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SATISH SCIENCE ACADEMY
DHANORI PUNE - 411015
Mhtcet pcm 3 ENTRANCE EXAM - MHT - CET
Time Allowed: 3 hours Maximum Marks : 200
General Instructions:
- All questions are compulsory.
- There are two sections.
- Section A has 100 questions from Physics and Chemistry.
- Section B has 50 questions from Mathematics.
Section - A (Physics)
The position of an object moving along x - axis is given by x = a + bt^2 where a = 8.5 m and b = 2.5 m and t is measured in second. If the object starts from t = 0, the velocity at t = 2 s is [1] a) 9.25 m/s b) 1.5 m/s c) 18.5 m/s d) 10 m/s
Two particles of masses m 1 , m 2 move with initial veloc- ities u 1 and u 2. On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v 1 and v 2 then we must have [1]
a) 12 m 1 u^21 + 12 m 2 u^22 = 12 m 1 v^21 + 12 m 2 v^22 − ε b) 12 m^21 u^21 + 12 m^22 u^22 + ε = 12 m^21 v^21 + 12 m^22 v^22 c) 12 m 1 u^21 + 12 m 2 u^22 − ε = 12 m 1 v^21 + 12 m 2 v^22 d) m^21 u 1 + m^22 u 2 − ε = m^21 v 1 + m^22 v 2
If the density of the earth is tripled keeping its radius constant, then acceleration due to gravity will be (g = 9.8 m/s^2 ) [1] a) 4.9 m/s^2 b) 2.45 m/s^2 c) 9.8 m/s^2 d) 29.4 m/s^2
The coefficient of thermal conductivity depends upon [1]
a) Temperature difference of two surfaces. b) Material of the plate. c) Area of the plate. d) Thickness of the plate.
Which of the following is NOT the characteristic of the progressive wave? i. All the vibrating particles of medium have different amplitudes and frequency. ii. State of oscillation changes from particle to particle. iii. For its propagation, medium should have elasticity and inertia. iv. The form of wave repeats itself at equal intervals. [1] a) Option (a) b) Option (d) c) Option (b) d) Option (c)
A circular disc of which 23 part is coated with yellow and 1 3 part is with blue.^ It is rotated about its central axis with high velocity, then it will be seen as [1] a) Yellow b) Green c) White d) Blue
A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are n 0 , n 20 , n 60 and n 80 , respectively. The angle of incidence θ for which the beam just misses entering
Region IV is
[1] a) sin−^1
4
b) sin−^1
3
c) sin−^1
8
d) sin−^1
4
- Match the corresponding entries of column - 1 with col- umn - 2 [where m is the magnification produced by the mirror] Column - 1 Column - 2 I. m = - 2 A. Convex mirror
Ii. m = - 12 B. Concave mirror
Iii. m = +2 C. Real image
Iv. m = + 12 D. Virtual image
[1] a) I - b and c; ii - b and c; iii - b and d; iv - a and d b) I - a and c; ii - a and d; iii - a and b; iv - c and d c) I - c and d; ii - b and d; iii - b and c; iv - a and d d) I - a and d; ii - b and c; iii - b and d; iv - b and c
- The graph below has two curves plotted indicating the variation of electric potential with distance.
The dotted curve and solid curve respectively represent variation of potential for [1] a) A charge and an electric dipole. b) A charge and system of charged particles. c) An electric dipole and a charge. d) A charge and a dielectric constant.
- A wheel of M.I. of 5× 10 -^3 kg m^2 is making 20 rev/s. The torque required to stop it in 10 s is [1]
a) π × 10 -^2 Nm b) 2 π × 10 -^2 Nm c) 2 π × 102 Nm d) 4 π × 10 -^2 Nm
- Differential equation for angular S.H.M. is given by [1]
a) m d
(^2) x dt^2 +b^
dx dt^2 +^ kx^ = 0 b) d
(^2) x dt^2 +ω
(^2) x = 0 c) d
(^2) x dt^2 −^
k m x^ = 0 d) d
(^2) θ dt^2 +^
( (^) c I
θ = 0
Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7 : 8, then the ratio of lengths of the two pendulums will be [1] a) 49 : 64 b) 7 : 8 c) 64 : 49 d) 8 : 7
The displacement of a particle performing simple har- monic motion is given by, x = 8 sinω t + 6 cos ω t, where distance is in cm and time is in second. What is the amplitude of motion? [1] a) 8 cm b) 14 cm c) 6 cm d) 10 cm
The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the frequency is 10 kHz. When the container is filled with a gas, the frequency changes by 100 Hz. The dielectric constant of the gas is [1] a) 1.001 b) 2. c) 1.02 d) 2.
The ratio of the pressure (P) on a swimmer 10 m below the water surface of a lake to that of the pressure on the surface of water (Pa) is (Atmospheric pressure = 1 × 105 Pa, ρ = 1000 kg m -^3 , g = 10 m/s^2 ) is [1] a) 3 b) 1 c) Zero d) 2
A stringed instrument is provided with hollow boxes. This helps to increase loudness of sound by. i. Setting string into natural vibrations ii. Setting string into forced vibrations iii. Setting hollow boxes into natural vibrations along with the stringes iv. Setting hollow boxes into forced vibrations along with the stringes [1] a) Option (c) b) Option (a) c) Option (b) d) Option (d)
An open and closed organ pipe have the same length. The ratio of ’p’th mode of frequency of vibration of air in two pipes is [1] a) P(2p + 1) b) 1 c) P d) (^2) p^2 −p 1
A transverse wave is represented by, y = y 0 sin 2 π λ (vt^ −^ x)^.^ For^ what^ value^ of^ λ^ , maximum^ parti- cle velocity will be equal to twice the wave velocity? [1]
a) λ = πy 20 b) λ = 2π y 0 c) λ = π y 0 d) λ = π 3 y^0
Absorption coefficient of totally blackbody is [1] a) More than one b) Infinity c) Zero d) One
If the speed of light in glass and water are 2× 108 m/s and 2.25 × 108 m/s respectively, then the refractive index of the water with respect to the glass is [1] a) 1.25 b) 0. c) 1.125 d) 1.
Kirchhoff’s junction rule is a reflection of [1]
a) Conservation of current density vector. b) Conservation of charges. c) Conservation of momentum. d) Conservation of energy.
- A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves [1]
a) Potential gradients. b) Cells. c) A condition of no current flow through the gal- vanometer. d) A combination of cells, galvanometer and resistances.
- The internal resistances of two cells shown are 0.1Ω and 0.3 Ω. If R = 0.2 Ω , the potential difference across the
[1]
a) Cell A will be zero and B will be greater than 2V. b) Cells A and B will be 2V. c) Cell A will be > 2V and B will be < 2V. d) Cell B will be zero and A will be less than 2V.
- For the measurement of potential difference, voltmeter is connected [1]
a) In parallel with the circuit. b) Beyond the circuit. c) In series with the circuit. d) In open circuit.
- Magnetic field due to a ring having n turns at a distance x on its axis is proportional to (if a = radius of ring) [1]
a) na
2 (a^2 +x^2 ) 32 b) (^) (a (^2) +ax (^2) ) c) a
2 (a^2 +x^2 ) (^32) d) n (^2) a 2 (a^2 +x^2 ) 32
- A straight wire of length 50 cm carrying a current of 2. A is suspended in mid - air by a uniform magnetic field of 0.5 T (as shown in figure). The mass of the wire is (g = 10 ms -^2 )
[1] a) 62.5 g b) 250 g c) 100 g d) 125 g
- A long conducting wire carrying a current I is bent at 120°(see figure). The magnetic field B at a point P on the right bisector of bending angle at a distance d from
In an atom, two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the times taken by them to complete one revolution is [1] a) 21 b) (^41) c) 641 d) (^18)
Atomic weight of boron is 10.81 and it has two isotopes 5 B^10 and 5 B^11. Then ratio of 5 B^10 : 5 B^11 in nature would be [1] a) 15 : 16 b) 81 : 19 c) 10 : 11 d) 19 : 81
Which pair is isobaric? [1] a) 12 Mg^24 , 11Na^24 b) 11 Na^23 , 12 M^24 c) 11 Na^23 , Na^22 d) 11 Na^23 , 11 Na^24
In a half wave rectifier the AC input source of frequency 50 Hz is used. The fundamental frequency of the output is [1] a) 200 Hz b) 50 Hz c) 150 Hz d) 75 Hz
If a, b, c, d are inputs to gate and x is its output, then, as per the following time graph, the gate is:
[1] a) OR b) AND c) NOT d) NAND
- In a transistor circuit shown here, the base current is 35μ A. The value of the resistor Rb is
[1] a) 257 kΩ b) 123.5 kΩ c) 380.05 kΩ d) 280.0 kΩ
- N - p - n transistors are preferred to p - n - p transistors because they have [1] a) Electrons having high mobility than holes. b) Capability of handling large power. c) Low cost. d) Low dissipation energy.
Section - A (Chemistry)
The natural isotopic abundance of^10 B is 19.60 % and 11 B is 80.40 %. The exact isotopic masses are 10.13 and 11.009 u respectively. The average atomic mass of boron is u. [1] a) 10.84 b) 10. c) 11.00 d) 10.
The SI unit of frequency of radiation is. [1] a) Cm -^1 b) Metre c) Hertz d) Nm
In the balanced redox reaction, xH 2 O 2 (aq) + Cr 2 O^2 7(−aq) + 8H+(aq) −→ yO 2 (g) + 2Cr(3+aq)
- zH 2 O(l) the values of x, y and z are respectively. [1] a) 5, 2, 3 b) 2, 7, 3 c) 2, 3, 2 d) 3, 3, 7
- 10 volume H 2 O 2 is about. [1] a) 3% b) 10% c) 30% d) 1%
- Liquids rise or sink in capillaries due to. [1] a) Surface tension b) Vapour pressure c) Volume d) Viscosity
- The INCORRECT statement is: [1] a) Colour of colloidal solution is independent of the wavelength of light scattered by dispersed particles. b) Tyndall effect is useful in determining number of particles in colloidal system. c) The bright cone of the light observed when light passes through a colloidal dispersion is called Tyn- dall cone. d) The colour of colloidal dispersion changes with the manner in which the observer receives the light.
- A hydrocarbon containing one double bond gave on re- ductive ozonolysis, ethanal, and propanone. The name of the hydrocarbon is. [1] a) 3 - methylbut - 1 - ene
b) Pent - 2 - ene
c) 2 - methylbut - 2 - ene
d) 2 - methylbut - 1 - ene
- How many structural isomers can be represented by alkene, C 5 H 10? [1] a) Three b) Six c) Five d) Four
- The common element in all the organic compounds is
. [1] a) Sulphur b) Carbon c) Nitrogen d) Phosphorus
- Doping of silicon with boron leads to. [1] a) Insulator b) Metal c) P - type semiconductor d) N - type semiconductor
- Silicon doped with gallium forms. [1] a) P - type semiconductor b) Both n and p type semiconductor c) An intrinsic semiconductor d) N - type semiconductor
- Which of the following statements are CORRECT? [1] a) Osmotic pressure is useful to determine molar masses of very expensive substances. b) The semipermeable membrane selectively allows pas- sage of solute molecules. c) For calculating osmotic pressure, it is necessary to express concentration in a temperature independent unit like molality. d) If two hypotonic solutions are separated by a semipermeable membrane, there is no flow of solvent in either direction.
- The addition of common salt to a sample of the water will. [1] a) Decrease its freezing point and increase the boiling point
b) Increase both the boiling point and freezing point c) Decrease both the boiling point and freezing point d) Increase its freezing point and increase the boiling point
- Enthalpy associated with the following reaction is. CH4(g) → C(g) + 4H(g) [1]
a) Enthalpy of solution b) Enthalpy of sublimation c) Enthalpy of ionization d) Enthalpy of atomization
The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy? [1] a) Zero b) > 0 kJ c) 40 kJ d) < 40 kJ
How many Coulombs are required for the reduction of 1 mole of Cu^2 + to Cu? [1] a) 1.23× 105 C b) 2.12× 105 C c) 1.23× 105 C d) 1.93× 105 C
In dry cell, what acts as negative electrode? [1] a) Ammonium chloride b) Manganese dioxide c) Graphite d) Zinc
What fraction of molecules in a gas at 300 K collide with an energy equal to the activation energy of 60 kJ/mol? [1] a) 10 ( -^ 104)^ b) 10 ( -^ 1.04) c) 10 ( -^ 10.4)^ d) 10 ( -^ 20.4)
The rate qf a reaction is expressed as follows: + 12 d[ dtC]
= - 15 d[ dtD ] = + 13 d[ dtA ] = - d[ dtB ] the reaction is. [1]
a) B + 12 D → 4A + 2C b) 4A + 2B→ 2C + 3D c) 4A + B→ 2C + 3D d) B + 5D→ 3A + 2C
Solubility products (Ksp) of the salts of types MX, MX 2 and M 3 X at temperature T are 4.0 × 10 -^8 , 3.2 × 10 -^14 and 2.7 × 10 -^15 respectively. Solubilities (in mol dm -^3 ) of the salts at temperature T are in the order: [1] a) M 3 X > MX 2 > MX b) MX 2 > M 3 X > MX c) MX > M 3 X > MX 2 d) MX > MX 2 > M 3 X
According to Lewis theory, an acid is any species which
. [1]
a) Accepts a proton b) Donates a proton c) Donates a share in an electron pair d) Accepts a share in an electron pair
- When equal volumes of the following solutions containing Ag+^ ions and Cl -^ ions are mixed, precipitation of AgCl (Ksp = 1.8 × 10 -^10 ) will occur only with. [1]
a) 10 -^5 M Ag+^ and 10 -^5 M Cl - b) 10 -^4 M Ag+^ and 10 -^4 M Cl - c) 10 -^10 M Ag+^ and 10 -^10 M Cl - d) 10 -^6 M Ag+^ and 10 -^6 M Cl -
- The noble gas which forms the maximum number of compounds is. [1]
a) Ne b) He c) Xe d) Ar
- Considering thermal stability, the halide which is most stable is. [1] a) HCl b) HI c) HBr d) HF
- Which of the following reactants are used in the laboratory preparation of sulfur dioxide? [1] a) Sulfur + oxygen b) Sodium sulfite + dilute sulfuric acid c) Zinc sulphide + oxygen d) Iron pyrites + oxygen
- Which metal is found in free state? [1] a) Iron b) Sodium c) Aluminium d) Platinum
- Which of the following elements is alloyed with copper to form brass? [1] a) Lead b) Tin c) Antimony d) Zinc
- The name of the complex ion, [Fe(CN) 6 ]3 -^ is. [1] a) Tricyanoferrate(III) ion b) Hexacyanoiron(III) ion c) Hexacyanoferrate(III) ion d) Hexacyanitoferrate(III) ion
- The bonds in K 4 [Fe(CN) 6 ]are. [1]
a) Ionic and covalent b) All covalent c) All ionic d) Ionic, covalent and coordinate covalent
[Cr(NH 3 ) 6 ][Cr(SCN) 6 ]and [Cr(NH 3 ) 2 (SCN) 4 ][Cr(NH 3 ) 4 (SCN) 2 ]a examples of what type of isomerism? [1] a) Ionisation isomerism b) Solvate isomerism c) Coordination isomerism d) Linkage isomerism
The reactivity of various types of alkyl halides towards SN1 reaction is. [1] a) Secondary > primary > tertiary b) Secondary > tertiary > primary c) Primary > secondary > tertiary d) Tertiary > secondary > primary
The reaction which involves the conversion of the alkyl halide to alkyl iodide using sodium iodide and dry acetone is known as. [1] a) Swarts reaction b) Finkelstein reaction c) Stephen reaction d) Sandmeyer reaction
Identify the INCORRECT statement from the following regarding halomethanes. i. C - X bond length increases from fluoromethane to iodomethane. ii. C - X bond enthalpy of fluoromethane is least amongst others. iii. C - I bond exhibits least polarity. iv. Both C - X bond enthalpy of fluoromethane is least amongst others and C - I bond exhibits least polarity. [1] a) Option (C) b) Option (A) c) Option (B) d) Option (D)
- If n is any positive integer, then the value of i
4 n+1−i 4 n− 1 2 equals [2] a) I b) 1 c) - 1 d) - i
- The value of (^7 C 0 + 7 C 1 ) + (^7 C 1 + 7 C 2 ) + ... + (^7 C 6
- 7 C 7 ) is [2] a) 28 b) 28 - 1 c) 28 - 2 d) 28 + 1
- If f(x) = sin^2 x + sin^2
x + π 3
x + π 3
cos x and g
4
= 1, then gof(x) is [2] a) A polynomial of third degree in sin x and cos x b) A polynomial of first degree in sin x and cos x c) A constant function d) A polynomial of second degree in sin x and cos x
- The converse of the statement,If
x is a complex number, then x is a negative number is [2]
a) If x is not a negative number, then
x is not a complex number. b) If x is a negative number, then
x is a complex number. c) If
x is a real number, then x is a positive number. d) If
x is not a complex number, then x is not a negative number.
- The matrix A satisfying A
[
]
[
]
is [2]
a)
[
]
b)
[
]
c)
[
]
d)
[
]
If A and B are non - singular matrices, then [2] a) AB = BA b) (AB) -^1 = B -^1 A -^1 c) (AB) -^1 = A -^1 B -^1 d) (AB)’ = A’B’
If A and B are two square matrices such that B = - A -^1 BA, then (A + B)^2 = [2] a) 0 b) A^2 + 2AB + B^2 c) A^2 + B^2 d) A + B
If sin -^1
2 a 1+a^2
2 b 1+b^2
= 2 tan -^1 x, then x = [2] a) 1 a−+abb b) (^) 1+a−abb c) (^) 1+bab d) (^1) −bab
- If tan -^1 x x−+2^1 + tan -^1 x x+1+2 = π 4 , then x = [2]
a) ±
5 2 b) √^12 c) − √^12 d) ± (^12)
- Ifα = cos -^1
5
, β = tan -^1
3
, where 0 < α , β = π 2 , then α - β is equal to [2]
a) sin−^1
9 5 √ 10
b) cos−^1
9 5 √ 10
c) tan−^1
14
d) tan−^1
9 5 √ 10
- Given 0≤ x ≤ 12 , then the value of tan
[
sin−^1 √x 2 +
√ (^1) √−x^2 2 −^ sin
− (^1) x
]
is [2] a)
3 b) 1 c) √^13 d) - 1
General solution of tan 5θ = cot 2θ is [2] a) θ = nπ 7 + 14 π b) θ = nπ 7 + π 3 c) θ = nπ 7 + π 5 d) θ = n 7 π + π 2
If
∫ (^) e 2
[
1 log x −^
1 (log x)^2
]
dx = α + (^) logβ 2 , then [2]
a) α = e, β = 2 b) α = - e, β = - 2 c) α = e, β = - 2 d) α = - e, β = 2
- The value of
0 [
x + 2] dx, where [.]is the greatest func- tion, is [2] a) 22 b) 25 c) 23 d) 31
- The value of
∫ π 4 − 4 π^ sin (^103) x · cos (^101) x dx is [2]
a) 2 b)
( (^) π 4
c) 0 d)
( (^) π 4
0
tan−^1 x 1+x^2 dx =^ [2] a) π
2 16 b)^
π^2 4 c) π
2 8 d)^
π^2 32
∫ π 2 0
sin^1000 x dx sin^1000 x+cos^1000 x is equal to^ [2] a) 1 b) π 2 c) π 4 d) 1000
If⃗ a = ˆi +ˆj + ˆk , ⃗a · ⃗b = 1 and ⃗a ×⃗ b = ˆj − ˆk , then ⃗b = [2] a) ˆi b) ˆi − ˆj + ˆk c) 2ˆi d) 2ˆj − ˆk
A unit vector which is perpendicular toˆi + 2ˆj − 2 ˆk and −ˆi + 2ˆj + 2ˆk is [2] a) √^15 (−2ˆi + ˆk) b) √^15 (2ˆi + ˆk) c) √^15 (2ˆi + ˆj + ˆk) d) √^15 (2ˆi − ˆk)
If the points (5, - 2, 7), (2, 2,β ) and ( - 1, 6, - 1) are collinear, then the value of β is [2] a) - 3 b) 3 c) 0 d) 4
The vectorsa⃗ and ⃗b are non - collinear. The value of x for which the vectors ⃗c = (x − 2)⃗a + ⃗b and ⃗d = (2x + 1)⃗ a − ⃗b are collinear, is [2] a) 3 b) 1 c) 12 d) (^13)
Which of the following represents a pair of lines? [2] a) 2x^2 + 3xy - 4y^2 + 5x + 5y + 3 = 0 b) 2x^2 - 2y^2 + 5x + 5y + 3 = 0 c) 2x^2 + 5xy - 2y^2 + 5x + 5y + 3 = 0 d) 2x^2 + 3xy - 2y^2 + 5x + 5y + 3 = 0
If x− l 1 = y− m^2 = z+1 n is the equation of the line through (1, 2, - 1) and ( - 1, 0, 1), then (l, m, n) is [2] a) (0, 1, 0) b) (1, 2, - 1) c) (1, 1, - 1) d) ( - 1, 0, 1)
The equation of the plane passing through Z - axis and perpendicular to line x cos− 1 θ = y sin+2 θ = z− 0 3 is [2] a) X + y tanθ = 0 b) Y + z tanθ = 0 c) Y + x tanθ = 0 d) X + z tanθ = 0
If the lines x− k 1 = y+1 3 = z− 41 and x− 1 3 = 2 y 2 −k 9 = z 1 intersect, then the value of k is [2] a) - 4 b) - 2 c) 2 d) 4
If y =xlog^ x, then d dyx equals [2]
a) Xlog x -^1. 2 log x b) Log x xlog x -^1 c) (^) x log^1 x · x(log^ x−1) d) X log (log x)
- If y = x 2
a^2 + x^2 + a
2 2 log^
x +
x^2 + a^2
, then d dyx = [2] a)
x^2 + a^2 b) √x (^21) +a 2 c) 2
x^2 + a^2 d) √x (^22) +a 2
If the function y = (^) (x−ax4)(+xb−1) has an extreme at P(2, - 1), then the values of a and b are [2] a) A = 0, b = 1 b) A = 0, b = - 1 c) A = 1, b = 0 d) A = - 1, b = 0
The approximate value of 52.01^ is , where (loge5 = 1.6095) [2] a) 25.2525 b) 25. c) 25.4024 d) 25.
If a spherical balloon has a variable diameter 3x + 92 , then the rate of change of its volume with respect to x is [2] a) 2716 π (2x + 3)^2 b) 274 π (2x + 3)^2 c) 27 π (2x + 3)^2 d) 278 π (2x + 3)^2
The sides of two squares are x and y respectively, such that y = x + x^2. The rate of change of area of second square with respect to area of first square is. [2] a) X^2 + 3x - 1 b) 1 + 2x c) 2x^2 + 3x + 1 d) 2x^2 - 3x + 1
∫ (^) x 5 √1+x 3 dx = [2]
a) (^29)
(1 + x^3 ) (x^3 + 4) + c b) (^29)
(1 + x^3 ) (x^3 − 2) + c c) (^29)
1 + x^3 (x^3 - 2) + c d) (^23)
(1 + x^3 ) (x^2 + 2) + c
- 2
∫ (^) 1+cos 4 x 1 −cos 4 x dx^ =^ [2] a) - cot 2x - 2x + c b) - cot 2x + 2x + c c) Cot 2x - 2x + c d) Cot 2x + 2x + c
√ 3 − 6 x− 9 x^2 dx is equal to^ [2] a) Sin -^1
( (^3) x+ 6
( (^2) x+ 3
( (^3) x+ 2
( (^3) x+ 2
sec^3 θ dθ = [2]
a) 14 (sec θ tan θ + log |sec θ tan θ |) + c b) 12 (sec θ + tan θ + log |sec θ + tan θ |) + c c) 12 (sec θ tan θ + log |sec θ + tan θ |) + c d) Secθ tan θ + log |sec θ tan θ |) + c
- The area enclosed by the parabolas y = x^2 - 1 and y = 1 - x^2 is [2] a) 43 b) (^23) c) 13 d) (^83)
- The area of region (x, y) : x^2 + y^2 ≤ 1 ≤ x + y is [2] a) π
2 2 b) π
2 5 c) π 4 − (^12) d) π 2 3
- The order of the differential equation whose solution is x^2 + y^2 + 2gx + 2fy + c = 0, is [2] a) 4 b) 3 c) 2 d) 1
- If y(t) is a solution of (1 + t) dy dt - ty = 1 and y(0) =
- 1, then y(1) is equal to [2] a) − (^12) b) e − (^12) c) e + (^12) d) (^12)
- The order and degree of
[
d^2 y dx^2
) 3 ]^45
m m+
d^3 y dx^3 are respectively [2] a) 3, 2 b) 3, 3 c) 2, 5 d) 3, 5
- The solution ofye
−x y (^) dx − (xe −x y (^) + y^3 )dy = 0 is [2]
a) y
2 2 −^ e^
− yx = k b) x
2 2 +^ e^
−x y (^) = k c) x
2 2 −^ e^
−x y (^) = k d) y
2 2 +^ e^
− yx = k
- If the p.d.f of a c.r.v. X is f(x) =
ae−ax; x≥ 0 , a > 0 0; otherwise
. If P(0 < X < K) = 0.5, then K = [2] a) (^1) a log a b) 12 log 2 c) 12 log a d) (^) a^1 log 2
- The p.m.f. of a r.v. X is given by X = x 0 1 2 3 P(X = x)
Q^3 3q^2 p 3qp^2 P^3
If p + q = 1, then E(X) = [2] a) 4p b) 2p c) P d) 3p
- If a die is thrown 7 times, then the probability of obtaining 5 exactly 4 times is [2]
a)
6
6
b)
6
6
c) 7 C 4
6
6
d) 7 C 4
6
6
- A coin is tossed 3 times by 2 persons. The probability that both get equal number of heads, is [2] a) 165 b) 163 c) 19 d) (^38)
