Free Printable IIT jee mains and advanced free mock test

Worksheets

IIT jee mains and advanced free mock test

Total questions: 75

Worksheet time: 1hrs 15mins

Name

Class

Date

resistance

charge

voltage

current

If the total energy of the particle is E, it will perform periodic motion only if

E < 0

E > 0

V0 > E > 0

E > V0

For periodic motion of small amplitude A, the time period T of this particle is proportional to

Electromagnetic radiations described by the equation: E=100[sin(2×1015)t+sin(6.28×1015)t]V/m are incident on a photosensitive surface having work function 1.5 eV. The maximum kinetic energy of photoelectrons will be (in eV)

0.125

2.625

4.125

6.125

A top is spinning at 28.6 rev/s about an axis making an angle of 34.0º with the vertical. Its mass is 492 g and its rotational inertia is 5.12×10^-4 kg.m². The center of mass is 3.88 cm from the pivot point. The spin is clockwise as seen from above. Find the magnitude (in rev/s) and direction of the angular velocity of precession.

0.324 rev/s,perpendicular to the plane of cone

0.324 rev/s,parallel to the plane of cone

0.894 rev/s,perpendicular to the plane of cone

0.894 rev/s,parallel to the plane of cone

An ideal gas taken round the cycle ABCA as shown in PV diagram

PV/2

2PV

PV/3

The specific heat of a metal at low temperature varies according to S=aT^3 where a is a constant and T is absolute temperature. The heat energy needed to raise unit mass of the metal from temperature T=1K to T=2K is

15a/4

2a/3

13a/4

10.

Suppose the temperature of gas is tripled and N2

molecules dissociate into atom. Then what will be the rms speed of atom.

v0 root 6

root 6 v0

v0 root 3

root 3 v0

11.

The value of angle of dip at a place on earth is 45^o. If the horizontal component of earth's magnetic field is 5×10^–5 Tesla then the total magnetic field of earth will be-

5/√2 × 10^–5 Tesla

10/√2 × 10^–5 Tesla

15/√2 × 10^–5 Tesla

zero

12.

A charged particle moving in a uniform magnetic field and losses 4% of its KE. The radius of curvature of its path changes by:

10%

none of these

13.

A transverse wave y = 0.05sin(20πx – 50πt) in meters, is propagating along +ve X-axis on a string. A velocity of 5 cm/s at t = 0 along the +ve X-axis from a point where x = 5 cm. After 5 s the difference in the phase of its position is equal to

150π

250π

-245π

-5π

14.

Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire

located at x = +R carries a constant current I1 and the wire located at x = −R carries a

constant current I2. A circular loop of radius R is suspended with its centre at (0, 0, √3R)

and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise

direction as seen from above the loop. The current in the wire is taken to be positive if it is

in the +ĵdirection. Which of the following statements regarding the magnetic field B is (are) true?

If I1 = I2, then B cannot be equal to zero at the origin (0, 0, 0)

If I1 > 0 and I2 < 0, then B can be equal to zero at the origin (0, 0, 0)

If I1 < 0 and I2 > 0, then B⃗⃗ can be equal to zero at the origin (0, 0, 0)

If I1 = I2, then the z-component of the magnetic field at the centre of the loop is (−μ0 (I/2R))

15.

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is (2 – root 3) / root 10 s, then the height of the top of the inclined plane, in metres, is (a) . Take g = 10 ms−2 .

16.

Sunlight of intensity 1.3 kWm−2 is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kWm−2 , at a distance 22 cm from the lens on the other side is (a) .

17.

Two thin prisms of flint glass have refracting angles of

10° and 20°. The dispersive powers of these prisms are

1:1

2:1

1:2

4:1

18.

Two resistors have resistances x = (24 ± 0.5) Ω and y = (8 ± 0.3)Ω .

Calculate the absolute error and the percentage relative error in

calculating the combination of two resistances when they are in

(b) Parallel

0.2, 3.33 %

0.3 , 6.66 %

0.2, 0.66 %

0.3, 3.33 %

19.

If λp and λe denote the de-Broglie wavelength of proton and

electron after they are accelerated from rest through the

same potential difference, then

λe = λp

λe < λp

λe > λp

λe = λp/2

20.

Two spheres of the same material have radii ‘r’ and ‘2r’ and temp. T and 2T kelvin respectively. The ratio of the energy radiated per second by the first sphere to that of the second is–

A. 1 : 31

B. 1 : 144

C. 1 : 16

D. 1 : 64

21.

A gaseous mixture contains 8gm of helium and 28gm of nitrogen, the ratio CP/CV of the mixture is–

A. 21/11 B. 17/13 C. 17/11 D. 21/13

22.

Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4 root(GM/L) .

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2 root(GM/L).

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is root(2GM/L) .

The energy of the mass m remains constant

23.

The kinetic energy (in keV) of the alpha particle, when the nucleus 210 Po 84 at rest undergoes alpha decay, is

5319

5422

5707

5818

24.

A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collision,

the speed of the particle when it returns to its equilibrium position is u0.

the time at which the particle passes through the equilibrium position for the first time is t = π root(m/k) .

the time at which the maximum compression of the spring occurs is t = 4π/3 root(m/k)

the time at which the particle passes through the equilibrium position for the second time is t = 5π/3 root(m/k)

25.

A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is sigma. The angle of contact between water and the wall of the capillary tube is theta. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

For a given material of the capillary tube, h decreases with increase in r

For a given material of the capillary tube, h is independent of sigma

If this experiment is performed in a lift going up with a constant acceleration, then h decreases

h is proportional to contact angle theta

26.

Determine all possible values of the expression A^3 + B^3 + C^3 − 3ABC where A, B, and C are nonnegative integers.

The possible values are the nonnegative integers that are either divisible by 3 or not divisible by 9.

The possible values are the negative integers that are either divisible by 9 or not divisible by 3.

The possible values are the nonnegative integers that are either divisible by 9 or not divisible by 4.

The possible values are the nonnegative integers that are either divisible by 9 or not divisible by 3.

27.

Tangents drawn from the point P(1,8) to the circle x^2+y^2−6x−4y−11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is

X^2 + y^2 + 4x – 6y + 19 = 0

X^2 + y^2 + 4x – 10y + 19 = 0

X^2 + y^2 - 2x + 6y - 29 = 0

X^2 + y^2 - 6x – 4y + 19 = 0

28.

For x∈R, f(x) = |log2 – sinx| and g(x) = f(f(x)), then:

g is differentiable at x = 0 and g'(0) = –sin(log2)

g is not differentiable at x = 0

g'(0) = cos(log2)

g'(0) = –cos(log2)

29.

If the sum of the first ten terms of the series is (1^3/5) + (1^3/5) + (1^3/5) + 4 + (1^3/5) +…, is (16/5)m, then m is equal to:

102

101

100

30.

If cosA+cosB+2cosC=2, where a, b and C are angles of triangle, then AB, BC and CA are in which progression?

Arithmetic progression

Geometric progression

Harmonic progression

data insufficient

31.

tan x + 2 tan 2x+ 4 tan 4x + 8 cot 8x=?

tan x

cot x

tan 2x

cot 2x

32.

A line y = mx + 1 intersect the circle (x – 3)^2 + (y + 2)^2 = 25 at points P and Q. If the midpoint of the line segment PQ has x-coordinate – 3/5 , then which one of the following options is correct

6 $\le$ m < 8

2 $\le$ m < 4

4 $\le$ m < 6

–3 $\le$ m < – 1

33.

In a non-right-angled triangle PQR, Let p, q, r denote the lengths of the sies opposite to the angles at P, Q, R respectively. The median form R meets the side PQ at S, the perpendicualr4 from P meets the side QR at E, and RS and PE intersect at O. If p = 3 , q = 1, and the radius of the circumcircle of PQR equals 1, then which of the following options is/are correct ?

Length of RS = $\frac{\sqrt{7}}{2}$

Area of $\Delta$ SOE = $\frac{\sqrt{3}}{12}$

Radius of incircle of $\Delta$ PQR = $\frac{\sqrt{3}}{2}\left(2-\sqrt{3}\right)$

Length of OE = $\frac{1}{6}$

34.

What do w, x, y and z equal in this matrix subtraction?

w = 13, x = 4, y = 7, z = 23

w = 13, x = -4, y = 11, z = 23

w = 13, x = 4, y = 11, z = 23

w = 13, x = 4, y = 11, z = 17

35.

INTEGRATE

36.

37.

Five persons A,B,C,D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the numbers of ways of distributing the hats such that the person seated in adjacent seats get different coloured hats is

(a)

38.

Let |X| denote the number of elements in a set X. Let S = {1,2,3,4,5,6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A,B) such that

1 $\le$ |B| < |A| equals

(a)

39.

A debate club consists of 6 girls and 4 boys. A team of 4 members is to

be selected from this club including the selection of a captain (from among

these 4 members) for the team. If the team has to include at most one boy,

then the number of ways of selecting the team is

380

320

260

40.

The number of integral solutions of the equation x + y + z + w = 20, if x ≥ 1,

y ≥ 2, z ≥ 3, w ≥ 4, is

286

715

1001

41.

The coefficient of three consecutive terms of

\left(1+x\right)^{\left(n+5\right)}

are in the ratio 5 : 10 : 14. Then n =

42.

If the standard deviation of the numbers 2, 3 , a and 11 is 3.5 then which of

the following is true?

$3a^2-34a+91=0$

$3a^2-23a+44=0$

$3a^2-26a+55=0$

$3a^2-32a+84=0$

43.

A value of b for which the equations

x^2+bx-1=0

x^2+x+b=0

have one root in common

$-\sqrt{2}$

$-i\sqrt{3}$

$i\sqrt{5}$

$\sqrt{2}$

44.

Let P (6, 3) be a point on the hyperbola

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is

$\sqrt{\frac{5}{2}}$

$\sqrt{\frac{3}{2}}$

$\sqrt{2}$

$\sqrt{3}$

45.

The number of distinct real roots of

$x^4-4x^3+12x^2+x-1=0$ is

(a)

46.

Two numbers are chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. The number of ways which will give us the product a multiple of 5, is

1030

1020

47.

48.

The area enclosed by the curves y = sin x + cos x and y = |cos x − sin x| over the interval

\left(0,\frac{\pi}{2}\right)

$4\left(\sqrt{2}-1\right)$

$2\sqrt{2}\left(\sqrt{2}-1\right)$

$2\left(\sqrt{2}+1\right)$

$2\sqrt{2}\left(\sqrt{2}+1\right)$

49.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:

$\left(4-\pi\right)x=\pi r$

$x=2r$

$2x=r$

$2x=\left(\pi+4\right)x$

50.

(a)

51.

The pair(s) of reagents that yield paramagnetic species is/are

Na and excess of NH3

K and excess of O2

Cu and dilute HNO3

O2 and 2ethylanthraquinol

52.

The correct statement(s) for orthoboric acid is/are

It behaves as a weak acid in water due to self ionisation

Acidity of its aqueous solution increases upon addition of ethylene glycol.

It has a three dimensional structure due to hydrogen bonding.

It is a weak electrolyte in water

53.

For the process H2O (l) →H2O (g) at T = 100 °C and 1 atmosphere pressure, the correct choice is

∆Ssystem >0 and ∆Ssurroundings >0

∆Ssystem >0 and ∆Ssurroundings <0

∆Ssystem<0 and ∆Ssurroundings>0

∆Ssystem <0 and ∆Ssurroundings <0

54.

55.

A straight glass tube has two inlets x and y at two ends. The length of the tube is 200 cm. HCl gas through inlet x and NH3 gas through inlet y are allowed to enter the tube at the same time. White fumes first appear at a point P inside the tube. The distance of P from x is

81.13 cm

105 cm

87.15 cm

125 cm

56.

All of the following salts are soluble except...

Lead(II) nitrate

Sodium carbonate

Magnesium chloride

Barium sulphate

57.

The ground state energy of hydrogen atom is –13.6 eV. Consider an electronic state $\psi$ of He+ whose energy, azimuthal quantum number and magnetic quantum number are –3.4 eV, 2 and 0, respectively. Which of the following statement(s) is(are) true for the state

\psi

It is a 4d state

The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge

It has 3 radial nodes

It has 2 angular nodes

58.

With reference to aqua regia, choose the correct option(s)

Reaction of gold with aqua regia produces NO2 in the absence of air

The yellow colour of aqua regia is due to the presence of NOCl and Cl2.

Aqua regia is prepared by mixing conc. HCl and conc. HNO3 in 3 : 1 (v/v) ratio.

Reaction of gold with aqua regia produces an anion having Au in +3 oxidation state.

59.

Choose the correct option(s) from the following

Teflon is prepared by heating tetrafluoroethene in presence of a persulphate catalyst at high pressure

Natural rubber is polyisoprene containing trans alkene units

Nylon-6 has amide linkages

Cellulose has only $\alpha$ -D-glucose units that are joined by glycosidic linkages

60.

The Mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is 1.2 g/cm3 , the molarity of urea solution is (a) `.

61.

Total number of cis N–Mn–Cl bond angles (that is, Mn–N and Mn–Cl bonds in cis position) present in a molecule of cis [Mn(en)2Cl2] complex is (a)

62.

The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. HNO3 to a compound with the highest oxidation state of sulphur is (a)

63.

Total number of isomers considering both structural and stereoisomers, of cyclic ethers with the molecular formula C4H8O is (a)

64.

write 1,2,3 or 4 as answer.

(a)

65.

Among the following compounds in which case central element uses d-orbital to make bonds with attached atom

$BeF_2$

$XeF_2$

$SiF_4$

$BF_3$

66.

67.

68.

Sodium phenoxide when heated with C02 under pressure at 125°C yields a product which on a acetylation produces C

69.

In Sn2 reactions, the correct order of reactivity for the following compounds

70.

71.

72.

73.

74.

Which series of reactions correctly represents chemical relations related to iron and its compound ?

75.

Reset

IIT jee mains and advanced free mock test

Total questions: 75

Worksheet time: 1hrs 15mins

Similar Resources on Wayground