Physics and Chemistry Questions (PDF)

# Physics and Chemistry Questions ## Page 1 A bullet of mass *m* moving with a speed hits a stationary block of mass *M* at the topmost point and gets embedded in it. If friction is sufficient to prevent slipping then the block: - Must topple down - Must not topple down - May topple down - Will r...

# Physics and Chemistry Questions ## Page 1 A bullet of mass *m* moving with a speed hits a stationary block of mass *M* at the topmost point and gets embedded in it. If friction is sufficient to prevent slipping then the block: - Must topple down - Must not topple down - May topple down - Will remain at rest ## Page 2 In an LRC series circuit at resonance current in the circuit is 10√2 A. If now frequency of the source is changed such that now current lags by 45° than applied voltage in the circuit, which of the following is correct: - Frequency must be increased and current after the change is 10 A - Frequency must be decreased and current after the change is 10 A - Frequency must be decreased and current is same as that of initial value - The given information is insufficient to conclude anything ## Page 3 The dimensions of magnetic field in *M*, *L*, *T* and *C* (coulomb) is given as? - [MLT-1C-1] - [MT2C-2] - [MT-1C-1] - [MT-2C-1] ## Page 4 Choose the correct statement in the shown circuit: (all the resistors are of 1ohms, *x* : is the Resistor in the middle also of 1ohms) - The maximum heat loss is observed in resistor "x". - The current through Battery is 10 A. - The current through resistor "x" is zero. - None of these ## Page 5 A body of mass 32 kg is suspended by a spring balance from the roof of a vertically operating lift and going downward from rest. At the instants the lift has covered 20 m and 50 m, the spring balance showed 30 kg & 36 kg respectively. The velocity of the lift is: - decreasing at 20 m & increasing at 50 m - increasing at 20 m & decreasing at 50 m - continuously decreasing at a constant rate throughout the journey - continuously increasing at constant rate throughout the journey ## Page 6 A small block of mass 20 g and charge 4mC is released on a long smooth inclined plane of inclination angle of 45°, A uniform horizontal magnetic field of 1 T is acting parallel to the surface, as shown in the figure. The time from the start when the block loses contact with the surface of the plane is: - 2s - 3s - 5s - 6s ## Page 7 In the process ABC for an ideal mono-atomic gas, the temperature at states A and C are equal. The heat released in the process BC is Q. The work done in the process A to B is equal to (AB is isobaric and BC is isochoric process): - Q - 2/2Q - 2/3Q - 2Q ## Page 8 If the wavelength of the first line of the Balmer series of hydrogen is 6561Å, find the wavelength of the second line of the series. - 13122Å - 3280Å - 4860Å - 2187Å ## Page 9 In a diode, the diffusion current is *idiffusion* and drift current is *idrift*, then match the column. | Column-I | Column-II | |---|---| | (1) Diode with no biasing | (p) *idiffusion* >> *idrift* | | (2) Diode in forward bias | (q) *idrift* >> *idiffusion* | | (3) Diode in reverse bias without breakdown | (r) *idrift* > *idiffusion* | | (4) Diode in reverse bias with breakdown | (s) *idrift* = *idiffusion* | - A ->s, B -> q, C -> r, D -> p - A -> s, B -> p, C -> r, D -> q - A -> s, B -> q, C -> p, D -> r - A -> q, B -> p, C -> r, D -> s ## Page 10 A body has maximum range *R₁* when projected up the inclined plane. It has the maximum range *R₂* when projected down the plane with same speed as in first case. Then which of the following is maximum range (*R*) for it when projected at certain angle with the horizontal ground and with same speed as in previous two cases? - R = R₁ + R₂ - R = R₂ - R₁ - R = (R₁R₂)/(R₁+R₂) - R = (2R₁R₂)/(R₁+R₂) ## Page 11 Suppose a container is evacuated to leave just one molecule of gas in it. Let, *va* and *urms* represent the average speed and the RMS speed of the gas. - *va* > *urms* - *va* < *urms* - *va* = *urms* - *urms* is undefined. ## Page 12 A circular freeway entrance and exit are commonly banked to control a moving car at 14 m/s. To design similar ramp for 28 m/s one should: - increase the radius by factor 2 - increase the radius by factor 4 - decrease the radius by factor 4 - decrease the radius by factor 2 ## Page 13 In vernier callipers instrument 20 vernier scale divisions concide with 18 main scale divisions where 1 mm =1 main scale division. The least count is: - 0.02 mm - 0.05 mm - 0.1 mm - 0.2 mm ## Page 14 A mercury drop lies between two glass plates separated by a very small distance (see figure). Surface tension of mercury is *T*. Radius of curvature of drop surfaces in a direction parallel to plates is *R*. The other surfaces are flat. The excess pressure for the mercury drop is given by: - *T/R* - *2T/R* - *3T/R* - *T/2R* ## Page 15 The power of biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is: - 3/2 - 4/3 - 9/8 - 5/3 ## Page 16 The amplitude of electric field in a parallel beam of light of intensity 4 Wm-2 is? (round off answer to nearest integer) - 50 - 55 - 60 - 45 ## Page 17 Two identical conducting spheres, *A* and *B*, have equal charges and are separated at a distance such that charge on each of them is essentially uniform on its surface. A third identical conducting neutral sphere *C*, is brought in contact with *A* and then in contact with *B* and removed far away. If initial force between the two spheres *A* and *B* was *F*, then the new force between them would be (Assuming that in calculating both the forces, distance of separation remains same) 3*F*/(*P*), Find integral value of *P*. - 6 - 10 - 8 - 12 ## Page 18 A photon of wavelength 300 nm interacts with a stationary hydrogen atom in ground state. During the interaction, whole energy the photon is transferred to the electron of the atom. State which possibility is correct. (Consider, Plank constant = 4 × 10-15 eVs, velocity of light = 3 x 10⁸m/s, ionisation energy of hydrogen = 13.6eV) - Electron will be knocked out of the atom - Electron will go to any excited state of the atom - Electron will go only to first excited state of the atom - Electron will keep orbiting in the ground state of the atom ## Page 19 A simple pendulum has a time period *T₁* when on the Earth's surface and *T₂* when taken to a height *R* above the Earth's surface, where *R* is the radius of the Earth. The value of *T₂/T₁* is- - 1 - √2 - 4 - 2 ## Page 20 Two coils have a mutual induction 0.005 H. The current changes in the first coil according to the equation *i = im* sin *wt* where *im* = 10 A and ω = 100 rads-1. The maximum value of the emf induced in the second coil is: - 5πV - 4πV - 2πV - πV ## Page 21 The intensity of magnetization of a bar magnet is 5.0 × 10⁴ Am⁻¹. The magnetic length and the area of cross-section of the magnet are 12cm and 1cm² respectively. The magnitude of magnetic moment of this bar magnet is (in SI unit) *M*, find 10*M*. ## Page 22 A wire of length 2 m is clamped horizontally between two fixed support. A mass *m* = 5 kg is hanged from middle of wire. What would be its vertical depression (in cm) in equilibrium? (Young modulus of wire = 2.4 × 10¹¹ N m², cross-sectional area = 1 cm²) Roundoff answer to nearest integer. ## Page 23 Two metal plates each of area 'A' form a parallel plate capacitor with air in between the plates. The distance between the plates is 'd'. A metal plate of thickness 'd/2' and of same area A is inserted between the plates to form two capacitors of capacitances C₁ and C₂ as shown in the figure. If the effective capacitance of the two capacitors is C' and the capacitance of the capacitor initially is C, then C'/C is ## Page 24 The velocity of an object moving in a straight line path is given as a function of time by v = 6t – 3t², where v is in ms-1, t is in s. The average velocity of the object between, t = 0 and t = 2 s is? ## Page 25 The densities of two solid spheres A and B of the same radii R vary with radial distance r as *ρA*(r) = *k*(r/R)⁵ and *ρB*(r) = *k*(r/R)⁵ respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are *IA* and *IB*, respectively. If *IB/IA* = *n*, the value of *n* is ## Page 26 In thin layer chromatography, a substance moved by a distance of 4 cm, whereas the solvent moved by a distance of 5 cm. Then the value of retardation factor (*Rf*) is--- - 0.8 - 1.0 - 9.0 - 1.25 ## Page 27 Match the following. | Column I | Column II | |---|---| | A. sp³² | (i) [Co(NH₃)₆]³⁺ | | B. dsp² | (ii) [Ni(CO)₄] | | C. sp³d² | (iii) [Pt(NH₃)₂Cl₂ | | D. dsp³ | (iv) [CoF₆]³⁻ | | | (v) [Fe(CO)₅] | A B C D are respectively - (v) (ii) (iv) (iii) - (ii) (iii) (iv) (v) - (ii) (iii) (i) (v) - (iii) (ii) (iv) (i) ## Page 28 For the cell reaction 2Fe³⁺(aq) + 2I⁻(aq) → 2Fe²⁺(aq) + I₂(aq) *E°cell* = 0.24 V at 298 K. The standard Gibbs energy (△rG°) of the cell reaction is: [Given that Faraday constant F = 96500 Cmol⁻¹] - -46.32 kJ mol⁻¹ - -23.16 kJ mol⁻¹ - 46.32 kJ mol⁻¹ - 23.16 kJ mol⁻¹ ## Page 29 Which reaction condition would be best to perform the following transformation? - (i) NaOH, (ii) MeI - (i) HBr, (ii) Mg, (iii) MeI - (i) H₃C-C=O, (ii) MeMgBr, (iii) POCl₃ - (i) PCC, (ii) MeMgBr, (iii) POCl₃ ## Page 30 Which among the following is an example of ionization isomer? - [Co(NH₃)₅SO₄]Br and [Co(NH₃)₅Br]SO₄ - [Co(NH₃)₅NO₂]Cl and [Co(NH₃)₅ONO]Cl₂ - [Co(H₂O)₆]Cl₃ and [Co(H₂O)₅Cl]Cl₂.H₂O - [Co(NH₃)₃][Cr(CN)₆] and [Cr(NH₃)₆][Co(CN)₆] ## Page 31 Assume that the decomposition of HNO₃ is 4HNO₃(g) = 4NO₂(g) + 2H₂O(g) + O₂(g) and the reaction approaches equilibrium at 400 K & 30 atm pressure. At equilibrium the partial pressure of HNO₃ is 2 atm. Find Kc at 400 K (R = 0.08l - atm/K - mol) - 4 - 8 - 16 - 32 ## Page 32 Give the reactivity in the decreasing order of the following nucleophiles towards nucleophilic addition reaction with compound A(F₃C- = -CF₃). - (I) CH₃O⁻ - (II) C₂H₅O⁻ - (III) CH₃COO⁻ - (IV) CH₃SO₃⁻ - (II) > (I) > (III) > (IV) - (IV) > (III) > (I) > (II) - (I) > (II) > (IV) > (III) - (III) > (IV) > (II) > (I) ## Page 33 A metal gives two chlorides A and B. A gives black precipitate with NH₄OH and B gives white. With KI, B gives a red precipitate soluble in excess of KI. A and B are respectively : - Hg₂Cl₂ and HgCl₂ - HgCl₂ and Hg₂Cl₂ - HgCl₂ and ZnCl₂ - ZnCl₂ and HgCl₂₄ ## Page 34 An organic compound 'X' on treatment with pyridinium chloro chromate in dichloromethane gives compound 'Y'. Compound 'Y', reacts with I₂ and alkali to form triiodomethane. The compound 'X' is- - C₂H₅OH - CH₃CHO - CH₃COCH₃ - CH₃COOH ## Page 35 Which of the following compounds is colored and paramagnetic? - CuCl - K₃[Cu(CN)₄] - CuF₂ - [Cu(CH₃CN)₄]BF₄ ## Page 36 Among the triatomic molecules/ions, BeCl₂, N₃⁻, N₂O, NO₂, O₃, SCl₂, ICl₂, I₃⁻ and XeF₂, the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the d-orbital(s) is [Atomic number: S = 16, Cl = 17, I = 53 and Xe = 54] - 3 - 5 - 6 - 4 ## Page 37 Which of the following statement(s) is/are not true about the following decomposition reaction? 2KClO₃ → 2KCl + 3O₂ - (i) Potassium is undergoing oxidation - (ii) Chlorine is undergoing oxidation - (iii) Oxygen is reduced - (iv) None of the species are undergoing oxidation or reduction - (i) and (ii) - (i) and (iv) - (i) and (iii) - All of these ## Page 38 Assertion: PbO₂ is an oxidising agent and reduced to PbO. Reason: Stability of Pb(II) > Pb(IV) on account of inert pair effect. - Both Assertion and Reason are true and Reason is the correct explanation *of* Assertion. - Both Assertion and Reason are true *but* Reason is NOT the correct explanation *of* Assertion. - Assertion is true but Reason is false - Assertion is false but Reason is true. ## Page 39 2 g of a non-electrolyte solute (molar mass is 500 g mol⁻¹) was dissolved in 57.3 g of xylene. If the freezing point depression constant *Kf* of xylene is 4.3 K kg mol⁻¹. Then, the depression in freezing point of xylene is. - 57.3 K - 0.3 K - 4.3 K - 0.002 K ## Page 40 Evaluate the following statements about Group 13 elements: - (A) Atomic radius decreases down the group from B to TI in a regular manner. - (B) Electronegativity decreases gradually down the group from B to TI. - (C) Aluminium can form compounds with a covalency of 6 due to the presence of vacant d-orbitals. - (D) Compounds of boron, like boric acid (H₃BO₃), exhibit significant pπ – pπ character. - (E) Boron and silicon exhibit similar chemical properties, such as covalent bonding and acidic oxide formation. Choose the correct combination of statements from the options below: - (A), (B), and (D) only - (B), (C), and (E) only - (C), (D), and (E) only - (B), (D), and (E) only ## Page 41 Consider the following compounds. Order of basicity of these compounds in decreasing order is - 4>1>2>3 - 1>3>4> 2 - 2>3>4> 1 - 1>3>2>4 ## Page 42 The correct option(s) to distinguish nitrate salts of Mn²⁺ and Cu²⁺ taken separately is (are) - (1) Mn²⁺ shows the characteristic green colour in the flame test - (2) only Cu²⁺ shows the formation of precipitate by passing H₂S in acidic medium - (3) only Mn²⁺ shows the formation of precipitate by passing H₂S in faintly basic medium - (4) Cu²⁺ | Cu has higher reduction potential than Mn²⁺ | Mn (measured under similar conditions) - 1,2 - 1,3 - 2,4 - 1,2,4 ## Page 43 A carbonyl compound of formula C₉H₁₀O(A), which is a benzene derivative gives orange precipitate with 2,4-D.N.P. and also gives yellow precipitate with I₂ in presence of aqueous NaOH. The total no. of isomers possible for 'A' are - 2 - 4 - 5 - 3 ## Page 44 HCl gas is passed into water, yielding a solution of density 1.095 g mL⁻¹ and containing 30% HCl by weight. Calculate the molarity of the solution. - 3 - 6 - 12 - 9 ## Page 45 Which one of the following statements is correct? - Starch on complete hydrolysis gives fructose - Lactose on hydrolysis gives glucose and fructose - Glucose on slow oxidation to CO₂ and H₂O by enzyme does not liberate energy - Cellulose is not digestible in human body ## Page 46 The following steps are involved in the manufacturing of potassium dichromate: Fused with Na₂CO₃ Chromite ore (x) Solid mass in the presence of air Brown residue Add water and filter conc.H₂SO₄ Solution (Y) Solution (Z) What is the difference in the oxidation number of Cr between X and Y? ## Page 47 Find the quantum number 'n' corresponding to the excited state of He⁺ ion, if on transition to the ground state that ion emits two photons in succession with wavelengths 108.5 and 30.4 nm. ## Page 48 For a compound with empirical formula C₇H₈O, how many aromatic structures are possible? ## Page 49 The following data were obtained during the first order thermal decomposition of SO₂Cl₂ at a constant volume SO₂Cl₂(g) → SO₂(g) + Cl₂(g) | Experiment | Time/s⁻¹ | Total pressure/ atm | |---|---|---| | 1 | 0 | 0.5 | | 2 | 100 | 0.6 | Calculate y when the rate of the reaction y × 10⁻⁴ when total pressure is 0.65 atm. Given (log5 = 0.699, log2 = 0.301) (round off to nearest integer) ## Page 50 Identify the total number of atoms in product Q in the given sequence of reaction NaNO₂+HCl C₆H₅NH₂ ← Cu₂(CN)₂ H₂O/H⁺ NaOH/CaO, X → YZ ← P Cl₂, hv(Excess) → Q ## Page 51 The sum of the roots (real or complex) of the equation x²⁰⁰¹ + (-x)²⁰⁰ = 0 is - 2000 - 2001 - 1000 - 500 ## Page 52 If f(1/(3x-2)) = x + 4, x≠2/3, and ∫f(x)dx = Ax + Bl*n*|3x - 2| *+ C*, then 3B - A = - 3 - 8/3 - 21 - 10 - 1/3 ## Page 53 If principal argument of *z₀* satisfying |*z* - 3| ≤ √2 and arg(*z* - 5i) = π/4 simultaneously is 0, then identify the incorrect statement? - *z₀* = √17 - tan(2*θ₀*) = 8/15 - tan(*θ₀*) = 4 - *z₀* - 5i = 4√2 ## Page 54 The minimum value of f(x) = |x-1|+|2x-1|+|3x-1| + ...... + |119x-1| occurs at x. Then *x* is equal to- - 1/84 - 1/51 - 1/80 - 1/94 ## Page 55 The reflection of the point P(1,0,0) in the line *(x-1)/2 = (y+1)/-3 = (z+10)/8 is- - (3,-4,-2) - (5,-8,-4) - (1,-1,-10) - (2,-3,8) ## Page 56 Let A = {1, 2, 3, 4}. Let R be a relation on A defined by *xRy* if and only if *x* < 2*y*. Let *m* be the total number of elements in *R*. Let *n* be the minimum number of elements to be added to make R symmetric, and *p* be the minimum number of elements to be added to make *R* reflexive. Find *m +2n + p*. - 17 - 18 - 19 - 20 ## Page 57 The orthocentre and the centroid of △ABC are (5,8) and (3,14/3) respectively. The equation of the side BC is *x - y = 0*. Given that the image of the orthocentre of a triangle with respect to any side lies on the circumcircle of that triangle, then the diameter of the circumcircle of △ABC is. - √10 - 2√10 - 4√10 - 8√10 ## Page 58 Consider all rectangles lying in the region {(x, y) ∈ R x R : 0 ≤ x ≤ π/2 and 0 ≤ y ≤ 2sin(2x)} and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is..... - 3π/2 - π - π/2 - π³/2 ## Page 59 The derivative of cos(2tan⁻¹(√(1+z²)/(1-z²))- 2cos⁻¹(√(1-z²)/(1+z²)) w.r. to z is - 1/(√(1-z²)) - 1/(√(1+z²)) - 2/(√(1-z²)) - 2/(√(1+z²)) ## Page 60 The line *x + y = 1* meets *x*-axis at *A* and *y*-axis at *B*; *P* is the mid-point of *AB*; *P₁* is the foot of the perpendicular from *P* to *OA*; *M₁* is that of *P₁* on *OP*; *P₂* is that of *M₁* on *OA*; *M₂* is that of *P₂* on *OP*; *P₃* is that of *M₂* on *OA*; and so on. If *Pₙ* denotes the *n*th foot of the perpendicular on *OA*; then *OPₙ* is equal to - (1/2)⁻¹ - (1/2)ⁿ/(n+1) - (1/2)ⁿ⁻¹/(n+1) - None of these. ## Page 61 A function *y = f(x)* satisfies (*x + 1*)*f'(x)* - 2(*x² + x*)*f(x)* = *e^(z²)* / (*x+1)*, ∀*x* > -1. If *f(0) = 5*, then *f(x)* is - *e^(z²)* / (*x+1)* - *e^(z²)* / (*x+1)* - *e^(z²)* / (*x+1)* - *e^(z²)* / (*x+1)* ## Page 62 A is one among the 8 horses in a race. A is to be ridden by one of the 3 jockeys P, Q, R. If P rides A, all the horses are equally likely to win, if Q rides A, his chances are doubled and if R rides A, his chance are tripled. A die is thrown. If 1 or 2 or 3 appears then P rides A, if 4 or 5 appears then Q rides A, otherwise R rides A. Then the probability that A wins is - 1/12 - 3/16 - 5/24 - 7/44 ## Page 63 If A and B are square matrices of order 3 such that |A| = 3 and |B| = 2, then the value of |A⁻¹ adj(adj(3A⁻¹))| is equal to: - 27 - 27/4 - 1/108 - 1/4 ## Page 64 Let ABCD is a parallelogram where AB = a, AD = b, |a| = |b| = 2 and a x b + a. b = √2|a||b| (b.b > 0), then area of this parallelogram, is (in square units)- - 2√2 - 2 - √2 - 8√2 ## Page 65 Number of vectors *V₁* = *a₁i + b₁j + c₁k* and *V₂* = *a₂i + b₂j + c₂k* such that *V₁* and *V₂* are mutually perpendicular, where a₁, *b₁*, *c₁*, *a₂*, *b₂*, *c₂* ∈ {-2, -1, 1, 2} is equal to - 288 - 278 - 164 - 184 ## Page 66 If radii of the smallest and largest circle passing through origin and touching the circle *x² + y² + 4x + 6y - 3 = 0* are *r₁* and *r₂* respectively, then *r₁r₂* is equal to - - 1/4 - 7/4 - 3√4 - 9√4 ## Page 67 The range of the function *y = 2sin⁻¹x² + [1/x²] + cos⁻¹x²* is (where, [.] denotes the greatest integer function) - (0, π) - {π/2, π} - {π/4, π/2} - {0, π/2} ## Page 68 Let α and β be the roots of the equation *x² + 4x + 13 = 0*. Define *Sₙ* = *αⁿ + βⁿ*. *S₁₂ + 2S₁₁ - 3S₁₀* = 156. If: 4*S₁₀* = *aS₈* - *b*, find the value of *a + b* given that: - 80 - 85 - 91 - 95 ## Page 69 If *f(x) = limt→∞* (sin²(t-x))/(t+x)sin(t-x); ∀*x* ∈ R then number of roots of the equation *f(x)* (|*x² - 1*) = 1 is - 2 - 3 - 4 - 5 ## Page 70 All the words formed by writing all the letters of word ZENITH are arranged as in English dictionary. Now the position of word ZENITH is (from beginning) - 598 - 602 - 532 - 616 ## Page 71 The sequence (*aₙ*⁻¹)ₙ ∈ N is an arithmetical progression and d is its common difference. If Limₙ→∞ (1 converges to *1/4* and *a₁ = 8*, then find the value of *d* - 4 - 1 - 2 - 3 ## Page 72 Given *a, b ∈ {0,1,2,..., 6}*. Consider the system of equations *x + y + z = 4* *2x + y + 3z = 6* *x + 2y + az = b* If the number of ordered pairs (*a, b*), so that the system of equations has unique solution is *A*, then the value of *A* is equal to ## Page 73 Let *f[1,∞) → [2,0∞)* be a differentiable function such that *f(1) = 1*. If *6* ∫¹ˣ *f(t)dt* = 3*x f(x)* - *x³* for all *x ≥ 1*, then the value of 3*f(2)* is ## Page 74 The shortest distance between the following pair of lines: *λ = (1 + 2i) - 4k + x(2i + 3j + 6k)* and *μ = (3 + 3i - 5k + μ(2j + 3i) + 6k)* is √293/(K). Find the value of *K*. ## Page 75 The value of ∫₀¹⁰⁰ {√*x*}*dx* (where {*x*} is the fractional part of *x* is (mark answer to nearest integer)