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Let a, b, c be such that If then the value of n is

zero

any integer

any even integer

any odd integer

If the mean deviation of the numbers from their mean is , then the d is equal to

20.2

10.1

10.0

20.0

If the roots of the equation be imaginary, then for all real values of x, the expression is

greater than 4ab

less than â€“ 4ab

less than 4ab

greater than â€“ 4ab

Let A and Bdenote the statementsA: B: if ,then

both A and B are false

A is false and B is false

A is false and B is true

both A and B are true

The lines and are perpendicular to the common line for

exactly one value of p

no value of p

more than two values of p

exactly two values of p

If A, B and C are three sets such that and then

A = B

A = C

B = C

If are noncoplanar vectors and p, q are real numbers, then the equality holds for

more than two but not all values of (p, q)

exactly two values of (p, q)

all values of (p, q)

exactly one value of (p, q)

Let lie in the plane Then equals

(5, â€“ 15)

(â€“ 5, 5)

(â€“ 6, 7)

(6, â€“ 17)

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

at least 750 but less than 1000

at least 500 but less than 750

less than 500

at least 1000

For real let then

is neither one-one nor onto R

In a binomial distribution If the probability of at least one sussess is greater then or equal to then is greater then

If P and Q are the points of intersection of the circles , then there is a circle passing through P, Q and (1,1) for:

all values of p

all except one value of p

all except two values of p

The projections of a vector on the three coordinate axis are respectively. The direction cosines of the vector are:

If then the maximum value of | Z | is equal to

Three distinct points A, B and C are given in the 2dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (â€“1, 0) is equal to (1 / 3) . Then the circumcentre of the triangle ABC is at the point

The remainder left out when is divided by 9 is

7

0

2

8

The ellipse is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0) . Then the equation of the ellipse is

The sum to infinity of the series is

3

4

6

The differential equation which represents the family of curves where and are arbitrary constants, is

One ticket is selected at randon from 50 tickets numbered 00, 01, 02, ...., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals:

Let be an implicit function of defined by Then y’ (1) equals

The area of the region bounded by the parabola the tangent to the parabola at the point (2, 3) and the x-axis is :

12

9

Given such that is the only real root of If then in the interval [-1, 1] :

P (-1) is not minimum but P (1) is the maximum of P

neitherP (-1) is the minimum nor P (1) is the maximum of P

P (-1) is the minimum and P (1) is the maximum of P

P (-1) is the minimum but P (1) is not the maximum of P

The shortest distance between the line and the curve is :

Directions: Assertion Reason type questions. Question contains two statements:Statement 1 (Assertion) and Statement 2 (Reason). Each of the question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let ,Statement 1: The set Statement 2: f is a bijection. (1) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is a correct explanation for Statement 1. (2) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is not a correct explanation for Statement 1.(3) Statement 1 is true, Statement 2 is false.(4) Statement 1 is false, Statement 2 is true.

1 or 2

3 or 4

2 or 3

1 or 3

Directions: Assertion Reason type questions. Question contains two statements:Statement 1 (Assertion) and Statement 2 (Reason). Each of the question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let Statement -1 : gof is differentiable at x = 0 and its derivative is continuous at that point.Statement -2 : gof is twice differentiable at x = 0.(1) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is a correct explanation for Statement 1.(2) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is not a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is false.(4) Statement 1 is false, Statement 2 is true.

1

2 or 4

Statement 1: The variance of first n even natural numbers is Statement 2: The sum of first n natural numbers is and the sum of squares of first n natural numbers is (1) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is a correct explanation for Statement 1. (2) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is not a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

Statement 1: to Statement 2:$\backslash sim\; (p\; \backslash leftrightarrow\; \backslash sim\; q)\; is\; tautology.$ (1) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is a correct explanation for Statement 1. (2) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is not a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

Let A be a 2 X 2 matrix. Statement 1: adj (adj (A)) = A. Statement 2: | adj A | = | A |. (1) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is a correct explanation for Statement 1. (2) Statement 1 is true, Statement 2 is trueÍ¾ Statement 2 is not a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

This question contains Statement1 and Statement2 Of the four choices given after the statements, chooze the one that best describes the two statements. Statement1 :For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q.Statement 2 : The net work done by a conservative force on an object moving along a closed loop is zero. (1) Statement1 is true, Statement2 is false.(2) Statement1 is true, Statement2 is trueÍ¾ Statement 2 is the correct explanation of Statement1(3) Statement1 is true, Statement2 is trueÍ¾ Statement 2 is not the correct explanation of Statement1(4) Statement1 is false, Statement2 is true.

(ii) and (iv)

(i) and (iii)

(i) and (iv)

(ii) and (iii)

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lenss and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45Â° with the xaxis meets the experimental curve at P. The coordinates of P will be:

A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is . Its centre of mass rise to a maximum height of

Let be the charge density distribution for a solid sphere of radius R and total charge Q. For a point â€˜pâ€™ inside the sphere at distance from the centre of the sphere, the magnitude of electric field is:

The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. In frared radiation will be obtained in the transition from:

One kg of a diatomic gas is at a pressure of . The density of the gas is 4 kg . What is the energy of the gas due to its thermal motion?

Statement1 is true, Statement 2 is trueÍ¾ Statement2 is not the correct explanation of Statement 1.

Statement 1 is true, Statement 2 is false.

Statement 1 is false, Statement2 is true.

Statement 1 is true, Statement2 is trueÍ¾ Statement 2 is the correct explanation of Statement 1

Due to the presence of the current at the origin:

The magnitude of the net force on the loop is given by

The forces on AB and DC are zero.

The forces on AD and BC are zero.

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Youngâ€™s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is

776.8 nm

442.5 nm

885.0

393.4 nm

Two points P and Q are maintained at the potentials of 10 V and â€“4V, respectively. The work done in moving 100 electrons from P to Q is :

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is : (hc = 1240 eV. nm)

1.41 eV

3.09 eV

1.68 eV

1.51 eV

A particle has an initial velocity of and an acceleration of . Its speed after 10 s is :

7 units

8.5 units

10 units

A motor cycle starts from rest and accelerates along a straight path at . At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest ? (Speed of sound = 330 )

196 m

147 m

98

49 m

Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as

1:

2:

3:

4:

1 and 2

2 and 3

3 and 4

4 and 1

A charge Q is placed at each of the opposite corners of a square. A charge q is place at each of the other two corners. If the net electrical force on Q is zero, then Q / q equals :

-1

A long metallic bar is carrying heat from one of its ends to the other end under steadystate. The variation of temperature along the length x of the bar from its hot end is best described by which of the following figures ?

A transparent solid cylindrical rod has a refractive index of . it surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure. The incident angle q for which the light ray grazes along the wall of the rod is :

Three sound waves of equal amplitudes have frequencies (v â€“ 1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be :

The height at which the acceleration due to gravity becomes g / 9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is :

R / 2

2R

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2 has crosssectional area 3 A. If the length of wire 1 increases by on applying force F, how much force is needed to stretch wire 2 by the same amount ?

4 F

9 F

F

6 F

In a experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is halfâ€“aâ€“degree , then the least count of the instrument is :

one degree

half minute

half degree

one minute

Direction : Question are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the P â€“ T diagram.

Assuming the gas to be ideal the work done on the gas in taking it from A to B is :

400 R

300 R

500 R

200 R

The work done on the gas in taking it from D to A is :

+414 R

â€“690 R

+690 R

â€“414 R

The net work done on the gas in the cycle ABCDA is :

Zero

1904 R

1076 R

276 R

Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect?

Ln (III) hydroxides are mainly basic in character

The ionic sizes of Ln (III) decrease in general with increasing atomic number

ecause of the large size of the Ln (III) ions the bonding in its compounds is predominently ionic in character.

Ln (III) compounds are generally colourless

A liquid was mixed with ethanol and a drop of concentrated was added. A compound with a fruity smell was formed. The liquid was:

The alkene that exhibits geometrical isomerism is :

2 â€“ methyl propene

2 â€“ methyl â€“ 2 â€“ butene

2 â€“ butene

Propene

In which of the following arrangements, the sequence is not strictly according to the property written against it?

The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is:

Benzoic acid

Phthalic acid

Salicylaldehyde

Salicylic acid

Which of the following statements is incorrect regarding physisorptions?

Under high pressure it results into multi molecular layer on adsorbent surface

Enthalpy of adsorption is low and positive

It occurs because of van der Waalâ€™s forces

More easily liquefiable gases are adsorbed readily

Which of the following on heating with aqueous KOH, produces acetaldehyde?

In an atom, an electron is moving with a speed of 600 m / s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is ( kg , mass of electron, kg):

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is At 298 K standard Gibbâ€™s energies of formation for , and (g) are â€“ 166.2, â€“237.2 and â€“394.4 kJ respectively. If standard enthalpy of combustioin of methanol is â€“762 kJ , efficiency of the fuel cell will be:

87%

97%

80%

90%

Two liquids X and Y form an ideal solution. At 300 K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mm Hg) of X and Y in their pure states will be, respectively:

400 and 600

500 and 600

300 and 400

200 and 300

The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301) :

46.06 minutes

230.3 minutes

23.03 minutes

460.6 minutes

Given . The value of standard electrode potential for the change, will be :

â€“ 0.072 V

0.770 V

0.385 V

â€“ 0.270 V

â€“ 22.88 kJ

â€“ 343.52 kJ

+228.88 kJ

â€“ 228.88 k

Copper crystallises in fcc with a unit cell length of 361 pm. What is the radius of copper atom ?

157 pm

108 pm

127 pm

181 pm

Which of the following has an optical isomer?

Which one of the following reactions of Xenon compounds is not feasible?

Using MO theory predict which of the following species has the shortest bond length?

In context with the transition elements, which of the following statements is incorrect?

In addition to the normal oxidation states, the zero oxidation state is also shown by these elements in complexes.

In the highest oxidation states, the transition metal show basic character and form cathonic complexes.

In the higest oxidation states of the first five transition elements (Sc to Mn), all the 4s and 3d electrons are used for bonding.

Once the d 5 configuration is exceeded, the tendency to involves all the 3d electronss in bonding decreases.

0.40 nm

0.032 nm

14.0 nm

2.5 nm

A binary liquid solution is prepared by mixing nheptane and ethanol. Which one of the following statments is correct regarding the behaviour of the solution?

The solution is nonideal, shownign +ve deviation from Raoult’s Law.

The solution is nonideal, showing â€“ve deviation from Raoult’s Law.

The solution formed is an ideal solution

nheptane shows +ve deviation while ethanol shows â€“ ve deviation from Raoult’s Law.

The IUPAC name of neopentane is :

2-methylpropane

2,2-dimethylbutane

2,2-dimethylpropane

2-methylbutane

The set representing the correct order of ionic radius is :

The two functional groups present in a typical carbohydrate are :

The bond dissociation energy of B-F in is whereas that of C-F in is . The correct reason for higher B F bond dissociation energy as compared to that of C-F is :

significant interaction between B and F in whereas there is no possibility of such interaction between C and F in .

lower degree of interaction between B and F in than that between C and F in .

stronger s bond between B and F in as compared to that between C and F in.

smaller size of Batom as compared to that of Catom.

In Cannizzaro reaction given below the slowest step is :

the attack of :O H at the carboxyal group

the abstraction of proton from the carboxylic group

the deprotonation of

the transfer of hydride to the carbonyl group

Which of the following pairs represents linkage isomers?

Buna -Nsynthetic rubber is a copolymer of :

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