) through the resistor R is

7. A vehicle travels 4km with speed of 3 km/h and another 4 km with speed of 5 km/h, then its average speed is

8. A thin prism P_1 with an angle 6º and made of glass of refractive index 1.54 is combined with another prism P_2 made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P_2 is

9. A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source , the intensity produced by the electric field component is

10. As shown in figure, a cuboid lies in a region with electric field E^→ = (2x² iˆ -4yjˆ +6kˆ) N/C. The magnitude of charge within a cuboid is nε_0 C. The value of n is ______. (if dimension of cuboid is 1×2×3 m³)

11. A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m/s at t =0 s on a rough horizontal surface. It starts off with a purely sliding motion at t =0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be _____J (Given, coefficient of friction is 0.3 and g = 10 m/s²)

12. A faulty thermometer reads 5ºC in melting ice and 95ºC in stream. The correct temperature on absolute scale will be ______K when the faulty thermometer reads 41ºC.

13. A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of  constant power P. Its displacement in 4 s is 1/3 α² √P m. The value of  α will be  _____.

14. If the potential difference between B and D is zero, the value of x is 1/n Ω. The value of n is _______.

15. A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936/x  ms^-2 . The value of x is  _________. (Take π = 22/7)

16. In a Young's double slit experiment, the intensities at two points, for the path differences λ/4  and λ/3 (λ being the wavelength of light used) are I_1 and I_2 respectively. If I_o denotes the intensity produced by each one of the individual slits, then I_1 +I_2 / I_o = ______.

17.  In an ac generator, a rectangular coil of 100 turns each having area 14 x 10-² m² is rotated at 360 rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be ________V.  (Take π=22/7)

18. The velocity of a particle executing SHM varies with displacement (x) as 4v²= 50 - x². The time period of  oscillations is x/7  s. The value of x is_____ . (Take Take π = 22/7)

19. A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be α/11 s. The value of α is ________.

20. If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to form a single drop. In the process the released surface energy is (Take π = 22/7)

21. At a certain depth "d" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400 km). The depth d is equal to

22. A rod with circular cross-section area 2 cm² and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is 4π × 10^-6 Wb. The relative permeability of the rod is (Given: Permeability of vacuum µ_0 = 4π × 10^-7            ΝΑ-²)

23. Two polaroid A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarized light is I_0 then intensity of transmitted light after passing through polaroid B will be

24. Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The beam of electrons show wave nature and exhibit interference and diffraction.

Reason (R) : Davisson Germer Experimentally verified the wave nature of electrons.

In the light of the above statement choose the most appropriate answer from the options given below.

25. 100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time t s. The total force exerted by the balls on the wall is

CHEMISTRY

1. The products A and B in the following reactions, respectively are

2. The compounds that produce CO_2 with aqueous NaHCO_3 solution are

choose the correct answer from the options given below:

3. Both acetaldehyde and acetone (individually) undergo which of the following reactions?

A. Iodoform Reaction

B. Cannizzaro Reaction

C. Aldol Condensation

D. Tollen's Test

E. Clemmensen Reduction

Choose the correct answer from the options given below:

4. What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non-volatile solute (molar mass 256 g mol-¹) and the decrease in freezing point is 0.40 K?

5. Given below are two statements:

Statement I: In the oxalic acid vs KMnO4 (in the presence of dil H_2 SO_4 ) titration the solution needs to be heated initially to 60º C but no heating is required in ferrous ammonium sulphate (FAS) vs KMnO4 titration (in the presence of dil H_2 SO_4) .

Statement II: In oxalic acid vs KMnO4 titration, the initial formation of MnSO4 takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs KMnO4, heating oxidizes Fe^2+ into Fe^3+ by oxygen of air and error may be introduced in the experiment.

In the light of the above statements, choose the correct answer from the options given below :

6. A weak acid HA has degree of dissociation x. Which option gives the correct expression of (pH - pK_a) ?

7.

8.  Which of the following oxidation reactions are carried out by both K_2 Cr_2 O_7 and KMnO4 in acidic medium?

Choose the correct answer from the options given below:

9. The molecules having square pyramidal geometry are

10. In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?

A. n = 1, l = 0, m_l = 0

B. n = 2, l = 0, m_l = 0

C. n = 2, l = 1, m_l = 1

D.  n = 3, l = 2, m_l = 1

E. n = 3, l = 2, m_l = 0

Choose the correct answer form the options given below:

11. Consider 'n' is the number of lone pair of electrons present in the equatorial position of the most stable structure of ClF_3. The ions from the following with 'n' number of unpaired electrons are

A. V^3+

B. Ti^3+

C. Cu^2+

D. Ni^2+

E. Ti^2+

Choose the correct answer from the options given below:

12. Given below are two statements:

Statement I: D-glucose pentaacetate reacts with 2, 4-dinitrophenylhydrazine.

Statement II: Starch, on heating with concentrated sulfuric acid at 100°C and 2-3 atmosphere pressure produces glucose.

In the light of the above statements, choose the correct answer from the options given below :

13. The incorrect decreasing order of atomic radii is

14. Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K. If pressure of the system is increased 2 times, keeping temperature constant. then identify correct observation from following.

15.

16.

Choose the correct answer from the options given below:

17. A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q"). ("Q") on ozonolysis followed by reflux under alkaline condition gives ("R"). The structure of ("R") is given below :

18. Consider the following elements In, Tl, Al, Pb, Sn and Ge. The most stable oxidation states of elements with highest and lowest first ionization enthalpies, respectively, are

19. The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

20.

For a given reaction R → P, t_1/2 is related to [A]_0 as given in table. (given: log 2 = 0.30)

Which of the following is true?

A. The order of the reaction is 1/2.

B. If [A]_0 is 1M, then t_1/2 is 200 √10 min.

C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100M to 0.500M.

D. t_1/2 is 800 min for [A]_0 = 1.6 M.

Choose the answer from the options given below:

21. Quantitative analysis of an organic compound (X) shows following % composition.

C: 14.5%           Cl: 64.46%        H: 1.8%

Empirical formula mass of the compound (X) is ________×10^-1

(given molar mass in g mol^-1 of C : 12, H : 1, O : 16, Cl : 35.5)

22. The molarity of a 70% (mass/mass) aqueous solution of a monobasic acid (X) is ____ ×10^-1 M (Nearest integer)

[Given: Density of aqueous solution of (X) is 1.25 g mL^-1 Molar mass of the acid is 70 g mol^-1]

23. Consider the following sequence of reaction:

11.25 mg of chlorobenzene will produce _____×10^-1 mg of product B. (Consider the reaction results in complete conversion.)

[Given molar mass of C, H, O, N and Cl as 12, 1, 16, 14 and 35.5 g mol^-1 respectively]

24. The formation enthalpies, ΔHº_f for H_(g) and O_(g) are 220.0 and 250.0 kJ mol^-1, respectively at 298.15 K, and ΔHº_f for H_2 O(g) is -242.0 kJ mol^-1 at the same temperature. The average bond enthalpy of the        O - H bond in water at 298.15 K is _____kJ mol^-1 (nearest integer).

25. Given below is the plot of the molar conductivity vs √concentration for KCl in aqueous solution.

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100 Ω, then the resistance of the same cell with the dilute solution is 'x' Ω. The value of x is _____. (Nearest integer)

MATHS

2.

3.

4.

5. Consider an A.P. of positive integers, whose sum of the first three is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is:

6.

7.

8.

9. Two parabolas have the same focus (4,3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersects at the points A and B, then (AB)² is equal to:

10. Let the line x + y = 1 meet the circle x²+y² = 4 at the points A and B. If the line perpendicular to AB and passing through the mid point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ADBC is equal to:

11.

12. Let the ellipse E_1 : x²/a² + y²/b² = 1, a> b and E_2 : x²/A² + y²/B² = 1, A < B have same eccentricity 1/√3. Let the product of their lengths of latus rectums be 32/√3, and the distance between the foci of E_1 be 4. If E_1 and E_2 meet  at A, B, C and D, then the area of the quadrilateral ABCD equals:

13. Define a relation R on the interval [0, π/2) by x R y if and only if sec²x - tan²y = 1. Then R is:

14. Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set P is:

15. Let |z_1 - 8 - 2i| ≤ 1 and |z_2 - 2 + 6i| ≤ 2, z_1, z_2 ∈ C. Then the minimum value of |z_1 - z_2| is:

16. The least value of n for which the number of integral terms in the Binomial expansion of (3√7 +12√11)^n is 183, is:

17.

18. Let the area of the region {(x, y): 2y ≤ x²+3, y +|x|≤ 3, y ≥ |x-1|} be A. Then 6A is equal to:

19. Let ABC be a triangle formed by the lines 7x - 6y + 3 = 0, x + 2y - 31 = 0 and 9x - 2y - 19 = 0. Let the point (h, k) be the image of the centroid of triangle ΔABC in the line 3x + 6y - 53 = 0. Then h^2 + k^2 + hk is equal to:

20.

21.

22. The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice,  is ______.

23.

24.

25.