CHEMISTRY

1.  Which of the following pairs of gases contains the same number of molecules?

2. Formation of CO and CO2 illustrates the law of ————–.

3. Which of the following statements is/are true for pure substances?

4. Assertion (A): At 273 K & 1 bar 22.4 L of both oxygen & CO2 contains an equal number of molecules.

Reason (R): According to Avogadro’s law, at a constant temperature & pressure equal volumes of all gases contain an equal number of molecules

5. What will be the molarity of a solution, which contains 5.85 g of NaCl(s) per 500 mL?

6. The number of atoms present in one mole of an element is equal to Avogadro number. Which of the following element contains the greatest number of atoms?

7. One mole of any substance contains 6.022 × 10²³ atoms/molecules. Number of molecules of H2 SO4 present in 100 mL of 0.02M H2SO4 solution is ______.

8. The empirical formula and molecular mass of a compound are CH2O and 180 g respectively. What will be the molecular formula of the compound?

9. Which of the following reactions is not correct according to the law of conservation of mass.

10. Assertion (A): One atomic mass unit is defined as one twelfth of the mass of one carbon-12 atom.

Reason (R): Carbon-12 isotope is the most abundant isotope of carbon and has been chosen as standard.

11. Match the following:

(i) 88 g of CO2                                               (a) 0.25 mol

(ii) 6.022 ×1023 molecules of H2O           (b) 2 mol

(iii) 5.6 litres of O2 at STP                          (c) 1 mol

(iv) 96 g of O2                                               (d) 6.022 × 1023 molecules

(v) 1 mol of any gas                                      (e) 3 mol

12. Which of the following is not an example of redox reaction?

13. The oxidation number of an element in a compound is evaluated on the basis of certain rules. Which of the following rules is not correct in this respect?

14. In which of the following compounds, an element exhibits two different oxidation states.

15. Identify disproportionation reaction

16. Which of the following elements does not show disproportionation tendency?

17. Which of the following arrangements represent increasing oxidation number of the central atom?

18. Match Column I with Column II for the oxidation states of the central atoms.

Column I               Column I

(i) Cr2O7 2–        (a) + 3

(ii) MnO4 –         (b) + 4

(iii) VO3 –           (c) + 5

(iv) FeF6 3–       (d) + 6

                              (e) + 7

19. Assertion (A): The decomposition of hydrogen peroxide to form water and oxygen is an example of disproportionation reaction.

Reason (R): The oxygen of peroxide is in –1 oxidation state and it is converted to zero oxidation state in O2 and –2 oxidation state in H2O.

20. Assertion (A): Among halogens fluorine is the best oxidant.

Reason (R): Fluorine is the most electronegative atom .

21. The most powerful oxidising agent among the following is:

22. Consider the following reaction:

Zn + Cu^2+ → Zn^2+ + Cu

With reference to the above, which one of the following is the correct statement?

23. Reduction never involves:

24. In the reaction

3Br2 + 6CO3²- + 3H2O → 5Br – + BrO3– + 6HCO3–

25. The oxidation number of Cr in K2Cr2O7 is:

MATHS

1. n-1ˆC_r = (kˆ2−8)nˆC_r+1 if and only if :

2. The distance, of the point (7, -2, 11) from the line x-6/1 = y-4/0=z-8/3 along the line x-5/2 = y-1/-3=z-5/6 is

3. The number of common terms in the progressions 4, 9, 14, 19,..., up to 25th term and 3, 6, 9, 12, ..., up to 37th term is:

4. If the shortest distance between the lines x-4/1 = y+1/2= z/-3 and x-λ/2  =y +1/4 = z-2/-5 is 6/√5

then the sum of all possible values of λ is

5. Let S = {1, 2, 3, ..., 10}. Suppose M is the set of all the subsets of S, then the relation R = {(A, B): A∩ B ≠ Φ; А, B ∈ M} is:

6. Statement-I: f(-x) is the inverse of the matrix f(x).

Statement-II: f(x) f(y) = f(x + y).

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

7. The function f: N - {1} → N; defined by f(n) = the A highest prime factor of n, is:

8.

9.

10. The 20th term from the end of the progression 20, 19(1/4), 18(1/2), 17(3/4), ....–129 (1/4) is:

11.

12. If the sum of squares of all real values of α, for which the lines 2x-y+3=0,6x+3y+1=0 and αx+2y-2= 0 do not form a triangle is p, then the greatest integer less than or equal to p is.... .

13. If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

14. In an A.P., the sixth terms a_6 = 2. If the a_1, a_4, a_5, is the greatest, then the common difference of the A.P., is equal to

15. If z = 1/2 -2i, is such that | z+ 1| = α z +β(1+i), i =√-1 and α, β∈R, then α+β is equal to

16. Let (5, a/4) be the circumcenter of a triangle with vertices A(a, -2), B(a, 6)  and C(a/4, -2). Let α denote the circumradius, β denote the area and γ denote the perimeter of the triangle. Then α + β + γ is

17.

18. Let PQR be a triangle with R(-1, 4, 2). Suppose M(2, 1, 2) is the mid point of PQ. The distance of the centroid of ΔPQR from the point of intersection of the line x-2/0 = y/2 = z+3/-1 and x-1/1 = y+3/-3 = z+1/1 is

19. All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is ___________________ .

20. If 11ˆ C_1/2 +11ˆC_2/3+ ... + 11ˆC_9/10 = n/m with gcd (n,m) = 1, then n +m is equal to ____________

21.  The sum of the |p^-1 AP-2l| is equal to

22. Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

23. Let P(3, 2, 3); Q(4, 6, 2) and R(7, 3, 2) be the vertices of ΔPQR. Then, the angle ∠QPR is

24. If each term of a geometric progression a_1, a_2, a_3, ... with a_1 = 1/8 and a_2 ≠ a_₁, is the arithmetic mean of the next two terms and S_n = a_1 + a_₂ + ... + a_n, then S_20-S_18 is equal to

25. Let O be the origin, and M and N be the points on the lines x-5/4 = y-4/1 = z-5/3 and x+8/12 = y +2/5 = z +11/9 respectively such that MN is the shortest distance between the given lines. Then vector OM. vector ON is equal to

PHYSICS

1. A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a^4b^3/c^2.  The percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is

2. Two resistances are given as R_₁ = (10 ± 0.5) Ω and R_2 = (15 ± 0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is

3. A cylindrical wire of mass (0.4 ± 0.01) g has length (8 ± 0.04) cm and radius (6±0.03) mm. The maximum error in its density will be

4. Given below are two statements:

Statement I: Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statement II: Au < Parsec (Pc) < ly In the light of the above statements, choose the most appropriate answer from the options given below

5. Match List I with List II.

List-I                                                                List-II

A. Torque                                                    I. [M^1L^1T^-2A^-2]

B. Magnetic field                                       II. [L^2A^1]

C. Magnetic moment                                III. [M^1T^-2A^-1]

D. Permeability of free space                  IV. [M^1L^2T^-2]

Choose the correct answer from the options given below.

6. Match List I with List II.

List I                                                                                         List II

A. Torque                                                                             I. ML^-2T^-2

B. Stress                                                                              II. ML^2T^-2

C. Pressure gradient                                                         III. ML^-1T^-1

D. Coefficient of viscosity                                                IV. ML^-1T^-2

Choose the correct answer from the options given below.

7. From the v-t graph shown, the ratio of distance to displacement in 25 s of motion is

8. 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

9. An object moves with speed v_1, v_2 and v_3 along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be

10. A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10s the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity- time curve for total time t = 20 s will be (Take g = 10 m/s²).

11. The velocity of a particle is v = v_o + gt + Ft². Its position is x = 0 at t = 0; then its displacement after time        (t = 1) is

12. The velocity of a particle is v = v_o + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

13. Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?

14. A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be

15. A particle moves in a straight line so that its displacement x at any time t is given by x² = 1 + t². Its acceleration at any time t is x^-n where n =________________

16. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at        (4 + x) cm inside the block. The value of x is

17. A ball is thrown up with a certain velocity so that is reaches a height h. Find the ratio of the two different times of the ball reaching h/3 in both the directions.

18. A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is

19. The speed of a swimmer is 4 km h^-1 in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km, he reaches a point 750 m down the stream on the opposite bank. The speed of the river water is ____________ km h^-1.

20. At time t = 0 a particle starts travelling from a height 7z ̂ cm in a plane keeping z coordinate constant. At any instant of time it's position along the x ̂ and y ̂ directions are defined as 3t and 5t^3 respectively. At t = 1 s acceleration of the particle will be

21. Two projectile thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

22. 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

23. A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s² and then climbs up with an acceleration of 5 m/s². Choose the correct option (g = 10 m/s²)

24. Two masses M₁ and M₂ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M₂ is twice that of M₁, the acceleration of the system is a₁. When the mass M₂ is thrice that of M₁, the acceleration of the system is a₂. The ratio a_1/a_2 will be

25. A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne)