End Test Now

The equation – 4 = 0 has :

infinite number of real roots

no real roots

exactly one real root

exactly four real roots

Let be two unit vectors. If the vectors and are perpendicular to each other, then the angle between is :

A spherical balloon is filled with 4500 cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is :

9/7

7/9

2/9

9/2

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + … + (361 + 380 + 400) is 8000.

Statement 2: , for any natural number n.

Statement 1 is false, Statement 2 is true.

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1.

Statement 1 is true, Statement 2 is false.

The negation of the statement

“If I become a teacher, then I will open a school”, is :

I will become a teacher and I will not open a school.

Either I will not become a teacher or I will not open a school.

Neither I will become a teacher nor I will open a school.

I will not become a teacher or I will open a school.

If the integral dx = x + a n |sin x – 2 cos x| + k then a is equal to :

- 1

- 2

1

2

Statement 1 : An equation of a common tangent to the parabola X and the ellipse is y = 2x + .

Statement 2 : If the line y = mx + , a common tangent to the parabola x and the ellipse , then m satisfies .

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

If n is a positive integer, then is :

an irrational number

an odd positive integer

an even positive integer

a rational number other than positive integers

If 100 times the term of an AP with non zero common difference equals the 50 times its term, then the term of this AP is :

- 150

150 times its term

150

zero

In a PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to :

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is :

x – 2y + 2z – 3 = 0

x – 2y + 2z + 1 = 0

x – 2y + 2z – 1 = 0

x – 2y + 2z + 5 = 0

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals :

29/5

5

6

11/5

Let be n observations, and let be their arithmetic mean and be their variance.

Statement 1 : Variance of is

Statement 2 : Arithmetic mean of is

The population p(t) at time t of a certain mouse species satisfies the differential equation = 0.5 p(t) – 450. If p(0) = 850, then the time at which the population becomes zero is :

2 n 18

Let a, b R be such that the function f given by f(x) = | x | + has extreme values at x = – 1 and x = 2

Statement 1 : f has local maximum at x = – 1 and at x = 2.

Statement 2 : a = and b=

The area bounded between the parabolas = and and the straight line y = 2 is :

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is :

880

629

630

879

If f : R R is a function defined by f(x) = [x] cos , where [x] denotes the greatest integer function, then f is :

continuous for every real x.

discontinuous only at x = 0.

discontinuous only at non-zero integral values of x.

continuous only at x = 0.

If the lines = = and = = intersect, then k is equal to :

0

Three numbers are chosen at random without replacement from {1, 2, 3, …, 8}. The probability that their minimum is 3, given that their maximum is 6, is :

3/8

1/5

1/4

2/5

If z 1 and is real, then the point represented by the complex number z lies:

either on the real axis or on a circle passing through the origin.

on a circle with centre at the origin.

either on the real axis or on a circle not passing through the origin.

on the imaginary axis.

Let P and Q be 3×3 matrices with P Q. If , then determinant of is equal to :

If g(x) = cos 4t dt, then g(x + ) equals :

g(x) + g( )

g(x) – g( )

g(x) . g( )

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is :

10/3

3/5

6/5

5/3

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y X, Z X and Y Z is empty, is :

An ellipse is drawn by taking a diameter of the circle as its semi-minor axis and a diameter of the circle as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axis, then the equation of the ellipse is :

Consider the function, f(x) = |x – 2| + |X – 5|, X R.

Statement 1 : f’ (4) = 0

Statement 2 : f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

Statement 1 is false, statement 2 is true.

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

Statement 1 is true, statement 2 is false.

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is :

- 1/4

- 4

- 1/2

Let ABCD be a parallelogram such that = , = and BAD be an acute angle. If is the vector that coincides with the altitude directed from the vertex B to the side AD, then is given by

A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than . To fit the ring on the wheel, it is heated so that its temperature rises by T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is , and its Young’s modulus is Y, the force that one part of the wheel applies on the other part is :

The figure shows an experimental plot for discharging of a capacitor in an R C circuit. The time constant of this circuit lies between :

150 sec and 200 sec

0 and 50 sec

50 sec and 100 sec

100 sec and 150 sec

In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

An electromagnetic wave in vacuum has the electric and magnetic fields , which are always perpendicular to each other. The direction of polarization is given by and that of wave propagation by . Then :

If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t – s, then may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ‘b’ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :

b

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be :

3

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

development of air current when the plate is placed.

induction of electrical charge on the plate

shielding of magnetic lines of force as aluminium is a paramagnetic material

electromagnetic induction in the aluminium plate giving rise to electromagnetic damping

The mass of spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of earth) are 10 and 6400 km respectively. The required energy for this work will be :

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

15.4%

9.1%

10.5%

12.5%

In Young’s double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If be the maximum intensity, the resultant intensity I when they interfere at phase difference is given by :

A liquid in a beaker has temperature (t) at time t and is temperature of surroundings, then according to Newton’s law of cooling the correct graph between and t is :

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F 0 in the x direction. Its speed v(t) is depicted by which of the following curves?

Two electric bulbs marked 25 W – 220 V and 100 W – 220 V are connected in series to a 440 V supply. Which of the bulbs will fuse?

both

100 W

25 W

neither

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is :

6%

1%

3%

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be :

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement 1 : Davisson – Germer experiment established the wave nature of electrons.

Statement 2 : If electrons have wave nature, they can interfere and show diffraction.

Statement 1 is true, Statement 2 is false

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

A thin liquid film formed between a U shaped wire and a light slider supports a weight of N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is :

0.0125

0.1

0.05

0.025

A charge Q is uniformly distributed over the surface of non – conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity . As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure :

Truth table for system of four NAND gates as shown in figure is :

A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = 6.4 x m)

80 km

16 km

40 km

64 km

Assume that a neutron breaks into a proton and an electron. The energy released during this process is :

(Mass of neutron = 1.6725 x kg Mass of proton = 1.6725 x kg Mass of electron = 9 x kg)

0.73 MeV

7.10 MeV

6.30 MeV

5.4 MeV

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :

efficiency of Carnot engine cannot be made larger than 50%

1200 K

750 K

600 K

It two springs of force constants , respectively, are stretched by the same force, it is found that more work is done on spring than on spring . Statement 1 :9 If stretched by the same amount, work done on , will be more than that on *Statement 2 :

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

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

Two cars of masses are moving in circles of radii respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :

1 : 1

A cylindrical tube, open at both ends, has a fundamental frequency f, in air. The tube is dipped vertically in water so that half of it is water. The fundamental frequency of the air-column is now:

f

2f

An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

7.2 m

2.4 m

3.2 m

5.6 m

A diatomic molecule is made of two masses which are separated by a distance r. If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantization, its energy will be given by : (n is an integer)

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data :

58.59 degree

58.77 degree

58.65 degree

59 degree

An insulating solid sphere of radius R has a uniformly positive charge density . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.

Statement 1 : When a charge ‘q’ is taken from the centre to the surface of the sphere, its potentialenergy changes by .

Statement 2 : The electric field at a distance r (r < R) from the centre of the sphere is

Statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation of Statement 1.

Statement 1 is true Statement 2 is false.

Statement 1 is false Statement 2 is true

Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation of Statement 1

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively .

Which one of the following relations is correct?

Which among the following will be named as dibromidobis ( ethylene diamine) chromium (III) bromide ?

Which method of purification is represented by the following equation :

Zone refining

Cupellation

Poling

Van Arkel

Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

75 pm

300 pm

240 pm

152 pm

The molecule having smallest bond angle is :

Which of the following compounds can be detected by Molisch’s test ?

Nitro compounds

Sugars

Amines

Primary alcohols

The incorrect expression among the following is :

In isothermal process, = nRT ln

lnK =

K =

The density of a solution prepared by dissolving 120 g of urea (mol. mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is :

0.50 M

1.78 M

1.02 M

2.05 M

The species which can best serve as an initiator for the cationic polymerization is :

Which of the following on thermal-decomposition yields a basic as well as an acidic oxide ?

The standard reduction potentials for , and / Fe are – 0.76, – 0.23 and – 0.44 V respectively. The reaction X + + Y will be spontaneous when :

X = Ni, Y = Fe

X = Ni, Y = Zn

X = Fe, Y = Zn

X = Zn, Y = Ni

According to Freundlich adsorption isotherm, which of the following is correct ?

All the above are correct for different ranges of pressure.

The equilibrium constant for the reaction at temperature T is . The value of for the reaction, at the same temperature is :

The compressibility factor for a real gas at high pressure is :

1 + RT / pb

1 + pb / RT

1 – pb / RT

Which one of the following statements is correct ?

All amino acids except lysine are optically active.

All amino acids are optically active.

All amino acids except glycine are optically active

All amino acids except glutamic acid are optically active.

Aspirin is known as :

Acetyl salicylic acid

Phenyl salicylate

Acetyl salicylate

Methyl salicylic acid

Ortho – Nitrophenol is less soluble in water than p – and m – Nitrophenols because :

o – Nitrophenol is more volatile in steam than those of m – and p – isomers

o – Nitrophenol shows Intramolecular H – bonding

o – Nitrophenol shows Intermolecular H – bonding

Melting point of o – Nitropehnol is lower than those of m – and p – isomers.

How many chiral compounds are possible on monochlorination of 2 – methyl butane ?

8

4

Very pure hydrogen (99.9 %) can be made by which of the following processes ?

Reaction of methane with steam

Mixing natural hydrocarbons of high molecular weight

Electrolysis of water

Reaction of salt like hydrides with water

The electrons identified by quantum numbers n and 1 : (a) n = 4, l = 1(b) n = 4, l = 0(c) n = 3, l = 2(d) n = 3, l = 1can be placed in order of increasing energy as :

(c) < (d) < (b) < (a)

(d) < (b) < (c) < (a)

(b) < (d) < (a) < (c)

(a) < (c) < (b) < (d)

For a first order reaction, (A) products, the concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of A is 0.01 M, is :

Iron exhibits +2 and +3 oxidation states. Which of the following statements about iron is incorrect ?

Ferrous oxide is more basic in nature than the ferric oxide.

Ferrous compounds are relatively more ionic than the corresponding ferric compounds.

Ferrous compounds are less volatile than the corresponding ferric compounds.

Ferrous compounds are more easily hydrolysed than the corresponding ferric compounds.

The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of this acid is :

Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of mono substituted alkyl halide ?

Tertiary butyl chloride

Neopentane

Isohexane

Neohexane

72 g

93 g

39 g

27 g

What is DDT among the following :

Greenhouse gas

A fertilizer

Biodegradable pollutant

Non – biodegradable pollutant

The increasing order of the ionic radii of the given isoelectronic species is :

2 – Hexyne gives trans – 2 – Hexene on treatment with :

Iodoform can be prepared from all except :

Ethyl methyl ketone

Isopropyl alcohol

3 – Methyl – 2 – butanone

Isobutyl alcohol

In which of the following pairs the two species are not isostructural ?

In the given transformation, which of the following is the most appropriate reagent ?

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