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An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:

The position of a projectile launched from the origin at is given by at If the projectile was launched at an angle from the horizontal, then is (take ).

The position of a projectile launched from the origin at is given by at If the projectile was launched at an angle from the horizontal, then is (take ).

Water is flowing at a speed of

through a horizontal tube of cross-sectional area

and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water

Water is flowing at a speed of

through a horizontal tube of cross-sectional area

and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water

A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the maximum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:

A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the maximum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:

Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force (in N) exerted by the system on the floor is (take

Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force (in N) exerted by the system on the floor is (take

A cylinder of mass

and sphere of mass

are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio

A cylinder of mass

and sphere of mass

are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio

India’s Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth’s orbit is that of Mars's orbit taken Kepler’s laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to :

India’s Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth’s orbit is that of Mars's orbit taken Kepler’s laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to :

In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is :

In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is :

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to

Q.10 In-correct

A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio

A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio

Q.11 In-correct

Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27^oC to 77^oC? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).

Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27^oC to 77^oC? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).

Q.12 In-correct

The equation of state for a gas is given by

where n is the number of moles and

is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are

respectively. The work done by the gas when its temperature doubles isobarically will be :

The equation of state for a gas is given by

where n is the number of moles and

is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are

respectively. The work done by the gas when its temperature doubles isobarically will be :

Q.13 In-correct

Modern vacuum pumps can evacuate vessel down to a pressure

at room temperature (300 K). Taking

the mean distance between molecules of gas in an evacuated vessel will be of the order of :

Modern vacuum pumps can evacuate vessel down to a pressure

at room temperature (300 K). Taking

the mean distance between molecules of gas in an evacuated vessel will be of the order of :

Q.14 In-correct

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by ;

traces a curve given by

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by ;

traces a curve given by

Q.15 In-correct

A transverse wave is represented by :

For what value of the wavelength (in cm) the wave velocity is twice the maximum particle velocity?

A transverse wave is represented by :

For what value of the wavelength (in cm) the wave velocity is twice the maximum particle velocity?

Q.16 In-correct

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be :
[Given

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be :
[Given

Q.17 In-correct

Three capacitances, each of

are provided. These cannot be combined to provide the resultant capacitance of :

Three capacitances, each of

are provided. These cannot be combined to provide the resultant capacitance of :

Q.18 In-correct

A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of

The battery terminals are connected to an external resistance ‘R’. The minimum value of ‘R’, so that a current passes through the battery to charge it is :

A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of

The battery terminals are connected to an external resistance ‘R’. The minimum value of ‘R’, so that a current passes through the battery to charge it is :

Q.19 In-correct

The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance

The force between them is proportional to

The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance

The force between them is proportional to

Q.20 In-correct

The magnetic field of earth at the equator is approximately

The radius of earth is

Then the dipole moment of the earth will be nearly of the order of :

The magnetic field of earth at the equator is approximately

The radius of earth is

Then the dipole moment of the earth will be nearly of the order of :

Q.21 In-correct

When the rms voltages

are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio

If the rms voltage of the AC source is 100 V, then

When the rms voltages

are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio

If the rms voltage of the AC source is 100 V, then

Q.22 In-correct

Match List I (wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists.

List I		List II
(a)	700 nm to 1 nm	(i)	Vibrations of atoms and molecule
(b)	1 nm to 400 nm	(ii)	Inner shell electron in atom moving from one energy level to lower level.
(c)	<0.0001 nm	(iii)	Radioactive decay of the nucleus
(d)	1 mm to 0.1 m	(iv)	Magnetron value

Match List I (wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists.

List I		List II
(a)	700 nm to 1 nm	(i)	Vibrations of atoms and molecule
(b)	1 nm to 400 nm	(ii)	Inner shell electron in atom moving from one energy level to lower level.
(c)	<0.0001 nm	(iii)	Radioactive decay of the nucleus
(d)	1 mm to 0.1 m	(iv)	Magnetron value

Q.23 In-correct

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is

and the diver’s eyes are 15 cm below the surface of water. Then the radius of the circle is :

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is

and the diver’s eyes are 15 cm below the surface of water. Then the radius of the circle is :

Q.24 In-correct

Using monochromatic light of wavelength

an experimentalist sets up the Young’s double slit experiment in the three ways as shown.
If she observes that

the wavelength of light used is :

Using monochromatic light of wavelength

an experimentalist sets up the Young’s double slit experiment in the three ways as shown.
If she observes that

the wavelength of light used is :

Q.25 In-correct

The focal lengths of objective lens and eye lens of a Gallelian Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Gallelian Telescope should be :

The focal lengths of objective lens and eye lens of a Gallelian Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Gallelian Telescope should be :

Q.26 In-correct

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

Q.27 In-correct

If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of

If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of

Q.28 In-correct

Identify the gate and match A, B, Y in bracket to check.

Identify the gate and match A, B, Y in bracket to check.

Q.29 In-correct

A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?

A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?

Q.30 In-correct

An n-p-n transistor has three leads A, B and C. Connecting B and C by moist fingers, A to the positive lead of an ammeter, and C to the negative lead of the ammeter, one finds large deflection. Then, A, B and C refer respectively to :

An n-p-n transistor has three leads A, B and C. Connecting B and C by moist fingers, A to the positive lead of an ammeter, and C to the negative lead of the ammeter, one finds large deflection. Then, A, B and C refer respectively to :

In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is :

In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is :

Van der Wall’s equation for a gas is stated as,

This equation reduces to the perfect gas equation,

Van der Wall’s equation for a gas is stated as,

This equation reduces to the perfect gas equation,

The standard electrode potentials

of four metals A, B, C and D are -1.2 V, 0.6 V, 0.85 V and -0.76 V, respectively. The sequence of deposition of metals on applying potential is :

The standard electrode potentials

of four metals A, B, C and D are -1.2 V, 0.6 V, 0.85 V and -0.76 V, respectively. The sequence of deposition of metals on applying potential is :

At a certain temperature, only 50% HI is dissociated into

at equilibrium. The equilibrium constant is :

At a certain temperature, only 50% HI is dissociated into

at equilibrium. The equilibrium constant is :

Dissolving 120 g of a compound of (mol. Wt. 60) in 1000 g of water gave a solution of density 1.12g /mL. The molarity of the solution (in M)is :

Dissolving 120 g of a compound of (mol. Wt. 60) in 1000 g of water gave a solution of density 1.12g /mL. The molarity of the solution (in M)is :

The half-life period of a first order reaction is 15 minutes. The amount of substance left after one hour will be :

The half-life period of a first order reaction is 15 minutes. The amount of substance left after one hour will be :

A current of 10.0 A flows for 2.00 h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250 mol of metal X at the cathode. The oxidation state of X in the molten salt is : (F = 96,500 C)

A current of 10.0 A flows for 2.00 h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250 mol of metal X at the cathode. The oxidation state of X in the molten salt is : (F = 96,500 C)

The energy of an electron in first Bohr orbit of H-atom is -13.6eV. The energy value of electron in the excited state of Li²⁺ is :

The energy of an electron in first Bohr orbit of H-atom is -13.6eV. The energy value of electron in the excited state of Li²⁺ is :

The temperature(in K) at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is : (Atomic masses : He = 4 u, O = 16 u)

The temperature(in K) at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is : (Atomic masses : He = 4 u, O = 16 u)

Q.10 In-correct

The standard enthalpy of formation of

is -46.0 kJ/mol. If the enthalpy of formation of

from its atoms is -436 kJ/mol and that of

is -712 kJ/mol, the average bond enthalpy of N – H bond in

The standard enthalpy of formation of

is -46.0 kJ/mol. If the enthalpy of formation of

from its atoms is -436 kJ/mol and that of

is -712 kJ/mol, the average bond enthalpy of N – H bond in

Q.11 In-correct

The amount of oxygen in 3.6 moles of water is :

The amount of oxygen in 3.6 moles of water is :

Q.12 In-correct

The gas evolved on heating

with concentrated

on hydrolysis gives a white gelatinous precipitate. The precipitate is :

The gas evolved on heating

with concentrated

on hydrolysis gives a white gelatinous precipitate. The precipitate is :

Q.13 In-correct

Chloro compound of Vanadium has only spin magnetic moment of 1.73 BM. This Vanadium chloride has the formula :
(at. No. of V = 23)

Chloro compound of Vanadium has only spin magnetic moment of 1.73 BM. This Vanadium chloride has the formula :
(at. No. of V = 23)

Q.14 In-correct

An octahedral complex of

is diamagnetic. The hybridization involved in the formation of the complex is :

An octahedral complex of

is diamagnetic. The hybridization involved in the formation of the complex is :

Q.15 In-correct

Which of the following is not formed when

reacts with acidic

Which of the following is not formed when

reacts with acidic

Q.16 In-correct

Which of the following species has paired electrons?

Which of the following species has paired electrons?

Q.17 In-correct

In the following sets of reactants which two sets best exhibit the amphoteric character of

In the following sets of reactants which two sets best exhibit the amphoteric character of

Q.18 In-correct

The number and type of bonds in

The number and type of bonds in

Q.19 In-correct

The form of iron obtained from blast furnace is :

The form of iron obtained from blast furnace is :

Q.20 In-correct

The correct statement about the magnetic properties of

The correct statement about the magnetic properties of

Q.21 In-correct

Which one of the following reactions will not result in the formation of carbon-carbon bond?

Which one of the following reactions will not result in the formation of carbon-carbon bond?

Q.22 In-correct

In the hydroboration – oxidation reaction of propene with diborane, and the

In the hydroboration – oxidation reaction of propene with diborane, and the

Q.23 In-correct

The major product of the reaction

The major product of the reaction

Q.24 In-correct

For the compounds

the correct order of increasing C-halogen bond length is :

For the compounds

the correct order of increasing C-halogen bond length is :

Q.25 In-correct

Allyl phenyl ether can be prepared by heating :

Allyl phenyl ether can be prepared by heating :

Q.26 In-correct

In a nucleophilic substitution reaction :

Which one of the following undergoes complete inversion of configuration?

In a nucleophilic substitution reaction :

Which one of the following undergoes complete inversion of configuration?

Q.27 In-correct

In which of the following pairs A is more stable than B?

In which of the following pairs A is more stable than B?

Q.28 In-correct

Structure of some important polymers are given. Which one represents Buna-S?

Structure of some important polymers are given. Which one represents Buna-S?

Q.29 In-correct

Which is the major product formed when acetone is heated with iodine and potassium hydroxide?

Which is the major product formed when acetone is heated with iodine and potassium hydroxide?

Q.30 In-correct

Which one of the following class of compounds is obtained by polymerization of acetylene?

Which one of the following class of compounds is obtained by polymerization of acetylene?

Let P be the relation defined on the set of all real numbers such that
P={(a,b):sec²a - tan²b=1}. Then P is :

Let P be the relation defined on the set of all real numbers such that
P={(a,b):sec²a - tan²b=1}. Then P is :

be a complex number. Then the set of all complex numbers z satisfying the equation

for some real number k, is :

be a complex number. Then the set of all complex numbers z satisfying the equation

for some real number k, is :

have a common root, then a : b :c equals

have a common root, then a : b :c equals

are the roots of the equation, ax² +bx+1=0, (a≠0, a,b∈R) then the equation, x(x+b³)+(a³- 3abx)=0 has roots :

are the roots of the equation, ax² +bx+1=0, (a≠0, a,b∈R) then the equation, x(x+b³)+(a³- 3abx)=0 has roots :

If a, b, c are non-zero real numbers and if the system of equations

has a non-trivial solution, then

If a, b, c are non-zero real numbers and if the system of equations

has a non-trivial solution, then

If B is a 3×3 matrix such that B²=0 then determinant |(I+B)⁵⁰ - 50B| is equal to

If B is a 3×3 matrix such that B²=0 then determinant |(I+B)⁵⁰ - 50B| is equal to

The number of terms in the expansion of (1+x)¹⁰¹(1+x²-x)¹⁰⁰ in powers of x is :

The number of terms in the expansion of (1+x)¹⁰¹(1+x²-x)¹⁰⁰ in powers of x is :

The sum of the digits in the unit’s place of all the 4-digit numbers by using the numbers formed by using the numbers 3, 4, 5 and 6, without repetition, is :

The sum of the digits in the unit’s place of all the 4-digit numbers by using the numbers formed by using the numbers 3, 4, 5 and 6, without repetition, is :

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4^th term is:

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4^th term is:

Q.10 In-correct

up to 20 terms is equal to

then k is equal to :

up to 20 terms is equal to

then k is equal to :

Q.11 In-correct

If f(x) is continuous and f(9/2)=2/9 then

If f(x) is continuous and f(9/2)=2/9 then

Q.12 In-correct

Q.13 In-correct

If the Rolle’s theorem holds for the function f(x)=2x³+ax²+bx in the interval

then the value of 2a+b is :

If the Rolle’s theorem holds for the function f(x)=2x³+ax²+bx in the interval

then the value of 2a+b is :

Q.14 In-correct

then the equation

then the equation

Q.15 In-correct

Q.16 In-correct

Q.17 In-correct

The area (in square units) of the region A is :

The area (in square units) of the region A is :

Q.18 In-correct

If the differential equation representing the family of all circles touching x-axis at the origin is

If the differential equation representing the family of all circles touching x-axis at the origin is

Q.19 In-correct

Let a and b be any two numbers satisfying

Then, the foot of perpendicular from the origin on the variable line,

Let a and b be any two numbers satisfying

Then, the foot of perpendicular from the origin on the variable line,

Q.20 In-correct

80. Given three points P, Q, R with P(5, 3) and R lies on the x-axis. If the equation of RQ is x-2y=2 and PQ is parallel to the x-axis, then the centroid of ΔPQR lies on the line :

80. Given three points P, Q, R with P(5, 3) and R lies on the x-axis. If the equation of RQ is x-2y=2 and PQ is parallel to the x-axis, then the centroid of ΔPQR lies on the line :

Q.21 In-correct

If the point (1, 4) lies inside the circle x²+y²-6x-10y+p=0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval :

If the point (1, 4) lies inside the circle x²+y²-6x-10y+p=0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval :

Q.22 In-correct

If OB is the semi-minor axis of an ellipse,

are its foci and the angle between F₁B and F₂B is a right angle, then the square of the eccentricity of the ellipse is :

If OB is the semi-minor axis of an ellipse,

are its foci and the angle between F₁B and F₂B is a right angle, then the square of the eccentricity of the ellipse is :

Q.23 In-correct

Equation of the plane which passes through the point of intersection of lines

and has the largest distance from the origin is :

Equation of the plane which passes through the point of intersection of lines

and has the largest distance from the origin is :

Q.24 In-correct

A line in the 3-dimensional space makes an angle

with both the x and y axes. Then the set of all values of θ is the interval :

A line in the 3-dimensional space makes an angle

with both the x and y axes. Then the set of all values of θ is the interval :

Q.25 In-correct

Q.26 In-correct

In a set of 2n distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations :

In a set of 2n distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations :

Q.27 In-correct

If A and B are two events such that P(A∪B)=P(A∩B), then the incorrect statement amongst the following statements is :

If A and B are two events such that P(A∪B)=P(A∩B), then the incorrect statement amongst the following statements is :

Q.28 In-correct

The number of values of α in [0,2π] for which 2sin³ α - 7sin²α+7sinα=2 is :

The number of values of α in [0,2π] for which 2sin³ α - 7sin²α+7sinα=2 is :

Q.29 In-correct

Q.30 In-correct

The contrapositive of the statement “I go to school if it does not rain” is:

The contrapositive of the statement “I go to school if it does not rain” is:

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