1. A ball of mass 100 g is projected with  velocity 20m/s at 60° with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

2.  A small rigid spherical ball of mass  M is dropped in a long vertical tube containing glycerine.  The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (Consider g as acceleration due to gravity)

3.A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of green light of wavelength 550 nm? [Assume that the light is incident nearly perpendicular to the glass surface.]

4. Given are statements for certain thermodynamic variables.

(A) Internal energy, volume (V) and mass (M) are extensive variables.

(B) Pressure (P), temperature (T) and density (p) are intensive variables.

(C) Volume (V), temperature (T) and density (p) are intensive variables.

(D) Mass (M), temperature (1) and internal energy are extensive variables. Choose the correct answer from the options given below.

5. A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

6. A light source of wavelength A illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV. If the same surface is illuminated by a light source of wavelength λ/2, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV)

7. To obtain the given truth table, following logic gate should be placed at G

8. A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is Io. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

9. The maximum percentage error in the measurement of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g, radius of wire =(0.50± 0.01)cm, length of wire = (10.00±0.05)cm]

10. The torque due to the force (2 î + j + 2k) about the origin, acting on a particle whose position vector is (î+j+k), would be

11. A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 x 10^5 ms^-1. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is x × 10^4 N/C. The value of x is_________________

Take the mass of the proton = 1.6 x 10^-27 kg.

12.Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5A and 4A respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is x × 10^-5T. The value of x is_________________. Take permeability of free space as μο = 4π × 10^-7 SI units.

13. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below.

14. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on Earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below.

15. A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be

Chemistry

1. The alkane from below having two secondary hydrogens is

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

3. 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 :

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

5. The species which does not undergo disproportionation reaction is

6. Arrange the following compounds in increasing order of their dipole moment: HBr, H2S, NF3 and CHCl3

7. 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:

8. 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:

9. Given below are two statements: Statement (I): A spectral line will be observed for a 2px →2py transition. Statement (II): 2px and 2py are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below :

10. The compound with molecular formula C6H6, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has____________ π electrons.

11. The complex of Ni^2+ ion and dimethyl glyoxime contains___________  number of hydrogen (H) atoms.

12. 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)

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

14. Given below are two statements: . Statement I: Fructose does not contain an group but still reduces Tollens' reagent. aldehydic Statement II: In the presence of base, fructose undergoes rearrangement to give glucose. In the light of the above statments, choose the correct answer from the options given below

15. The element that does not belong to the same period of the remaining elements (modern periodic table) is

Mathematics

1. 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:

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

3. Suppose that the number of terms in an A.P. is 2k, k∈N. 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 :

4. Let a line pass through two distinct points P(-2, -1, 3) and Q, and be parallel to the vector 3i + 2j + +2k. 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:

5. 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 = adj(adj(2A)),|A| then the value of |B| + trace (B) equals :

6. Let α, β, γ and δ be the coefficients of x^7, x^5, x^3 and x respectively in the expansion of S +(x-√x³-1)^5+(x-√x^3-1)^5, x> 1. If u and v satisfy 3 -1 the equations αu + βν = 18, ϒυ + δv = 20, then u + v equals :

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

8. 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

9. Let the distance between two parallel lines be 5 units a 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 ____________

10.Let A = {1, 2, 3}. The number of relations on A, 10 containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is _________________

11. One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is

12. Let the area of a ΔPQR with vertices P(5, 4), Q(-2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are o(2,14/5) and C(c, d) respectively, then c + 2d is equal to

13. Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on 3 the set (1, 2, 3, 4). Then the minimum number of elements, needed to be added in so that becomes an equivalence relation, is:

14. If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

15. The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is