4. Match the List -I with List -II

Choose the correct answer from the options given below:

5. The sequence from the following that would result in giving predominantly 3, 4, 5-tribromoaniline is

6. Given below are two statements:

Statement I: Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes.

Statement II: Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes.

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

7. Given below are two statements:

Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.

Statement II: At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point.

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

8. 10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 moles of HCl and made the volume upto the mark with distilled water. The solution in this flask is

9. Consider the following statements related to temperature dependence of rate constants. Identify the correct statements.

A. The Arrhenius equation holds true only for an elementary homogeneous reaction.

B. The unit of A is same as that of k in Arrhenius equation.

C. At a given temperature, a low activation energy means a fast reaction.

D. A and E_a as used in Arrhenius equation depend on temperature.

E. When E_a >> RT, A and E_a become interdependent.

Choose the correct answer from the options given below:

10. In the following series of reactions identify the major products A and B respectively.

11. Given below are two statements:

Statement I: CrO3 is a stronger oxidizing agent than M0O3.

Statement II: Cr(VI) is more stable than Mo(VI).

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

12.  Fat soluble vitamins are:

A. Vitamin B₁                                            B. Vitamin C                                  C. Vitamin E

D. Vitamin B12                                          E. Vitamin K

Choose the correct answer from the options given below:

13. In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is (Given: Aqueous tension at 300 K = 15 mm Hg)

14. Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCI is (Given: Molar mass of Mg is 24 g mol^-¹.)

15. The major product (P) in the following reaction is :

16. Identify the diamagnetic octahedral complex ions from below:

A. [Mn(CN)_6]³-                                   B. [Co(NH3)_6]^3+                     C. [Fe(CN)_6]^4-        D. [Co(H2O)3F3] Choose the correct answer from the options given below:

17. For electrons in '2s' and '2p' orbitals, the orbital angular momentum values, respectively are

18. Given below are two statements:

Statement I: Hyperconjugation is not a permanent effect.

Statement II: In general, greater the number of alkyl groups attached to a positively charged C-atom, greater is the hyperconjugation interaction and stabilization of the cation.

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

19. Compounds that should not be used as primary standards in titrimetric analysis are:

A. Na_2 Cr_2 O_7                            B. Oxalic acid                        C. NaOH                D. FeSO4.6H₂O

E. Sodium tetraborate

Choose the most appropriate answer from the options given below:

20. What is the correct IUPAC name of

SECTION-B (NUMERICAL VALUE TYPE QUESTIONS)

21. X g of nitrobenzene on nitration gave 4.2 g of m-dinitrobenzene. X =  ______________ g. (nearest integer) [Given: molar mass (in g mol^-¹) C: 12, H: 1, O: 16, N: 14]

22. A perfect gas (0.1 mol) having vector c_v = 1.50R (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is (-) _______________J. (nearest integer) [Given: R = 0.082 L atm K-¹ mol-¹]

23. A sample of n-octane (1.14 g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is 5 kJ K-¹. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K. The magnitude of the heat of combustion of octane at constant volume_____________ kJ mol-¹ (nearest integer).

24. The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula C9H12 is___________

25. Among, Sc, Mn, Co and Cu, identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is _______ B.M.  (in nearest integer).

Mathematics

SECTION-A (MULTIPLE CHOICE QUESTIONS)

1. The area of the region {(x, y): |x - y|≤ y ≤4√x} is

2. The number of solutions of the equation (4-√3) sinx-2√3 cos²x = -4/ 1+√3, x ∈ [-2π, 5π/2] is

3. The sum 1+ 1+3 / 2!+1+3+5/3!+1+3+5+7/4!+... upto ∞ terms, is equal to

4. Each of the angles β and γ that a given line makes with the positive y- and z-axes, respectively, is half of the angle that this line makes with the positive x-axes. Then the sum of all possible values of the angle β is

5. Let A = {-2,-1, 0, 1, 2, 3). Let R be a relation on A defined by xRy if and only if y = max{x, 1). Let l be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l + m + n is equal to

6. If the domain of the function f(x) = log_7 (1 - log_4 (x²- 9x + 18)) is (α, β) ∪ (γ, δ), then α + β + γ+ δ is equal to

7.

8. The distance of the point (7, 10, 11)  from the line x-4/1 = y-4/0 = z-2/3 along the line x-9/2 = y-13/3 = z-17/6 is

9. If the four distinct points (4, 6), (-1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k +r^2 is equal to

10. If the probability that the random variable X takes the value x is given by P(X= x) = k(x+1)3^-x, x = 0, 1, 2, 3 ___________ where k is a constant, then P(X ≥ 3), is equal to

11. Let f: R→R be a function defined by f(x) = ||x+2|-2|x||. If m is the number of points of local minima and n is the number of points of local maxima of f, then m+n is

12. The shortest distance between the curves y² = 8x and x² + y² + 12y + 35 = 0 is :

13. Let C be the circle of minimum area enclosing the ellipse E: x^2/a^2+y^2/b^2 = 1 with eccentricity 1/2 and foci (±2, 0). Let PQR be a variable triangle, whose vertex P is on the circle C and the side QR of length 2a is parallel to the major axis of E and contains the point of intersection of E with the negative y-axis. Then the maximum area of the triangle PQR is:

14. Let f be a function such that f(x) + 3f  (24/x) = 4x, x ≠ 0. Then f(3) + f(8) is equal to

15.

16. Let the equation x(x + 2)(12-k) = 2 have equal roots. Then the distance of the point (k, k/2) from the line 3x + 4y + 5 = 0 is

17. Consider the lines x(3λ + 1) + y (7λ + 2) = 17λ + 5, λ being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the distance of L from the point (3, 6) is d, then the value of d² is

18. Line L₁ of slope 2 and line L₂ of slope 1/2 intersect at the origin O. In the first quadrant, P1, P2, ..., P12 are 12 points on line L₁ and Q1, Q2, ...., Q_9 are 9 points on line L2. Then the total number of triangles, that can be formed having vertices at three of the 22 points O, P1, P2,..., P12, Q1, Q2, ..., Q9, is:

19. Let the Mean and Variance of five observations x_₁ = 1, x_2 = 3, x_3 = a, x_4 = 7 and x_5 = b, a > b, be 5 and 10 respectively. Then the Variance of the observations n + x_n,  n = 1, 2, ...., 5 is

20. Let y = y(x) be the solution of the differential equation dy/dx + 3 (tan²x) y+3y = sec²x, y(0) =  1/3 + e³. Then y (π/4) is equal to

21.

22.

23. Let (1 + x + x²)¹º = a_0 + a_₁ x + a_2 x² +...+ a_20 x²º. If (a_1 + a_3 + a_5 + ..... + a_19) - 11a_2 = 121k, then k is equal to____

24. If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x² - y² - αx + βy + γ = 0, then a + β + γ is equal to ___________.

25.