BITSAT - Paper 2020

An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is

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An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is

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Q.2 Correct

Q.2 In-correct

Q.2 Unattempt

A vessel of depth 2d‌cm is half filled with a liquid of refractive index µ1 and the upper half with a liquid of refractive index µ2. The apparent depth of the vessel seen perpendicularly is

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A vessel of depth 2d‌cm is half filled with a liquid of refractive index µ1 and the upper half with a liquid of refractive index µ2. The apparent depth of the vessel seen perpendicularly is

The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

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The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

A body of density ρ′ is dropped from rest at a height h into a lake of density ρ where ρ>ρ′ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface :

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A body of density ρ′ is dropped from rest at a height h into a lake of density ρ where ρ>ρ′ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface :

If the forward voltage in a semiconductor diode is changed from 0.5V to 0.7V, then the forward current changes by 1.0‌mA. The forward resistance of diode junction will be

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If the forward voltage in a semiconductor diode is changed from 0.5V to 0.7V, then the forward current changes by 1.0‌mA. The forward resistance of diode junction will be

The heat generated in a circuit is given by Q=I2‌Rt, where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%,1% and 1% respectively, then the maximum error in measuring heat will be

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The heat generated in a circuit is given by Q=I2‌Rt, where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%,1% and 1% respectively, then the maximum error in measuring heat will be

The r.m.s. velocity of oxygen molecule at 16°C is 474 m/sec. The r.m.s. velocity in m/s of hydrogen molecule at 127°C is

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The r.m.s. velocity of oxygen molecule at 16°C is 474 m/sec. The r.m.s. velocity in m/s of hydrogen molecule at 127°C is

A projectile A is thrown at an angle of 30° to the horizontal from point P. At the same time, another projectile B is thrown with velocity v2 upwards from the point Q vertically below the highest point. For B to collide with A,

A projectile A is thrown at an angle of 30° to the horizontal from point P. At the same time, another projectile B is thrown with velocity v2 upwards from the point Q vertically below the highest point. For B to collide with A,

The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20m without skidding is (g=9.8m∕s2)

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The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20m without skidding is (g=9.8m∕s2)

A boy pushes a toy box 2.0m along the floor by means of a force of 10N directed downward at an angle of 60° to the horizontal. The work done by the boy is

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A boy pushes a toy box 2.0m along the floor by means of a force of 10N directed downward at an angle of 60° to the horizontal. The work done by the boy is

The engine of a truck moving along a straight road delivers constant power. The distance travelled by the truck in time t is proportional to

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The engine of a truck moving along a straight road delivers constant power. The distance travelled by the truck in time t is proportional to

The escape velocity from a planet is ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

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The escape velocity from a planet is ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

If the the earth is at one-fourth of its present distance from the sun, the duration of year will be

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If the the earth is at one-fourth of its present distance from the sun, the duration of year will be

A vessel with water is placed on a weighing pan and it reads 600g. Now a ball of mass 40g and density 0.80gcm−3 is sunk into the water with a pin of negligible volume, as shown in figure keeping it sunk. The weighing pan will show a reading

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A vessel with water is placed on a weighing pan and it reads 600g. Now a ball of mass 40g and density 0.80gcm−3 is sunk into the water with a pin of negligible volume, as shown in figure keeping it sunk. The weighing pan will show a reading

In an adiabatic process, the pressure is increased by

, then the volume decreases by nearly

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In an adiabatic process, the pressure is increased by

, then the volume decreases by nearly

The equation of a projectile is y=√3x−

gx2

2

The angle of projection is given by

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The equation of a projectile is y=√3x−

gx2

2

The angle of projection is given by

Frequency of oscillation is proportional to

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Frequency of oscillation is proportional to

Two wires A and B of the same material, having radii in the ratio 1:2 and carry currents in the ratio 4:1. The ratio of drift speed of electrons in A and B is

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Two wires A and B of the same material, having radii in the ratio 1:2 and carry currents in the ratio 4:1. The ratio of drift speed of electrons in A and B is

An instantaneous displacement of a simple harmonic oscillator is x=A‌cos(ωt+

π

4

). Its speed will be maximum at time

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An instantaneous displacement of a simple harmonic oscillator is x=A‌cos(ωt+

π

4

). Its speed will be maximum at time

The energy of electron in the nth orbit of hydrogen atom is expressed as En=

−13.6

n2

‌eV.
The shortest and longest wavelength of Lyman series will be

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The energy of electron in the nth orbit of hydrogen atom is expressed as En=

−13.6

n2

‌eV.
The shortest and longest wavelength of Lyman series will be

In the circuit given below, the charge in µC, on the capacitor having 5µF is

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In the circuit given below, the charge in µC, on the capacitor having 5µF is

A crystal has a coefficient of expansion 13×10−7 in one direction and 231×10−7 in every direction at right angles to it. Then the cubical coefficient of expansion is

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A crystal has a coefficient of expansion 13×10−7 in one direction and 231×10−7 in every direction at right angles to it. Then the cubical coefficient of expansion is

A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

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A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

A whistle of frequency 1000‌Hz is sounded on a car travelling towards a cliff with velocity of 18 ms−1 normal to the cliff. If c=330ms−1, then the apparent frequency of the echo as heard by the car driver is nearly

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A whistle of frequency 1000‌Hz is sounded on a car travelling towards a cliff with velocity of 18 ms−1 normal to the cliff. If c=330ms−1, then the apparent frequency of the echo as heard by the car driver is nearly

A thin sheet of glass (µ=1.5) of thickness 6 micron introduced in the path of one of the interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. Then the wavelength of light used is

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A thin sheet of glass (µ=1.5) of thickness 6 micron introduced in the path of one of the interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. Then the wavelength of light used is

M.I of a circular loop of radius R about the axis in figure is

Q.27 Correct

Q.27 In-correct

Q.27 Unattempt

Three charge q,Q and 4q are placed in a straight line of length l at points distant 0,

1

2

and l respectively from one end. In order to make the net force on q zero, the charge Q must be equal to

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Three charge q,Q and 4q are placed in a straight line of length l at points distant 0,

1

2

and l respectively from one end. In order to make the net force on q zero, the charge Q must be equal to

In series combination of R,L and C with an A.C source at resonance, if R=20‌ohm, then impedence Z of the combination is

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In series combination of R,L and C with an A.C source at resonance, if R=20‌ohm, then impedence Z of the combination is

An electron moves in a circular arc of radius 10 m at a constant speed of 2×107ms−1 with its plane of motion normal to a magnetic flux density of 10−5T. What will be the value of specific charge of the electron?

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An electron moves in a circular arc of radius 10 m at a constant speed of 2×107ms−1 with its plane of motion normal to a magnetic flux density of 10−5T. What will be the value of specific charge of the electron?

From a 200m high tower, one ball is thrown upwards with speed of 10ms−1 and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

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From a 200m high tower, one ball is thrown upwards with speed of 10ms−1 and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

A wheel is rotating at 900 r.p.m. about its axis. When power is cut off it comes to rest in 1 minute. The angular retardation in rad∕s2 is

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A wheel is rotating at 900 r.p.m. about its axis. When power is cut off it comes to rest in 1 minute. The angular retardation in rad∕s2 is

A particle executing simple harmonic motion along y-axis has its motion described by the equation y=A‌sin(ωt)+B. The amplitude of the simple harmonic motion is

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A particle executing simple harmonic motion along y-axis has its motion described by the equation y=A‌sin(ωt)+B. The amplitude of the simple harmonic motion is

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere.

The current induced in the loop is

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A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere.

The current induced in the loop is

A body of mass 2kg is placed on a horizontal surface having kinetic friction 0.4 and static friction 0.5. If the horizontal force applied on the body is 2.5N, the frictional force acting on the body will be (g=10ms2)

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A body of mass 2kg is placed on a horizontal surface having kinetic friction 0.4 and static friction 0.5. If the horizontal force applied on the body is 2.5N, the frictional force acting on the body will be (g=10ms2)

A nucleus splits into two nuclear parts which have their velocity ratio equal to 2:1 . What will be the ratio of their nuclear radius?

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A nucleus splits into two nuclear parts which have their velocity ratio equal to 2:1 . What will be the ratio of their nuclear radius?

A charge +q is at a distance

L

2

above a square of side L. Then what is the flux linked with the surface?

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A charge +q is at a distance

L

2

above a square of side L. Then what is the flux linked with the surface?

A plane electromagnetic wave is incident on a plane surface of area A, normally and is perfectly reflected. If energy E strikes the surface in time t then average pressure exerted on the surface is (c = speed of light)

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A plane electromagnetic wave is incident on a plane surface of area A, normally and is perfectly reflected. If energy E strikes the surface in time t then average pressure exerted on the surface is (c = speed of light)

There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be

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There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be

Determine the current in 2Ω resistor.

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Determine the current in 2Ω resistor.

Q.40 Correct

Q.40 In-correct

Q.40 Unattempt

The potential energy of a satellite of mass m and revolving at a height Rc above the surface of earth where Rc= radius of earth, is

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The potential energy of a satellite of mass m and revolving at a height Rc above the surface of earth where Rc= radius of earth, is

If 0.2 gram of an organic compound containing carbon, hydrogen and oxygen on combustion, yielded 0.147 gram carbon dioxide and 0.12 gram water. What will be the content of oxygen in the substance ?

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If 0.2 gram of an organic compound containing carbon, hydrogen and oxygen on combustion, yielded 0.147 gram carbon dioxide and 0.12 gram water. What will be the content of oxygen in the substance ?

The Lassaigne’s extract is boiled with dil. HNO3 before testing for halogens because

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The Lassaigne’s extract is boiled with dil. HNO3 before testing for halogens because

What is X in the following conversion ?

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What is X in the following conversion ?

Q.44 Correct

Q.44 In-correct

Q.44 Unattempt

Maleic acid and fumaric acids are

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Maleic acid and fumaric acids are

For which one of the processes represented by the following equations the enthalpy (heat) change is likely to be negative

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For which one of the processes represented by the following equations the enthalpy (heat) change is likely to be negative

A cyclic process ABCD is shown in P-V diagram for an ideal gas. Which of the following diagram represents the same process?

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A cyclic process ABCD is shown in P-V diagram for an ideal gas. Which of the following diagram represents the same process?

In a monoclinic unit cell, the relation of sides and angles are respectively:

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In a monoclinic unit cell, the relation of sides and angles are respectively:

Phosphine is not obtained by which of the following reaction?

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Phosphine is not obtained by which of the following reaction?

An ideal gaseous mixture of ethane (C2H6) and ethene (C2H4) occupies 28 litre at 1 atm and 273 K. The mixture reacts completely with 128 g O2 to produce CO2 and H2O. Mole fraction at C2H6 in the mixture is:

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An ideal gaseous mixture of ethane (C2H6) and ethene (C2H4) occupies 28 litre at 1 atm and 273 K. The mixture reacts completely with 128 g O2 to produce CO2 and H2O. Mole fraction at C2H6 in the mixture is:

What is the maximum wavelength line in the Lyman series of He+ ion?

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What is the maximum wavelength line in the Lyman series of He+ ion?

The correct order of acidic strength :

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The correct order of acidic strength :

In the reaction 2PCl5⇌PCl4++PCl6−, the change in hybridisation is from

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In the reaction 2PCl5⇌PCl4++PCl6−, the change in hybridisation is from

Arrange the following ions in the order of decreasing X−O bond length, where X is the central atom

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Arrange the following ions in the order of decreasing X−O bond length, where X is the central atom

Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molecular existence at the respective temperature of 27 °C and 227 °C and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is

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Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molecular existence at the respective temperature of 27 °C and 227 °C and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is

For the combustion reaction at 298 K
2‌Ag(s)+

1

2

O2(g)→2Ag2O(s)
Which of the following alternatives is correct?

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For the combustion reaction at 298 K
2‌Ag(s)+

1

2

O2(g)→2Ag2O(s)
Which of the following alternatives is correct?

for the reaction
CO(g)+

for the reaction
CO(g)+

A solution of NH4‌Cl and NH3 has pH=8.0. Which of the following hydroxides may be precipitated when this solution is mixed with equal volume of 0.2M of metal ion.

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A solution of NH4‌Cl and NH3 has pH=8.0. Which of the following hydroxides may be precipitated when this solution is mixed with equal volume of 0.2M of metal ion.

Which of the following is not a disproportionation reaction?

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Which of the following is not a disproportionation reaction?

The amount of H2O2, present in 1 litre of 1.5 N H2O2, solution, is :

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The amount of H2O2, present in 1 litre of 1.5 N H2O2, solution, is :

BeF2 is soluble in water whereas fluorides of other alkaline earth metals are insoluble because of

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BeF2 is soluble in water whereas fluorides of other alkaline earth metals are insoluble because of

Identify the incorrect statement :

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Identify the incorrect statement :

The alcohol product(s) of the reduction of 2-methyl-3-pentanone with LiAlH4 is (are)

Q.63 Correct

Q.63 In-correct

Q.63 Unattempt

Br• will abstract which of the hydrogen most readily?

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Br• will abstract which of the hydrogen most readily?

The vapour pressure of two pure liquids A and B that form an ideal solution, are 400 and 800mm of Hg respectively at a temperature t°C. The mole fraction of A in a solution of A and B whose boiling point is t°C will be

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The vapour pressure of two pure liquids A and B that form an ideal solution, are 400 and 800mm of Hg respectively at a temperature t°C. The mole fraction of A in a solution of A and B whose boiling point is t°C will be

On reaction with sodium, 1‌mol of a compound X gives 1‌mol of H2. Which one of the following compounds might be X?

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On reaction with sodium, 1‌mol of a compound X gives 1‌mol of H2. Which one of the following compounds might be X?

The following change can be carried out with

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The following change can be carried out with

The greenhouse effect is because of the

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The greenhouse effect is because of the

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25°C. For this process, which of the following statement is correct?

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Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25°C. For this process, which of the following statement is correct?

The final product obtained in the reaction

Q.70 Correct

Q.70 In-correct

Q.70 Unattempt

What is the product of the following reaction ?

The d -electron configurations of Cr2+,Mn2+,Fe2+ and Co2+ are d4,d5,d6 and d7 respectively. Which one of the following will exhibit the lowest paramagnetic behaviour?
(Atomic no. Cr=24,Mn=25,Fe=26,Co=27 ).

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The d -electron configurations of Cr2+,Mn2+,Fe2+ and Co2+ are d4,d5,d6 and d7 respectively. Which one of the following will exhibit the lowest paramagnetic behaviour?
(Atomic no. Cr=24,Mn=25,Fe=26,Co=27 ).

An organic compound with the formula C6H12O6 forms a yellow crystalline solid with phenylhydrazine and gives a mixture of sorbitol and mannitol when reduced with sodium. Which among the following could be the compound?

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An organic compound with the formula C6H12O6 forms a yellow crystalline solid with phenylhydrazine and gives a mixture of sorbitol and mannitol when reduced with sodium. Which among the following could be the compound?

Compounds I and II may be grouped as

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Compounds I and II may be grouped as

Which is not the correct statement? (At. nos. Ce=58,Lu=71,La=57,Yb=70)

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Which is not the correct statement? (At. nos. Ce=58,Lu=71,La=57,Yb=70)

Which of the following reactions will not give N, N- dimethyl benzamide ?

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Which of the following reactions will not give N, N- dimethyl benzamide ?

Select the incorrect statement.

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Select the incorrect statement.

Product (D) in above reaction is:

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Product (D) in above reaction is:

ΔfG− vs T plot in the Ellingham diagram slopes downward for the reaction

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ΔfG− vs T plot in the Ellingham diagram slopes downward for the reaction

A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope?

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A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope?

One of them would keep a look-out on the road behind to warn us ________ approaching vehicles.

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One of them would keep a look-out on the road behind to warn us ________ approaching vehicles.

The top-ranking manager __________ his success in the profession to his managing director's guidance.

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The top-ranking manager __________ his success in the profession to his managing director's guidance.

Mother Teresa asked a building where she and her workers could care for the poor people always.

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Mother Teresa asked a building where she and her workers could care for the poor people always.

You may not realize it but the weather in Barbados during Christmas is like New York in June.

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You may not realize it but the weather in Barbados during Christmas is like New York in June.

The parents decided it was worth the risk because these children would have succumbed their disease before adulthood.

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The parents decided it was worth the risk because these children would have succumbed their disease before adulthood.

The statement that 'he later threw off the security bug' means that

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The statement that 'he later threw off the security bug' means that

Which one of the following phrases best helps to bring out the precise meaning of 'loathsome creatures'?

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Which one of the following phrases best helps to bring out the precise meaning of 'loathsome creatures'?

In his dream, Harold found the loathsome creatures

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In his dream, Harold found the loathsome creatures

Harold's dream was fearful because

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Harold's dream was fearful because

Which of the option figures bears the closest resemblance to the question figure?

In the following questions a piece of paper is folded and punched as shown in problem figures and four answer figure marked (a), (b), (c), (d) are given. Select the answer figure which indicates how the paper will appear when open (unfolded).

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In the following questions a piece of paper is folded and punched as shown in problem figures and four answer figure marked (a), (b), (c), (d) are given. Select the answer figure which indicates how the paper will appear when open (unfolded).

Which answer figure complete the form in question figure ?

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Which answer figure complete the form in question figure ?

From the answer figure choose the box that is similar to the box formed by folding the question figure.

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From the answer figure choose the box that is similar to the box formed by folding the question figure.

In each of the following question select the missing number from the given responses.

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Q.101 Correct

Q.101 In-correct

Q.101 Unattempt

A clock with only dot markings 3, 6, 9 and 12 positions has been kept upside down in front of a mirror. A person reads the time in the reflections of the clock as 12: 30 the actual that will be

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A clock with only dot markings 3, 6, 9 and 12 positions has been kept upside down in front of a mirror. A person reads the time in the reflections of the clock as 12: 30 the actual that will be

Six friends −A,B,C,D,E and F are sitting in a circle facing center. F is to the immediate left of A and B is sitting opposite to F, E and Dare sitting opposite to each other. Who is sitting third right to A ?

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Six friends −A,B,C,D,E and F are sitting in a circle facing center. F is to the immediate left of A and B is sitting opposite to F, E and Dare sitting opposite to each other. Who is sitting third right to A ?

Ganesh cycles towards South-West a distance of 8 m. Then he moves towards East a distance of 20 m. From there he moves towards North-East a distance of 8 m, then he moves towards West a distance of 6m. From there he moves towards North-East a distance of 2 m. Then he moves towards West a distance of 4 m and then towards South-West 2 m and stops at that point. How far is he from the starting point ?

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Ganesh cycles towards South-West a distance of 8 m. Then he moves towards East a distance of 20 m. From there he moves towards North-East a distance of 8 m, then he moves towards West a distance of 6m. From there he moves towards North-East a distance of 2 m. Then he moves towards West a distance of 4 m and then towards South-West 2 m and stops at that point. How far is he from the starting point ?

If in a code language, LAPTOP is written as PNSOZL and NOTEBOOK and KNNADSNN, then which letter will be there in first and seventh letter from left after coding MEDICINE in the same way?

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If in a code language, LAPTOP is written as PNSOZL and NOTEBOOK and KNNADSNN, then which letter will be there in first and seventh letter from left after coding MEDICINE in the same way?

Find the next term in the following series:
X24C, V22E, T20G______

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Find the next term in the following series:
X24C, V22E, T20G______

Let [x] denote the greatest integer ≤x. If f(x)= [x] and g(x)=|x|, then the value of f(g(

Let [x] denote the greatest integer ≤x. If f(x)= [x] and g(x)=|x|, then the value of f(g(

If a chord of the circle x2+y2=8 makes equal intercets of length a on the coordinate axes, then

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If a chord of the circle x2+y2=8 makes equal intercets of length a on the coordinate axes, then

In the given figure, the equation of the larger circle is x2+y2+4y−5=0 and the distance between centres is 4. Then the equation of smaller circle is

Q.109 Correct

Q.109 In-correct

Q.109 Unattempt

The equation sin4x−(k+2)sin2x−(k+3)=0 possesses a solution if

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The equation sin4x−(k+2)sin2x−(k+3)=0 possesses a solution if

If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils. The number of ways of distributing the pencils is

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If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils. The number of ways of distributing the pencils is

If a,b,c are positive numbers, then least value of (a+b+c)(

If a,b,c are positive numbers, then least value of (a+b+c)(

is

is

are non-zero constant vectors and thescalar b is chosen such that |

| is minimum, then the value of |b

are non-zero constant vectors and thescalar b is chosen such that |

| is minimum, then the value of |b

Statement-1 : If the general equation x2+y2+2xy+2gx+2fy+4=0 represents a pair of real lines then |g|≥2.
Statement- 2 : The equation ax2+2hxy+by2+2gx+2fy+c=0 represents pair of real lines if abc+2fgh−af2−bg2−ch2=0

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Statement-1 : If the general equation x2+y2+2xy+2gx+2fy+4=0 represents a pair of real lines then |g|≥2.
Statement- 2 : The equation ax2+2hxy+by2+2gx+2fy+c=0 represents pair of real lines if abc+2fgh−af2−bg2−ch2=0

If |z1|=|z2|=.......|zn|=1, then the value of |z1+z2+......zn|− |

If |z1|=|z2|=.......|zn|=1, then the value of |z1+z2+......zn|− |

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V. is

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In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V. is

The domain of the function f(x)=√x−√1−x2 is

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The domain of the function f(x)=√x−√1−x2 is

If the coordinates at one end of a diameter of the circle x2+y2−8x−4y+c=0 are (−3,2), then the coordinates at the other end are

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If the coordinates at one end of a diameter of the circle x2+y2−8x−4y+c=0 are (−3,2), then the coordinates at the other end are

The value of sin[nπ+(−1)n

The value of sin[nπ+(−1)n

The number of possible outcomes in a throw of n ordinary dice in which at least one of the dice shows an odd number is

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The number of possible outcomes in a throw of n ordinary dice in which at least one of the dice shows an odd number is

The sum of the infinite series

The sum of the infinite series

The solution of the differential equation (x+1)

The solution of the differential equation (x+1)

Consider the function f(x)=

Consider the function f(x)=

A straight rod of length 9 units slides with its ends A,B always on the X and Y -axis respectively. Then the locus of the centroid of ΔOAB is

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A straight rod of length 9 units slides with its ends A,B always on the X and Y -axis respectively. Then the locus of the centroid of ΔOAB is

If xy+y2=tan‌x+y, then find

dy

dx

is

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If xy+y2=tan‌x+y, then find

is

The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is

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The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is

Let x+y=3−cos‌4‌θ and x−y=4‌sin‌2‌θ then the greatest of xy is

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Let x+y=3−cos‌4‌θ and x−y=4‌sin‌2‌θ then the greatest of xy is

Total number of ways of selecting 2 white squares on a normal chess board if the squares are not from the same row or column is equal to

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Total number of ways of selecting 2 white squares on a normal chess board if the squares are not from the same row or column is equal to

The length of the latus rectum of the parabola which has focus at (−1,1) and the directrix is 4x+3y−24=0 is

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The length of the latus rectum of the parabola which has focus at (−1,1) and the directrix is 4x+3y−24=0 is

x‌sin(π[x]−x)‌d‌x is equal to

x‌sin(π[x]−x)‌d‌x is equal to

A student read common difference of an A. P. as -2 instead of 2 and got the sum of first 5 terms as -5 . Actual sum of first five terms is

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A student read common difference of an A. P. as -2 instead of 2 and got the sum of first 5 terms as -5 . Actual sum of first five terms is

The number of real solutions of the equation (x−1)2+(x−2)2+(x−3)2=0 is

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The number of real solutions of the equation (x−1)2+(x−2)2+(x−3)2=0 is

The least positive non-integral solution of the equation sin‌π(x2+x)=sin‌π‌x2 is

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The least positive non-integral solution of the equation sin‌π(x2+x)=sin‌π‌x2 is

ABC is a triangular park with AB=AC=100m. ATV tower stands at the mid-point of BC. The angles of elevation of the top of the tower at A, B, C are 45°,60°,60° respectively. The height of the tower is

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ABC is a triangular park with AB=AC=100m. ATV tower stands at the mid-point of BC. The angles of elevation of the top of the tower at A, B, C are 45°,60°,60° respectively. The height of the tower is

If x,y,z are real and distinct, then f(x,y,z)=x2+4y2+9z2−6yz−3zx−2xy is always

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If x,y,z are real and distinct, then f(x,y,z)=x2+4y2+9z2−6yz−3zx−2xy is always

A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is

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A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is

If a>0,b>0,c>0 and a,b,c are distinct, then (a+b)(b+c)(c+a) is greater than

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If a>0,b>0,c>0 and a,b,c are distinct, then (a+b)(b+c)(c+a) is greater than

The equation of the tangent to the curve y=be−x∕a at the point where it crosses the y -axis is

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The equation of the tangent to the curve y=be−x∕a at the point where it crosses the y -axis is

The solutions of (x+y+1)dy=dx are

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The solutions of (x+y+1)dy=dx are

If y=3x+6x2+10x3+....∞, then

If y=3x+6x2+10x3+....∞, then

Suppose p,q,r≠0 and system of equation
(p+a)x+by+cz=0
ax+(q+b)y+cz=0
ax+by+(r+c)z=0
has a non-trivial solution, then value of

Suppose p,q,r≠0 and system of equation
(p+a)x+by+cz=0
ax+(q+b)y+cz=0
ax+by+(r+c)z=0
has a non-trivial solution, then value of

If a,c,b are in G.P., then the area of the triangle formed by the lines ax+by+c=0 with the coordinates axes is equal to

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If a,c,b are in G.P., then the area of the triangle formed by the lines ax+by+c=0 with the coordinates axes is equal to

Suppose that f(0)=−3 and f′(x)≤5 for all values of x.
Then, the largest value which f(2) can attain is

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Suppose that f(0)=−3 and f′(x)≤5 for all values of x.
Then, the largest value which f(2) can attain is

The maximum value of z=6x+8y subject to constraints 2x+y≤30,x+2y≤24 and x≥0,y≥0 is

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The maximum value of z=6x+8y subject to constraints 2x+y≤30,x+2y≤24 and x≥0,y≥0 is

If a,b,c are three natural numbers in AP and a+b+c=21 then the possible number of values of the ordered triplet (a,b,c) is

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If a,b,c are three natural numbers in AP and a+b+c=21 then the possible number of values of the ordered triplet (a,b,c) is

=1 touches the ellipse

=1 touches the ellipse

Let f be the function defined by f(x)={

Let f be the function defined by f(x)={

The line y=mx bisects the area enclosed by lines x =0,y=0 and x=

3

2

and the curve y=1+4x−x2Then the value of m is

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The line y=mx bisects the area enclosed by lines x =0,y=0 and x=

3

2

and the curve y=1+4x−x2Then the value of m is

There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers are

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There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers are

The distance from the point (3,4,5) to the point where the line

meets the plane x+y+z=17 is

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The distance from the point (3,4,5) to the point where the line

meets the plane x+y+z=17 is

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