Chanakya Science Academy Physics Past Paper PDF 2024

CHANAKYA SCIENCE ACADEMY Std.: 11 & 12 STD P.C.B. Marks: 100 Date: 29-Aug-2024...

CHANAKYA SCIENCE ACADEMY Std.: 11 & 12 STD P.C.B. Marks: 100 Date: 29-Aug-2024 Chapter: 00 A) 1. 34 × 109 m B) 1. 43 × 109 m 1 The total plane angle subtended by a circle at its centre is C) 1. 34 × 108 m D) 1. 43 × 108 m A) π rad B) 2π rad C) 2π 3 rad 8 The density of material in the CGS D) π 2 rad system of units is 4g/cm3. In a system of units in which unit of length is 10cm 2 Unit of magnetic moment is and unit of mass is 100g when the A) Ampere − metre2 value of density of material in this system will be: B) Ampere − metre A) 0.4 B) 40 C) 400 D) 0.04 C) Weber − metre2 D) Weber/metre 9 The density of a liquid in the CGS 3 The dimensions of universal system is 0.625 g/cm3. What is its gravitational constant are magnitude in the SI system? A) M−2L2T−2 B) M−1L3T−2 A) 0.625 B) 0.0625 C) 0.00625 C) ML−1T−2 D) ML2T−2 D) 625 4 The density of the Sun is: 10 It is claimed that two caesium clocks if (Given, mass of the Sun = 2.0 x 1030 kg allowed to run for 100 years, free from and radius of the Sun = 7.0 x 108 m) any disturbance, may differ by only A) 2.9 x 103 kg m-3 about 0.02 sec. What does this imply for the accuracy of the standard B) 1.4 x 103 kg m-3 caesium clock in measuring a time C) 5.6 x 103 kg m-3 interval of 1 sec? D) 1.9 x 103 kg m-3 A) 1012 to 1013 B) 107 to 108 C) 1010 to 1013 D) 1011 to 1012 5 One pico Farad is equal to A) 10 −24F B) 10 −18F C) 10 −12F 11 If z = A×B A+B , and errors in the determination of A and B are D) 10 −6F respectively △ A and △ B, then the fractional error in the calculation of z is 6 If momentum (p), area (A), and time (T) : are taken to be fundamental quantities, then energy has the dimensional A) △A A + △B B + △ AA ++ B△ B formula ( △ A + △ B) B) △A A + △B B - A+B C) △A A + △B B A) [pA−1T1] B) [p2 AT] D) zero C) [pA −1/2 T] D) [pA1/2 T] 12 The unit of power is: 7 When the planet Jupiter is at a A) Joule B) Joule per second only distance of 824.7 million kilometres from the Earth, its angular diameter is C) Joule per second and watt both measured to be 35.72” of arc. Then the D) Only watt diameter of Jupiter is: 13 The unit of Stefan's constant σ is : A) W m−2 K−1 B) W m2 K−4 The pitch of a screw gauge is 1.0 mm and there are 100 divisions on the C) W m−2 K−4 D) W m−2 K4 circular scale. While measuring the 14 Dimensional formula for torque is diameter of a wire, the linear scale reads 1 mm and the 47th division on A) L2MT−2 B) L−1MT−2 C) L2MT−3 the circular scale coincides with the D) LMT−2 reference line. The length of the wire is 5.6 cm. Find the wire's curved surface 15 A student measures the distance area (in cm2) in an appropriate number traversed in free fall of a body, initially of significant figures. at rest in a given time. He uses this A) 2.4 cm2 B) 2.56 cm2 data to estimate g, the acceleration due to gravity. If the maximum C) 2.6 cm2 D) 2.8 cm2 percentage errors in measurement of the distance and the time are 21 Zero error in an instrument introduces e1 and e2 respectively, the percentage A) Systematic error error in the estimation of g is B) Random error A) e2 − e1 B) e1 + 2e2 C) e1 + e2 C) Least count error D) e1 − 2e2 D) Personal error 16 The dimensions of permittivity ε0 are: 22 The dimension of 1 √ε0 μ0 is that of A) A2T2M−1L−3 B) A2T4M−1L−3 A) Velocity B) Time C) A−2T−4ML3 D) A2T−4M−1L−3 C) Capacitance D) Distance 17 The displacement of a progressive 23 Which of the following represents a wave is represented by y = Asin (ωt — volt : kx), where x is distance and t is time. The dimensional formula of ω and k A) Joule/second B) Watt/Ampere are, respectively; C) Watt/Coulomb A) [LT−1] & [T−1] B) [L2T−1] & [LT−1] D) Coulomb/Joule C) [T−1] & [L−1] D) [LT−2] & [T−2] 24 The vernier scale of a travelling 18 The quantity 1 2 ∈0 E2 has dimensional microscope has 50 divisions which formula same as coincide with 49 main scale divisions. If each main scale division is 0.5 mm, A) 12 CV2 B) 12 LI2 D) Power 2 C) 1B 2 μ0 the minimum inaccuracy in the 19 The nearest star to our solar system is measurement of distance: 4.29 light-years away. How much is A) 0. 02 mm B) 0. 2 mm this distance in terms of parsecs? C) 0. 1 cm D) 0. 01 mm A) 1.11 parsec B) 1.22 parsec 25 The unit of self inductance of a coil is C) 1.32 parsec D) 1.39 parsec A) Farad B) Farad C) Weber 20 D) Tesla 26 A man wishes to estimate the distance D) If both the assertion and reason are of a nearby tower from him. He stands false. at point A in front of tower C and spots a very distant object O in line with AC. 30 Unit of stress is He then walks perpendicular to AC up A) N/m B) N − m C) N/m2 to B, a distance of 100 m, and looks at O and C again. Since O is very distant, D) N − m2 the direction BO is practically the same 31 The pair of the quantities having same as AO; but he finds the line of sight of dimensions is C shifted from the original line of sight by an angle θ = 40o(θ is known as A) Displacement, velocity ‘parallax’), the distance of the tower C B) Time, frequency from his original position A is: C) Wavelength, focal length A) 119 m B) 126 m C) 320 m D) Force, acceleration D) 219 m 32 A physical quantity X depends on four 27 Which of the following is the most 3 a2 b measurables a, b, c, and d as X = c5 d. precise measurement? To ensure maximum accuracy in the A) 3 × 10−3m B) 0. 0030 m determination of X, the quantity that should be measured with maximum C) 30 × 10−4 m D) 300 × 10−5 m accuracy is : 28 A SONAR (sound navigation and A) a B) b C) c D) d ranging) uses ultrasonic waves to detect and locate objects underwater. 33 A physical quantity X is related to four In a submarine equipped with a measurable quantities a, b, c, and d as SONAR, the time delay between the follows X = a2b3c5/2d−2. The generation of a probe wave and the percentage error in measuring a, b, c, reception of its echo after reflection and d is 1%, 2%, 3%, and 4%, from an enemy submarine is found to respectively. What is the percentage be 77.0 sec. What is the distance of error in quantity X? the enemy submarine? (Speed of A) 22.1 % B) 13.2 % C) 34.6 % sound in water = 1450 m/s ) D) 23.5 % A) 60.32 km B) 57.70 km C) 44.23 km D) 55.80 km 34 What are the units of K = 1/4πε0 A) C2N-1m-2 B) Nm2C-2 C) Nm2C2 29 Assertion Linear mass density has the : dimensions of [M1L−1To] D) Unitless Reason : Because density is always mass per unit volume. 35 The area of a sheet of length 10.2 cm A) If both the assertion and the reason and width 6.8 cm addressed up to are true and the reason is a correct proper number of significant figures is explanation of the assertion. A) 69.36 cm2 B) 69.4 cm2 B) If both the assertion and reason are C) 69 cm2 D) 70 cm2 true but the reason is not a correct explanation of the assertion. 36 The angle of 1o (degree) will be equal C) If the assertion is true but the reason to: is false. (Use 360o = 2π rad, 1o = 60' and 1' = 60') A) 1.034 × 10−3 rad Reason : Density cannot be derived from the fundamental B) 1.745 × 10−2 rad physical quantities. C) 1.524 × 10−2 rad A) If both the assertion and the reason D) 1.745 × 10+3 rad are true and the reason is a correct explanation of the assertion. 37 The equation of a wave is given by Y = B) If both the assertion and reason are A sin ω x v - k where ω is the angular true but the reason is not a correct velocity, x is length and ν is the linear explanation of the assertion. velocity. The dimension of k is C) If the assertion is true but the reason A) LT B) T C) T–1 D) T2 is false. 38 In which of the following systems of D) If both the assertion and reason are the unit, Weber is the unit of magnetic false. flux? 43 The number of significant figures in A) CGS B) MKS C) SI the measured value 0.0204 is D) None of these A) Five B) Three C) Four 39 An object is moving through the liquid. D) Two The viscous damping force acting on it 44 Dimensions of potential energy are is proportional to the velocity. Then the dimension of the constant of A) MLT-1 B) ML2T-2 C) ML-1T-2 proportionality is: D) ML−1T−1 A) ML-1T-1 B) MLT-1 C) M0LT-1 45 An athletic coach told his team that D) ML0T-1 muscle times speed equals power. 40 The relative error in Z, if Z = 4 A B 1/3 is : What dimensions does he view for 3/2 CD muscle? A) △A A + △B B + △C C + △D 𝐷 A) MLT–2 B) ML2T–2 C) MLT2 B) 4 △A A + 1 △B 3 B - △C C - 3 △D 2 𝐷 D) L C) 4 △A A + 13 △B B + △C C + 2 △D 3 𝐷 D) 4 △A A + 13 △B B + △C + 3 △D 46 The decimal equivalent of 1/20 up to C 2 𝐷 three significant figures is: 41 Find the zero correction in the given A) 0.0500 B) 0.05000 C) 0.0050 figure. D) 5.0 × 10-2 47 Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its A) 0.4 mm B) 0.5 mm length (l), the mass of the bob (m) and C) – 0.5 mm D) – 0.4 mm acceleration due to gravity (g). Expression for its time period is: 42 Assertion Density is a derived physical A) T = 1 √1 2π g B) T = 2π 1g C) T = 2π√ 1g : quantity. D) T = 2π√ g1 48 One astronomical unit is a distance 54 The dimensions of K in the equation W equal to = 1 2 Kx2 is A) 9.46 × 1015 m B) 1.496 × 1011 m A) M1L0T−2 B) M0L1T−1 C) 3 × 108 m D) 3.08 × 1016m C) M1L1T−2 D) M1L0T−1 49 One mole of an ideal gas at standard 55 One femtometer is equivalent to temperature and pressure occupies 22.4 L (molar volume). What is the A) 1015 m B) 10–15 m C) 10–12 m ratio of molar volume to the atomic D) 1012 m volume of a mole of hydrogen? (Take the size of the hydrogen molecule to 56 Dimension of R is: be about 1 Å). A) ML2T−1 B) ML2T−3A-2 A) 7. 08 × 104 B) 22.4 × 103 C) ML-1T−2 D) None of these C) 11.2 × 105 D) 8.0 × 103 57 If L,Q,R represent inductance, charge 50 Dimensions of the following three and resistance respectively, the units quantities are the same: of A) Work, energy, force A) QR will be those of current L B) Velocity, momentum, impulse B) 2 Q R 3 will be those of energy L2 C) Potential energy, kinetic energy, C) QL will be those of current R momentum Q3 R 2 D) L will be those of power D) Pressure, stress, coefficient of elasticity 58 ML3T−1Q−2 is dimension of A) Resistivity B) Conductivity 51 'Torr' is the unit of C) Resistance D) None of these A) Pressure B) Volume C) Density D) Flux 59 The period of a body under a b c SHM is presented by T = P D S ; where 52 To determine Young's modulus of a P is pressure, D is density and S is wire, the formula is Y = F A × L △L ; where L surface tension. The value of a, b and c = length, A = area of cross-section of are: the wire, △ L = change in length of the A) – 32 , 12 , 1 B) – 1, – 2, 3 wire when stretched with a force F. The conversion factor to change it from C) 12 , – 32 , – 1 2 D) 1, 2, 1 3 CGS to MKS system is 60 Assertion Dimensional constants are (1) 1 (2) 10 : the quantities whose values (3) 0.1 (4) 0.01 are constant. A) 1 B) 10 C) 0.1 D) 0.01 Reason : Dimensional constants are dimensionless. 53 If the length of rod A is 3.25 ± 0.01 cm A) If both the assertion and the reason and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by are true and the reason is a correct explanation of the assertion. A) 0.94 ± 0.00 cm B) 0.94 ± 0.01 cm B) If both the assertion and reason are C) 0.94 ± 0.02 cm true but the reason is not a correct D) 0.94 ± 0.005 cm explanation of the assertion. C) If the assertion is true but the reason Assertion A.U. is much bigger than Å. is false. : Reason : A.U. stands for astronomical D) If both the assertion and reason are unit and Å stands from false. Angstrom. 61 Assertion:Out of three measurements l A) If both the assertion and the reason = 0.7 m; l = 0.70 m and l = are true and the reason is a correct 0.700 m, the last one is explanation of the assertion most accurate. B) If both the assertion and reason are Reason : In every measurement, only true but the reason is not a correct the last significant digit is explanation of the assertion not accurately known. C) If the assertion is true but the reason A) If both the assertion and the reason is false are true and the reason is a correct explanation of the assertion D) If both the assertion and reason are false B) If both the assertion and reason are true but the reason is not a correct 67 If V denotes the potential difference explanation of the assertion across the plates of a capacitor of C) If the assertion is true but the reason capacitance C, the dimensions of 2 is false CV are D) If both the assertion and reason are A) Not expressible in MLT B) MLT−2 false C) M2LT−1 D) ML2T−2 62 Which one of the following formulas is 68 Which of the following are not a unit of dimensionally incorrect? time? A) y = asin 2πt B) y = a sin 2π + cos 2π T √2 T T (a) Second (b) Parsec C) y = asinvt D) y = asin 2πt T +π (c) Year (d) Light year A) (a, c, d) B) (a, c) C) (b, d) 63 Which is not a unit of electric field? D) (b, c) A) NC−1 B) Vm−1 C) JC−1 69 Assertion Units of Rydberg constant R D) JC−1m−1 : are m-1 Reason : It follows from Bohr’s 64 The percentage error in the measurement of the voltage V is 3% formula v̄ = R 1 2 n1 - 1 2 n2 , where the and in the measurement of the current symbols have their usual is 2%. The percentage error in the meaning. measurement of the resistance is A) If both the assertion and the reason are true and the reason is a correct A) 3% B) 2% C) 1% D) 5% explanation of the assertion 65 The dimensions of pressure are equal B) If both the assertion and reason are to: true but the reason is not a correct explanation of the assertion A) Force per unit volume C) If the assertion is true but the reason B) Energy per unit volume C) Force is false D) Energy D) If both the assertion and reason are false 66 70 Hertz is the unit of D) Decreased 16 times A) Frequency B) Force 76 The dimensional formula for Planck's C) Electric charge D) Magnetic flux constant (h) is A) ML−2T−3 B) ML2T−2 C) ML2T−1 71 If energy (E), velocity (v) and time (T) are chosen as the fundamental D) ML−2T−2 quantities, the dimensional formula of surface tension will be: 77 The dimensional formula for young's modulus is A) [Ev-2T-1] B) [Ev-1T-2] C) [Ev-2T-2] A) ML−1T−2 B) M0LT−2 C) MLT−2 D) [E-2v-1T-3] D) ML2T−2 72 Error in the measurement of radius of a sphere is 1%. The error in the 78 The moon is observed from two calculated value of its volume is diametrically opposite points A and B on Earth. The angle θ subtended at the A) 1% B) 3% C) 5% D) 7% moon by the two directions of o observation is 1 54′. Given the 73 Which of the following pair does not diameter of the Earth to be about have similar dimensions? 1.276 × 107 m, the distance of the A) Stress and pressure moon from the Earth is: B) Angle and strain A) 2. 91 × 108 m B) 3.11 × 109 m C) Tension and surface tension C) 3.84 × 108 m D) 1.91 × 107 m D) Planck'sconstant and angular 79 The dimensional formula of relative momentum density is: 74 In the given Vernier scale, 10 divisions A) ML-3 B) LT-1 C) MLT-2 of the vernier scale is matching with 9 D) Dimensionless divisions of the main scale as shown in the first figure. Find the diameter of 80 The numbers 2.745 and 2.735 on the object in the second figure. rounding off to 3 significant figures Assume the edge of the vernier as '0' will give: of the vernier. A) 2.75 and 2.74 B) 2.74 and 2.73 C) 2.75 and 2.73 D) 2.74 and 2.74 81 A) 15.6 mm B) 156 mm C) 1.56 mm D) 0.156 mm 75 If the unit of length and force be increased four times, then the unit of energy is A) Increased 4 times B) Increased 8 times C) Increased 16 times The main scale of a vernier callipers A) Frequency B) Energy reads 10 mm in 10 divisions. 10 C) Time period D) Current divisions of Vernier scale coincide with 9 divisions of the main scale. When the 88 From the equation tan θ = rg , one can 2 v two jaws of the callipers touch each obtain the angle of banking θ for a other, the fifth division of the vernier cyclist taking a curve (the symbols coincides with 9 main scale divisions have their usual meanings). Then say, and the zero of the vernier is to the it is right of zero of main scale. When a cylinder is tightly placed between the A) Both dimensionally and numerically two jaws, the zero of vernier scale lies correct slightly behind 3.2 cm and the fourth B) Neither numerically nor vernier division coincides with a main dimensionally correct scale division. The diameter of the C) Dimensionally correct only cylinder is. D) Numerically correct only A) 3.10 cm B) 3.8 cm C) 3.09 cm D) -3.09 cm 89 Candela is the unit of A) Electric intensity 82 Which of the following is the smallest unit? B) Luminous intensity A) Millimetre B) Angstrom C) Sound intensity D) None of these C) Fermi D) Metre 90 Which of the following is not a unit of time? 83 The dimensional formula of wave number is A) Leap year B) Micro second A) M0L0T−1 B) M0L-1T0 C) Lunar month D) Light year C) M-1L-1T0 D) M0L0T0 91 If the dimension of a physical quantity are given by MaLbTc, then the physical 84 The dimensions of surface tension are quantity will be A) ML−1T−2 B) MLT−2 C) ML−1T−1 A) pressure if a = 1, b = -1, c = -2 D) MT−2 B) velocity if a = 1, b = 0, c =-1 85 The dimensions of resistivity in terms C) acceleration if a = 1, b = 1,c =-2 of M, L, T and Q where Q stands for the D) force if a = 0, b = -1, c = -2 dimensions of charge, is A) ML3T−1Q−2 B) ML3T−2Q−1 92 The pair having the same dimensions is: C) ML2T−1Q−1 D) MLT−1Q−2 A) Angular momentum, work 86 If x = at + bt2, where x is the distance B) Work, torque travelled by the body in kilometres while t is the time in seconds, then the C) Potential energy, linear momentum units of b are D) Kinetic energy, velocity A) km/s B) km − s C) km/s2 93 Which of the following measurements D) km − s2 is most precise? 87 Dimensions of CR are those of A) 5.00 mm B) 5.00 cm C) 5.00 m 97 If L = 2.331 cm, B = 2.1 cm, then L + B D) 5.00 km =? A) 4.431 cm B) 4.43 cm 94 Two full turns of the circular scale of gauge cover a distance of 1 mm on C) 4.4 cm D) 4 cm scale. The total number of divisions on circular scale is 50. Further, it is found 98 Out of the following, the only pair that that screw gauge has a zero error of does not have identical dimensions is -0.03 mm. While measuring the A) Angular momentum and Planck's diameter of a thin wire a student notes constant the main scale reading of 3 mm and the number of circular scale division in B) Moment of inertia and moment of a line, with the main scale as 35. The force diameter of the wire is C) Work and torque A) 3.32 mm B) 3.73 mm D) Impulse and momentum C) 3.67 mm D) 3.38 mm 99 The dimensional formula of the 95 Mach number is equal to one when coefficient of thermal conductivity is : velocity of object is equal to: A) [M1L1T−3K−1] B) [M3L-1T−3K] A) Velocity of light C) [M1L−3T−1K−1] D) [M1L1T−3K] B) Velocity of sound (332 m/ sec) 100 If the size of a nucleus (in the range C) 1 km/ sec D) 1 m/ sec of 10−15 to 10−14 m is scaled up to the tip of a sharp pin, what roughly is the 96 X = 3YZ2 find dimension of Y in size of an atom? (MKSA) system, if X and Z are the Assume tip of the pin to be in the dimension of capacity and magnetic range 10−5 m to 10−4 m. field respectively A) 1 m B) 10 m C) 10–10 m A) M−3L−2T−4A−1 B) ML-2 D) 10–5 m C) M−3L−2T4A4 D) M−3L−2T8A4