1. A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 × 10^-15 eVs)

2. The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0 to 10 s is

3.A long solenoid is formed by winding 70 turns cm^-¹. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ________________ (μ₀ = 4π × 10^-7 TmA⁻¹)

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

Assertion (A): Steel is used in the construction of buildings and bridges.

Reason (R): Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer the from options given below.

5. The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by E_x = E₀ sin(kz−ωt); B_y = B₀ sin(kz – ωt) then the correct relation between E₀ and B₀ is given by

6. A cell of emf 90 V is connected across series combination of two resistors each of 100 Ω resistance. A voltmeter will be

7. A metallic rod of length ‘L’ is rotated with an angular speed of ‘ω’ normal to a uniform magnetic field ‘B’ about an axis passing through one end of rod as shown in figure. The induced emf will be

8. If the distance of the earth from sun is 1.5 × 10⁶ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is

9. An α-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength?

10. If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is___________ %.

11.  Three identical resistors with resistance R = 12 Ω and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12V as shown in figure. The current through the battery long after the switch has been closed will be _______A.

12. A body of mass 1 kg begins to move under the action of a time dependent force F^→= (t iˆ+3tˆ² jˆ)N, where  iˆ and  jˆ are the unit vectors along x and y axis. The power developed by above force, at the time t = 2s will be _______________ W.

13. The energy released per fission of nucleus of ²⁴⁰X is 200 MeV. The energy released if all the atoms in 120g of pure ²⁴⁰X undergo fission is _________ × 10²⁵ MeV. (Given N_A = 6 × 10²³)

14. A uniform solid cylinder with radius R and length L has moment of inertia I₁ about the axis of the cylinder. A concentric solid cylinder of radius R′ = R/2 and length L′ = L/2  is carved out of the original cylinder. If I₂ is the moment of inertia of the carved out portion of the cylinder then I₁/I₂ = ______________________ (Both I₁ and I₂ are about the axis of the cylinder)

15. A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be x/130 N. The value of x is _______________.

16. A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The Separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes x/4 pF. The Value of x is_______________.

17. A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be (Take g = 10 m/s²)

18. An electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

19. Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of λ₀. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be

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

Assertion (A): Photodiodes are used in forward bias usually for measuring the light intensity.

Reason (R): For a p-n junction diode, at applied voltage V the current in the forward bias is more than the current in the reverse bias for |V_Z| > ± V≥|V₀| where V₀ is the threshold voltage and V_Z is the breakdown voltage. In the light of the above statements, choose the correct answer from the options given below.

21. An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s²)

22. A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 × 10⁻³ kg, density is 8.92 × 10³ kg/m³ and resistivity is 1.7 × 10^-8 Ωm. The length of wire is

23. Match List I with List II.

24. A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be

25. A parallel plate capacitor has plate area 40 cm² and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is

CHEMISTRY:

1. The alkane from below having two secondary hydrogens is

2. Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is

3. Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.

4. When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is

5. Identify the homoleptic complex(es) that is/are low spin.

(A) [Fe(CN)-5,NO]^2-                                   (B) [CoF_6]^3-                   (C) [Fe(CN)_6]^4-

(D) [Co(NH_3)_6]^3+                                  (E) [Cr(H_2O)_6]^2+

Choose the correct answer from the options given below:

6. The most stable carbocation from the following is

7. Given below are two statements:

Statement (I): Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's test.

Statement (II): The elements present in the compound are converted from covalent form into ionic form by fusing the compound with magnesium in Lassaigne's test.

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

8. Match the Compounds (List-I) with the appropriate Catalyst/Reagents (List-II) for their reduction into corresponding amines.

Choose the correct answer from the options given below:

9. The maximum number of RBr producing 2-methylbutane by above sequence of reactions is ____________ (Consider the structural isomers only)

10. The maximum covalency of a non-metallic group 15 element 'E' with weakest E- E bond is

11. The species which does not undergo disproportionation reaction is

12. Arrange the following compounds in increasing order of their dipole moment: HBr, H_2S, NF_3 and CHCl_3

13. Given below are two statements:

Statement (I): An element in the extreme left of the periodic table forms acidic oxides.

Statement (II): Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table.

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

14. The molar solubility (s) of zirconium phosphate with molecular formula (Zr^4+)_3(PO^3-_4)_4 is given by relation

15. Match list -I with list -II.

Choose the correct answer from the options given below:

16. The correct order of the following complexes in terms of their crystal field stabilization energies is

17. Given below are two statements:

Statement (I): Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode.

Statement (II): The rate of corrosion is more in alkaline medium than in acidic medium.

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

18.

19. Consider the given figure and choose the correct option.

20. Given below are two statements :

Statement (I): A spectral line will be observed for a 2p_x→ 2p_y transition.

Statement (II): 2p_x and 2p_y are degenerate orbitals.

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

21. The compound with molecular formula C_6H_6, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has__________π electrons.

22. The complex of Ni²+ ion and dimethyl glyoxime contains_________________ number of hydrogen (H) atoms.

23.

24. 20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is ______________ x 10^-2 M. (Nearest integer)

25. Niobium (Nb) and ruthenium (Ru) have "x" and "y" number of electrons in their respective 4d orbitals. The value of x + y is____________

1.  The perpendicular distance, of the line x-1/2 = y+2/-1 = z + 3/2 from the point P(2,-10,1) is

2. Let E: x² / a² + y²/ b² = 1, a >b and H : x²/A² - y²/ B² = 1. Let the distance between the foci of E and the foci of H be 2√3. If a - A = 2, and the ratio of the eccentricities of E and H is 1/3, then the sum of the lengths of their latus rectums is equal to :

3.  If the system of linear equations:

x + y + 2z = 6, 2x + 3y + az = a + 1, - x - 3y + bz = 2b, where a, b ∈ R, has infinitely many solutions, then 7a + 3b is equal to :

4. The area of the region enclosed by the curves y = x² - 4x + 4 and y² = 16 - 8x is :

5. The sum of all values of θ ∈ [0, 2π] satisfying 2 sin² θ = cos 2θ and 2cos² θ = 3sinθ is :

6.

7. Let the curve z(1 + i) + z^¯  (1-i) = 4, z ∈ C, divide the region |z - 3| ≤ 1 into two parts of areas α and β. Then |α - β| equals:

8. If x = f(y) is the solution of differential of the equation

9. Suppose that the number of terms in an A.P. is 2k, k ∈ Ν. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to :

10. Let a line pass through two distinct points P(-2, -1, 3) and Q, and be parallel to the vector 3^i + 2^j +2 ^k . If the distance of the point Q from the point R(1, 3, 3) is 5, then the square of the area of ΔPQR is equal to :

11. Let P(4,4√3) be a point on the parabola y² = 4ax and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to:

12.

13. In a group of 3 girls and 4 boys, there are two boys B_₁ and B_2. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B_₁ and B_2 are not adjacent to each other, is:

14. For a 3 x 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 x 3 matrix such that |A| = 1/2 and trace (A) = 3. If B = 2 If B = adj(adj(2A)), then the value of |B| + trace (B) equals :

15.

Then the numbers of local maximum and local minimum points of f, respectively, are:

16.

17. Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16). Then the number of many-one functions f : A→B such that I ∈ f(A) is equal to :

18.

19. Let α_θ and β_θ be the distinct roots of 2x²+(cosθ) x - 1 = 0, θ ∈ (0, 2π). If m and M are the minimum and the maximum values of α^4_θ + β^4_θ, then 16(M + m) equals:

20. Let a^→ and b^→ be two unit vectors such that the angle between them is π/3 . If λa^→ +2b^→ and 3a→ − λb→  are perpendicular to each other, then the number of values of λ in [-1, 3] is:

21. Let A(6, 8), B(10 cos α, 10 sin α) and C(-10 sin α, 10 cos α), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid respectively, then (5a−3h+6k+100 sin 2α) is equal to

22. Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)² is equal to

23.

24.

25. Let A = {1, 2, 3). The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is________________