Mathongo Paper 6 (3) Physics PDF

# Question Paper ## Physics Single Correct (Maximum Marks: 80) ### Question No. 1 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. An electric dipole has the magnitude of its charge as *q* and its dipole moment is *p*. It is placed in a u...

# Question Paper ## Physics Single Correct (Maximum Marks: 80) ### Question No. 1 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. An electric dipole has the magnitude of its charge as *q* and its dipole moment is *p*. It is placed in a uniform electric field *E*. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively A. 2*q*E and minimum B. *q*E and *p*E C. Zero and minimum D. *q*E and maximum ### Question No. 2 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. What should be the characteristic of fuse wire? A. High melting point, high specific resistance. B. Low melting point, low specific resistance. C. High melting point, low specific resistance. D. Low melting point, high specific resistance. ### Question No. 3 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A charge *q* is uniformly distributed on a ring of radius *r*. A sphere of an equal radius is constructed with its centre lying on the periphery of the ring. The flux of electric field through the surface of the sphere will be A. $q/ε_0$ B. $q/2ε_0$ C. $q/3ε_0$ D. $q/4ε_0$ ### Question No. 4 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. In the circuit shown (figure), calculate the current through 6V battery. <br> The image describes a circuit with four resistors connected in a complex configuration. - One 6V battery is connected to two resistors in series: 2 Ω, 4 Ω. - Another 5V battery is connected to two resistors in series: 2 Ω, 3 Ω. - The two series are connected in parallel to each other. - There is also another 4V battery connected across one of the 2 Ω resistors in the first series. <br> A. (1/4) A B. (1/8) A C. (1/2) A D. None of these ### Question No. 5 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. **Assertion**: The force between the plates of a parallel plate capacitor is proportional to charge on it. **Reason**: Electric force is equal to charge per unit area. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion. C. If assertion is true but reason is false. D. If both assertion and reason are false. ### Question No. 6 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. In an experiment according to the set up, when *E1* = 12V and internal resistance zero, *e* = 2V. The galvanometer reads zero, then *X* would be- <br> The image describes a circuit with two batteries connected in series and a galvanometer in between. - Battery *E1* is connected to 500 Ω resistor and then to the galvanometer. - The galvanometer is then connected to another resistor *X* and then to battery *e*. A. 200 B. 500 C. 100 D. 10 ### Question No. 7 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Two thin dielectric slabs of dielectric constants *K1* and *K2*( *K1*<*K2* ) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field ' *E* ' between the plates with distance ' *d* ' as measured from plate *P* is correctly shown by : <br> The image describes a parallel plate capacitor with two dielectric slabs inserted in between the two plates. - Both slabs have different dielectric constants. <br> A. The graph of *E* against *d* is a horizontal line with a step up. B. The graph of *E* against *d* is a horizontal line with a step down. C. The graph of *E* against *d* is a step-like function with two steps, each of which is horizontal. D. The graph of *E* against *d* is a step-like function with two steps, each of which is horizontal; the first step is higher than the second. ### Question No. 8 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A hollow cylinder has a charge *q* placed at its centre. If *Φ* is the electric flux (in Vm) associated with the curved surface *B*, the flux linked with the plane surface *A* is <br> The image describes a cylindrical shape with an empty space inside, where a point charge is placed at the centre. The area *B* refers to the curved surface. The area *A* refers to one of the two flat ends of the cylinder. A. 1/2 (q/ε₀ - Φ) B. Φ/2ε₀ C. Φ/ε₀ D. ε₀Φ - Φ ### Question No. 9 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A fully charged parallel plate capacitor of 1μF capacity is discharging through a resistor. If the energy of the capacitor reduces to half in one second, then the value of resistance will be A. 2×10⁶ Ω/ln2 B. 2×10³ Ω/ln2 C. 10⁶ Ω/ln2 D. 10³ Ω/ln2 ### Question No. 10 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Column - I gives certain physical terms associated with flow of current through a metallic connector. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations: | Column -I | Column - II | |:---|:---| | (A) Drift Velocity | (P) m/τ | | (B) Electrical Resistivity | (Q) ne²ντ | | (C) Relaxation Period | (R) E/ρ | | (D) Current Density | (S) J/σ | A. (A) - (R), (B) - (S), (C) - (P), (D) - (Q) B. (A) - (R), (B) - (S), (C) - (Q), (D) - (P) C. (A) - (R), (B) - (P), (C) - (S), (D) - (Q) D. (A) - (R), (B) - (Q), (C) - (S), (D) - (P) ### Question No. 11 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Four metal plates are arranged as shown in the figure. Capacitance between X and Y (*A* → Area of each plate, *d* → distance between the plates) is: <br> The image describes four parallel metal plates, separated by a distance *d*. They are labeled 1, 2, 3, 4 from left to right. The leftmost plate is connected to point *X* and the rightmost plate is connected to point *Y*. <br> A. ε₀A/d B. 2ε₀A/d C. 3ε₀A/d D. 3ε₀A/d ### Question No. 12 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A charge particle is moving along electric field as shown in figure. What is horizontal displacement of the charge particle when it descends a distance of *y* meter? Given: *q*/*m* = 9.6×10⁷C/kg, *E* = 5×10⁵V/m, *y* = 84 cm, *g* = 10 m/s² <br> The image describes a charge particle moving along a vertical line. The direction of the electric field is downwards. <br> A. 4.03×10¹² m B. 4.03×10¹⁰ m C. 4.03×10^-8 m D. 4.03×10⁸ m ### Question No. 13 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A voltmeter of resistance 200000Ω reads 5 volt. To make it read 20 volt, the extra resistance required is A. 400000 Ω in parallel B. 600000 Ω in parallel C. 600000 Ω in series D. 400000 Ω in series ### Question No. 14 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A clock face has negative charges -*q*, -2*q*, 3*q*, ...., -12*q* fixed at the position of the corresponding numerals on the dial. The clock hands do not disturb the net field due to point charges. At what time does the hour hand point in the same direction of the electric field at the centre of the dial? A. 3:30 B. 9:30 C. 6:30 D. 12:30 ### Question No. 15 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A 10V battery with internal resistance 1Ω and a 15V battery with internal resistance 0.6Ω are connected in parallel to a voltmeter of resistance 1Ω (see figure). The readings in the ideal ammeter is: <br> The image describes the two batteries in parallel, connected to a voltmeter and an ammeter. A. 115A/11 B. 105A/11 C. 105A/21 D. 115A/21 ### Question No. 16 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A constant potential difference between A and B is applied. When the switch is shifted from position P to position Q, then <br> The image describes a circuit with a single battery connected to a resistor. Two switches are connected in parallel across the resistor. <br> A. Charge on 2μF capacitor is approximately 13μC. B. Potential difference across 3μF capacitor is approximately 4.3V. C. Potential difference across 1μF capacitor is approximately 11V. D. All of the above. ### Question No. 17 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Two concentric conducting thin spherical shells A and B having radii *r_A* and *r_B* (*r_B*>*r_A*) are charged to *Q_A* and -*Q_B* (*|Q_B|>|Q_A*). The electrical potential along a line (passing through the centre is) <br> The image describes two concentric spherical shells - A and B. Shell A is inside Shell B. <br> A. The potential decreases from its value at *r_A* to its value at *r_B*. B. The potential increases from its value at *r_A* to its value at *r_B*. C. The potential decreases from its value at *r_A* to its value at *r_B* and then increases to *∞*. D. The potential increases from its value at *r_A* to *∞* and then decreases to its value at *r_B*. ### Question No. 18 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Calculate *I* for the given circuit diagram. <br> The image describes a circuit with five resistors connected in a complex configuration. - Each resistor is 5Ω and is connected with the following configuration: - 5Ω resistor is connected to a battery of 25V. - Another 5Ω resistor is connected in series with the previous one. - Two more 5Ω resistors are connected in parallel to these two resistors. - The last 5Ω resistor is connected in series with the above parallel configuration. - The *I* is marked in the circuit, which is the voltage across the 25V battery. <br> A. 10A B. 5A C. 2.5A D. 20A ### Question No. 19 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. **Assertion:** A charged particle free to move in an electric field always moves along an electric field line. **Reason:** The electric field lines diverge from a negative charge and converge at a positive charge. A. If both assertion and reason are true and reason is the correct explanation of assertion. B. If both assertion and reason are true but reason is not the correct explanation of assertion. C. If assertion is true but reason is false. D. If both assertion and reason are false. ### Question No. 20 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A conducting sphere of radius *R* carrying charge *Q* lies inside an uncharged conducting shell of radius 2*R*. If they are joined by a metal wire, the amount of heat that will be produced is: A. 1/4πε₀ *Q²*/4*R* B. 1/4πε₀ *Q²*/2*R* C. 1/4πε₀ *Q²*/*R* D. 1/4πε₀ *Q²*/3*R* ## Physics Numerical (Maximum Marks: 20) ### Question No. 1 **Numerical Type ** The answer has to be filled into the input box provided below. A galvanometer, having a resistance of 500Ω, gives a full scale deflection for a current of 0.05A. The length in metre of a resistance wire of area of cross-section 2.97×10^-2cm² that can be used to convert the galvanometer into an ammeter which can read a maximum of 5A current is : (Specific resistance of the wire= 5×10^-7Ω-m) ### Question No. 2 **Numerical Type** The answer has to be filled into the input box provided below. A solid sphere of radius *R* has a charge *Q* distributed in its volume with a charge density ρ= *kr^a*, where *k* and *a* are constants and *r* is the distance from its centre. If the electric field at *r* = *R*/8 is *1/2* times that at *r* = *R*, the value of *a* is ### Question No. 3 **Numerical Type** The answer has to be filled into the input box provided below. Four bulbs of different power readings are arranged in a circuit as shown below: <br> The image describes a circuit with four bulbs connected in parallel: - Two bulbs are 100W. - One bulb is 300W. - One bulb is 100W. <br> The resultant power of the combination if rated voltage is applied across the combination is .......W. ### Question No. 4 **Numerical Type** The answer has to be filled into the input box provided below. An infinitely long solid cylinder of radius *R* has a uniform volume charge density *ρ*. It has a spherical cavity of radius *R*/2 with its centre on the axis of the cylinder as shown in the figure. The magnitude of the electric field at the point *P*, which is at a distance 2*R* from the axis of the cylinder, is given by the expression *23ρR*/16κε₀*. The value of *K* is <br> The image describes a solid cylinder with radius *R* and a cavity of radius *R/2* inside it. The point *P* is outside the cylinder on its axis. ### Question No. 5 **Numerical Type** The answer has to be filled into the input box provided below. In the given figure, the capacitance *C₁*, *C₃*, *C₄*, *C₅* have a capacitance 4μF each. If <br> The image describes a circuit with five capacitors connected in a complex configuration. - The battery is connected across an equivalent capacitor *C₁* in series with *C₂*. - The equivalent capacitor of this arrangement is then connected in series with *C₃*. - Another capacitor *C₄* is connected in parallel to *C₃*. - The equivalent capacitor of this configuration is then connected to a capacitor *C₅*. <br> Capacitor *C₂* has a capacitance 10μF, then the effective capacitance between *A* and *B* will be (in μF) ## Chemistry Single Correct (Maximum Marks: 80) ### Question No. 1 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. A single compound of the structure CH₃ CH OHC-CH₂ C H CH₂-C=O CH₃ is obtainable from ozonolysis of which of the following cyclic compounds? A. H₃C -CH₃ B. H₃C H₃C C. H₃C CH₃ D. CH₃ CH₃ ### Question No. 2 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. An organic compound (A) reacts with sodium metal and forms (B). On heating with conc. H₂SO₄, (A) gives diethyl ether, (A) and (B) are: A. C₂H₅OH and C₂H₅ONa B. C₃H₇OH and CH₃ONa C. CH₃OH and CH₃ONa D. C₄H₉OH and C₄H₉ONa ### Question No. 3 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Which of the following is an example of aldol condensation? A. 2CH₃COCH₃ Dil. NaOH → CH₃COHCH₃CH₂COCH₃ B. 2HCHO Dil.NaOH → CH₃OH C. C₆H₅CHO + HCHO Dil. NaOH → C₆H₅CH₂OH D. None of the above ### Question No. 4 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Which of the following will undergo oxidation reaction with MnO₂? A. Hex-3-ene-1-ol B. Cyclohex-3-ene-1-ol C. Hex-2-ene-1-ol D. All of these ### Question No. 5 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Compound (A), C₈H₈Br gives a pale yellow ppt when warmed with alcoholic AgNO₃. Treatment of A with aqueous KOH gave B which reacts as shown below to form phthalaldehyde: B MnO₂ (i) CrO₂Cl₂ (ii) H₃O⁺ → phthalaldehyde The structure of compound A is: A. C₇H₇ Br B. CH₂Br CH₃ C. C₆H₅ CH₂Br D. C₆H₅ CH₃ ### Question No. 6 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Which one of the following reaction sequence is incorrect method to prepare phenol? A. Aniline, NaNO₂ + HCl, H₂O, heating B. Cumene, O₂, H₃O⁺ C. C₆H₅CH(CH₃)₂, NaOH, STP condition D. C₆H₆, oleum, NaOH, H₃O⁺ ### Question No. 7 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Consider the following reaction, PBr₃ ethanol X Y The product Z, is A. CH₂=CH₂ alc. KOH (i) H₂SO₄ room temperature B. CH₃CH₂-O-CH₂-CH₃ C. CH₃-CH₂-O-SO₃H D. CH₃CH₂OH (ii) H₂O, heat →Z; ### Question No. 8 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. In the given reaction [X] CH₂=CH-CHO [X] will be CH₂=CH-CH₂OH A. H₂, Ni B. H₂, Pt C. NaBH₄ D. H₂/ Wilkinson catalyst ### Question No. 9 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Which of the following is not soluble in NaHCO₃ solution? A. OH O₂|| ||O₂ B. COOH ||O₂ C. OH NO₂ D. SO₃H ### Question No. 10 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. An aromatic compound 'X' with molecular formula C₉H₁₀O gives the following chemical tests: 1. Forms 2, 4-DNP derivative, 2. Reduces Tollen's reagent, 3. Undergoes Cannizaro reaction and, 4. On vigorous oxidation 1, 2-benzenedicarboxylic acid is obtained. X is: A. CHO C₂H₅ B. CHO C₂H₅ C. O C CH₃ CH₂ D. CHO C₂H₅ ### Question No. 11 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Phenol on reaction with a mixture of conc. HNO₃ and conc. H₂SO₄ produces a compound. The degree of unsaturation and the nature of compound is: A. 5, acidic B. 7, basic C. 6, neutral D. 7, acidic ### Question No. 12 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Match the compounds given in list I with list II and select the suitable option using the code given belows. | List I | List II| |:---|:---| | A. Benzaldehyde | 1. Phenolphthalein| | B. Phthalic anhydride | 2. Benzoin condensation| | C. Phenyl benzoate| 3. Oil of wintergreen| | D. Methyl salicylate | 4. Fries rearrangement| Code: | A | B | C | D | |:---|:---|:---|:---| |(a) 4 | 1 | 3 | 2 | |(b) 4 | 2 | 3 | 1 | |(C) 2 | 3 | 4 | 1 | |(d) 2 | 1 | 4 | 3 | A. (a) B. (b) C. (c) D. (d) ### Question No. 13 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Identify the final product [D] obtained in the following sequence of reactions. CH₃CHO i) LiAlH₄ H₃O⁺ [A] H₂SO₄ [B] HBr [C] Δ C₆H₅Br Na/Dry ether [D] A. CH≡C^-Na⁺ B. C₆H₅ C. C₆H₅ D. C₄H₁₀ ### Question No. 14 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. C₆H₅CH₂-O^- Identify A and B A. A= C₆H₅CH₂ and B= I^- B. A= C₆H₅CH₂ and B= OH C. A= C₆H₅CH₂OH and B= I^- D. A= C₆H₅CH₂ and B= OH ### Question No. 15 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. CH₃CHO and C₆H₅CH₂CHO can be distinguished chemically by: A. Benedict test B. Iodoform test C. Tollen's reagent test D. Fehling solution test ### Question No. 16 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. In a set of the given reactions, acetic acid yielded a product 'c'. CH₃COOH + PCl₅ Product 'c' would be: a C₆H₆ → b Anh. AlCl₃ C₂H₅MgBr ether C A. CH₃CH(OH)C₂H₅ B. CH₃COC₆H₅ C. CH₃CH(OH)C₆H₅ D. C₂H₅ CH₃-C(OH)C₆H₅ ### Question No. 17 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Given below are statements: Statement I: The acidic strength of mono substituted nitrophenol is higher than phenol because of electron withdrawing nitro group. Statement II: o-nitrophenol, m-nitrophenol and p-nitrophenol will have same acidic strength as they have one nitro group attached to the phenolic ring. In the light of the above statements, choose the most appropriate answer from the options given below: A. Both Statement I and Statement II are incorrect. B. Statement I is correct but Statement II is incorrect. C. Statement I is incorrect but Statement II is correct. D. Both Statement I and Statement II are correct. ### Question No. 18 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Acetophenone when reacted with a base, C₂H₅ONa, yields a stable compound which has the structure? A. O CH CH OH OH B. O C= CH CH₃ C. O CH₃C CH CH₃ D. O CH₃ CH₃ C C OH OH ### Question No. 19 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Which of the following reagents would distinguish cis-cyclopenta-1, 2-diol from the trans-isomer? A. Acetone B. Ozone C. MnO₂ D. Aluminium isopropoxide ### Question No. 20 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. The order of reactivity of phenyl magnesium bromide (PhMgBr) with the following compounds: CH₃ H₃C Ph C=O C=O and C=O H H₃C Ph (I) (II) (III) A. III > II > I B. II > I > III C. I > III > II D. I > II > III ## Chemistry Numerical (Maximum Marks: 20) ### Question No. 1 ** Numerical Type** The answer has to be filled into the input box provided below. The number of hydroxyl group(s) in Q is: H... HO H₂C CH₃ 3 3 H+ aqueous dilute KMnO₃(excess) P Q heat 0°C ### Question No. 2 **Numerical Type** The answer has to be filled into the input box provided below. Number of isomeric alcohols of molecular formula C₆H₁₄O which give positive iodoform test is: ### Question No. 3 **Numerical Type** The answer has to be filled into the input box provided below. OCH₃ H₂SO₄, H₂O HgSO₄ P H The product P is having how many chiral centres? ### Question No. 4 **Numerical Type** The answer has to be filled into the input box provided below. H OH MgBr HH (A) excess How many geometrical isomer of (A) is possible? Δ ### Question No. 5 **Numerical Type** The answer has to be filled into the input box provided below. Among the following MeO O H H I II III Me H H IV V Me the compounds which can be reduced with formaldehyde and conc. aq. KOH, are: ## Mathematics Single Correct (Maximum Marks: 80) ### Question No. 1 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Let *f*: *R* → *R* be defined as *f*(x) = { 1/3*x³ + 2*x² + 3x, x > 0 3xe^x, x ≤ 0 } Then f is increasing function in the interval A. (-1/2, 2) B. (0, 2) C. (-1, 3/2) D. (-3, -1) ### Question No. 2 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. If *f*(x) = { sin*x*, x < 0 cos*x* - |*x* - 1|, x ≥ 0 } then *g*(x) = *f*(|*x*|) is non-differentiable for A. all values of *x* B. 3 values of *x* C. exactly one value of *x* D. none of these ### Question No. 3 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Let *f*(x) = (*x* - 1)²(*x* - 2)³e^*x*. Then A. *f*(x) has local maximum at *x* = 1 B. *f*(x) has point of inflexion at *x* = 1 C. *f*(x) has local minimum at *x* = 2 D. all of these ### Question No. 4 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Let *a* > 0 be a real number. Then the limit lim*_x→₂ (a^*x* + a^3-*x* - (a² + a)^*x*/2) / (a^*x* - a^3-*x*) is A. 2 log *a* B. -*a*/4 C. a² + *a*/2 D. (1 - *a*)/3 ### Question No. 5 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Number of point(s) in [1, 2] where *f*(x) = (-2)^[x³] is non-differentiable (where [.] denotes greatest integer function) A. 6 B. 5 C. 9 D. 7 ### Question No. 6 **Only One Option Correct Type** Each question has multiple options out of which **ONLY ONE** is correct. Let *f*: *R* → *R* be a differentiable function given by *f*(x) = x³ - 3x + 2020 If *g*(x) is a continuous function defined by *g*(x) = { Minimum{*f*(t), 0 ≤ *t* ≤ *x*}, 0 ≤ *x* ≤ 1