ISEET(IIT-JEE) Math Previous Year Question Paper 2008

ISEET Sample Papers 2008 for Math

1. Consider the two curves

C1 : y2 = 4x

C2 : x2 + y2 - 6x + 1 = 0

then,

A C1 and C2 touch each other only at one point

B C1 and C2 touch each other exactly at two points

C C1 and C2 intersect (but do not touch) at exactly two points

D C1 and C2 neither intersect nor touch each other

2. If 0 < x < 1, then (A) (B) (C) (D) X

3. The edges of a parallelopiped are of unit length and are parallel

to non-coplanar unit vectors a , b , c such that

1

a.b = b.c = c.a =

2

Then, the volume of the parallelopiped is

(A) 1/ (B) 1/2 (C) /2

(D)  1/ 4. Let a and b non-zero real numbers. Then, the equation (ax2 + by2 +

c)(x2 - 5xy + 6y2) = 0 represents

(A) Four straight lines, when c = 0 and a, b are of the same sign

(B) Two straight lines and a circle, when a = b, and c is of sign

opposite to that of a

(C) Two straight lines and a hyperbola, when a and b are of the same

sign and c is of sign opposite to that of a

(D) A circle and an ellipse, when a and b are of the same sign and c

is of sign opposite to that of a

5. Let

g(x) = (x-1)/ log cos(m-1)

(A) n = 1, m = 1

(B) n = 1, m = -1

(c) n = 2, m = 2

(D) n > 2, m = n

6. The total number of local maxima and local minima of the function (A)0

(B)1

(C)2

(D)3

7. A straight line through the vertex P of a triangle PQR intersects

the side QR at the point S and the circumcircle of the triangle PQR

at the point T. If S is not the centre of the circumcircle, then

(A) (B) (C) (D) 8. Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the latus rectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latus rectum PQ are

(A) x2 + 2 y = 3 + (B) x2 - 2 y  = 3 + (C) x2 + 2 y = 3 - (D) x2 - 2 y = 3 - 9. Let (A) Sn <  Pi/3 (B) Sn > Pi/ 3 (C) Tn < Pi/ 3 (D) Tn > Pi/ 3 10. Let f(x) be a non-constant twice differentiable function defined

on (- ∞, ∞) such that f(x) = f(1 - x) and

(A) f'(x) vanishes at least twice on [0, 1]

(B) f ' (1/2)

(C) (D) 11. Let f and g be real valued functions defined on interval (-1, 1)

such that g''(x) is continuous, g(0) ≠ 0, g''(0) ≠ 0, g''(0) - 0, and

f(x) = g(x)sin x

STATEMENT-1 :

lim

[g(x)cot x - g(0)cosec x] = f''(0)

and

STATEMENT-2 :

f'(0) = g(0).

(A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a

correct explanation for STATEMENT-1

(B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a

correct explanation for STATEMENT-1

(C)STATEMENT-1 is True, STATEMENT-2 is False

(D)STATEMENT-1 is False, STATEMENT-2 is True

12. Consider three planes

P1 : x - y + z = 1

P2 : x + y - z = -1

P3 : x - 3y + 3z = 2

Let L1, L2, L3 be the lines of intersection of the planes P2 and P3,

P3 and P1, P1 and P2, respectively

STATEMENT-1 :

At least two of the lines L1, L2 and L3 are non-parallel.

and

STATEMENT-2 :

The three planes do not nave a common point.

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a

correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a

correct explanation for STATEMENT-1

(C) STATEMENT-1 is True, STATEMENT-2 is False

(D) STATEMENT-1 is False, STATEMENT-2 is True

13. Consider the system of equations

x - 2y + 3z = -1

-x + y - 2z = k

x - 3y + 4z = 1

STATEMENT-1 :

The system of equations has no solution for k ≠ 3.

and

STATEMENT-2 :

The determinant A ) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a

correct explanation for STATEMENT-1

B ) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a

correct explanation for STATEMENT-1

C ) STATEMENT-1 is True, STATEMENT-2 is False

D ) STATEMENT-1 is False, STATEMENT-2 is True

for k ≠ 3

14. Consider the system of equations

ax + by = 0, cx + dy = 0, where a, b, c, d ∈ {0, 1}.

STATEMENT-1 :

The probability that the system of equations has a unique solution is

3/8.

and

STATEMENT-2 :

The probability that the system of equations has a solution is 1.

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a

correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a

correct explanation for STATEMENT-1

(C) STATEMENT-1 is True, STATEMENT-2 is False

(D) STATEMENT-1 is False, STATEMENT-2 is True

15. A circle C of radius 1 is inscribed in an equilateral triangle

PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F

respectively. The line PQ is given by the equation

+ y - 6 = 0 and

the point D is (3 /2, 3/2). Further, it is given that the origin and

the centre of C are on the same side of the line PQ.

The equation of circle C is

A ) (x - 2 )2 + (y - 1)2 = 1

B ) (x - 2 )2 + (y + 1/2)2 = 1

C ) (x - )2 + (y + 1)2 = 1

D ) (x - )2 + (y - 1)2 = 1

16. A circle C of radius 1 is inscribed in an equilateral triangle

PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F

respectively. The line PQ is given by the equation

+ y - 6 = 0 and

the point D is (3 /2, 3/2). Further, it is given that the origin and

the centre of C are on the same side of the line PQ.

Points E and F are given by

(A) ( /2, 3/2), ( , 0)

B  ( /2, 1/2), ( , 0)

C ( /2, 3/2), ( /2, 1/2)

D ( 3/2, /2), ( /2, 1/2)

17. A circle C of radius 1 is inscribed in an equilateral triangle

PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F

respectively. The line PQ is given by the equation

+ y - 6 = 0 and

the point D is (3 /2, 3/2). Further, it is given that the origin and

the centre of C are on the same side of the line PQ.

Equations of the sides QR, RP are

A   y = 2/ x+1, y = -2/ x-1

B   y = 2/ x, y = 0

C   y = / 2  x + 1 , y = - /2 x - 1

D   y = x , y = 0

18. Consider the functions defined implicitly by the equation y3 - 3y

+ x = 0 on various intervals in the real line.

If x ∈ (-∞,-2) ∈ (2, ∞) , the equation implicitly defines a unique

real valued differentiable function y = f(x).

If x ∈ (2,2) , the equation implicitly defines a unique real valued

differentiable function y = g(x) satisfying g(0) = 0.

if f( - 10 ) = 2 , then f '' (-10, )

A  4 / 7332

B  - 4 / 7332

C  4 / 733

D  4 / - 733

19. Consider the functions defined implicitly by the equation y3 - 3y

+ x = 0 on various intervals in the real line.

If x ∈ (-∞,-2) ∈ (2, ∞) , the equation implicitly defines a unique

real valued differentiable function y = f(x).

If x ∈ (2,2) , the equation implicitly defines a unique real valued

differentiable function y = g(x) satisfying g(0) = 0.

The area of the region bounded by the curve y = f(x), the x-axis, and

the lines x = a and x = b, where -∞< a < b < -2, is

A B C D 20. Consider the functions defined implicitly by the equation y3 - 3y

+ x = 0 on various intervals in the real line.

If x ∈ (-∞,-2) ∈ (2, ∞) , the equation implicitly defines a unique

real valued differentiable function y = f(x).

If x ∈ (2,2) , the equation implicitly defines a unique real valued

differentiable function y = g(x) satisfying g(0) = 0. A    2g (- 1)

B    0

C   - 2g(1)

D    2g(1)

21. Let A, B, C be three sets of complex numbers as defined below

A = { z:Imz ≥ 1 }

B = { z:|z-2-i|=3}

C = { z:Re((1-i)z) =

Page 10 of 32

}

The number of elements in the set A ∩ B ∩ C is

A 0

B 1

C 2

D ∞

22. Let A, B, C be three sets of complex numbers as defined below

A = { z:Imz ≥ 1 }

B = { z:|z-2-i|=3}

C = { z:Re((1-i)z) =

}

Let z be any point in A ∩ B ∩ C. The |z+1-i|2 + |z-5-i|2 lies between

(A) 25 and 29

(B)  30 and 34

(C)  35 and 39

(D) 40 and 44

23. Let A, B, C be three sets of complex numbers as defined below

A = { z:Imz ≥ 1 }

B = { z:|z-2-i|=3}

C = { z:Re((1-i)z) =

}

Let z be any point in A ∩ B ∩ C and let w be any point satisfying |w-

2-i | < 3. Then, |z|-|w|+3 lies between

A -6  AND 3

B  -3 AND 6

C  -6 AND 6

D  -3 AND 9

24. Student I, II and III perform an experiment for measuring the

acceleration due to gravity (g) using a simple pendulum. They use

different lengths of the pendulum and / or record time for different

 Student Length of the Pendulam(cm) Number of oscillations (n) Total time for (n) oscillations (s) Time period (s) I 64 8 128 16 II 64 4 64 16 III 20 4 36 9

number of oscillations. The observations are shown in the table.

A EI=0

B  EI is minimum

C EI = EII

D EII is minimum

25. Figure shows three resistor configurations R1, R2 and R3

connected to 3 V battery. If the power dissipated by the

configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

Figure: (A)P1 > P2 > P3

(B)P1 > P3 > P2

(C)P2 > P1 > P3

(D)P3 > P2 > P1

26. Which one of the following statements is WRONG in the context of

X-rays generated from a X-ray tube?

(A) Wavelength of characteristic X-rays decreases when the atomic

number of the target increases

(B) Cut-off wavelength of the continuous X-rays depends on the

atomic number of the target

(C) Intensity of the characteristic X-rays depends on the electrical

power given to the X-ray tube

(D) Cut-off wavelength of the continuous X-rays depends on the

energy of the electrons in the X-ray tube

27. Two beams of red and violet colours are made to pass separately

through a prism (angle of the prism is 60°). In the position of

minimum deviation, the angle of refraction will be

A)30° for both the colours

B)Greater for the violet colour

C)Greater for the red colour

D ) Equal but not 30° for both the colours

28. An ideal gas is expanding such that PT2 = constant. The

coefficient of volume expansion of the gas is

A) 1/T

B) 2/T

C) 3/T

D) 4/T

29. A spherically symmetric gravitational system of particles has a

mass density Where ρ0 is a constant. A test mass can undergo circular motion under

the influence of the gravitational field of particles. Its speed V as

a function of distance

r (0 < r < ∞) from the centre of the system is represented by

A) B) C) D) 30. Two balls, having linear momenta p1 = pi and p2 = pi and undergo

a collision in free space. There is no external force acting on the

balls. Let p'1 and p'2 be their final momenta. The following option

(s) is (are) NOT ALLOWED for any non-zero value of p, a1, a2, b1, b2,

c1 and c2.

A) p'1 = a1i + b1j + c1k

p'2 = a2i + b2j

B) p'1 = c1k

p'2 = c2k

C) p'1 = a1i + b1j + c1k

p'2 = a2i + b2j - c1k

D) p'1 = a1i + b1j

p'2 = a2i + b1j

31. Assume that the nuclear binding energy per nucleon (B/A) versus

mass number (A) is as shown in the figure. Use this plot to choose

the correct choice(s) given below. A) Fusion of two nuclei with mass numbers lying in the range

A < 50 will release en

B) Fusion of two nuclei with mass numbers lying in the range

< A < 100 will release energy

C) Fission of a nucleus lying in the mass range of 100 < A <

will release energy when broken into two equal fragments

D) Fission of a nucleus lying in the mass range of 200 < A <

will release energy when broken into two equal fragments

32. A particle of mass m and charge q, moving with velocity V enters

Region II normal to the boundary as shown in the figure. Region II

has a uniform magnetic field B perpendicular to the plane of the

paper. The length of the Region II is l. Choose the correct choice A) The particle enters Region III only if its velocity

V > qlB/ m

(B) The particle enters Region III only if its velocity

V < qlB/m

(C) Path length of the particle in Region II is maximum when

velocity

V = qlB/ m

(D) Time spend in Region II is same for any velocity V as long as

the particle returns to Region I

33. In a Young's double slit experiment, the separation between the

two slits is d and the wavelength of the light is λ . The intensity

of light falling on slit 1 is four times the intensity of light

falling on slit 2. Choose the correct choice(s)

A) If d = λ, the screen will contain only one maximum

B) If λ < d < 2λ, at least one more maximum (besides the central

maximum) will be observed on the screen

C) If the intensity of light falling on slit 1 is reduced so that

it becomes equal to that of slit 2, the intensities of the

observed dark and bright fringes will increase

D) If the intensity of light falling on slit 2 is increased so that

it becomes equal to that of slit 1, the intensities of the

observed dark and bright fringes will increase

34. STATEMENT-1:

In a Meter Bridge experiment, null point for an unknown resistance is

measured. Now, the unknown resistance is put inside an enclosure

maintained at a higher temperature. The null point can be obtained at

the same point as before by decreasing the value of the standard

resistance.

STATEMENT-2

Resistance of a metal increases with increase in temperature.

A) Statement -1 is True, Statement-2 is True; Statement-2 is a

correct explanation for Statement-1.

B) Statement -1 is True, Statement-2 is True; Statement-2 is NOT a

correct explanation for Statement-1.

C) Statement-1 is True, Statement-2 is False.

D) Statement-1 is False, Statement-2 is True.

35. STATEMENT-1:

An astronaut in an orbiting space station above the Earth experiences

weightlessness.

and

STATEMENT-2

An object moving around the Earth under the influence of Earth'\'s

gravitational force is in a state of 'free-fall'.

A) Statement -1 is True, Statement-2 is True; Statement-2 is a

correct explanation for Statement-1.

B) Statement -1 is True, Statement-2 is True; Statement-2 is NOT a

correct explanation for Statement-1.

C) Statement-1 is True, Statement-2 is False.

D) Statement-1 is False, Statement-2 is True.

36. Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The

hollow cylinder will reach the bottom of the inclined plane first.

STATEMENT-2

By the principle of conservation of energy, the total kinetic

energies of both the cylinders are identical when they reach the

bottom of the incline.

A )Statement -1 is True, Statement-2 is True; Statement-2 is a

correct explanation for Statement-1.

B) Statement -1 is True, Statement-2 is True; Statement-2 is NOT a

correct explanation for Statement-1.

C) Statement-1 is True, Statement-2 is False.

D) Statement-1 is False, Statement-2 is True.

37. STATEMENT-1:

The stream of water flowing at high speed from a garden hose pipe

tends to spread like a fountain when held vertically up, but tends to

narrow down when held vertically down.

STATEMENT-2

In any steady flow of an incompressible fluid, the volume flow rate

of the fluid remains constant.

A)Statement -1 is True, Statement-2 is True; Statement-2 is a

correct explanation for Statement-1.

B) Statement -1 is True, Statement-2 is True; Statement-2 is NOT a

correct explanation for Statement-1.

C) Statement-1 is True, Statement-2 is False.

D) Statement-1 is False, Statement-2 is True.

38. A small spherical monoatomic ideal gas bubble (λ = 5/3) is

trapped inside a liquid of density ρl(see figure). Assume that the

bubble does not exchange any heat with the liquid. The bubble

contains n moles of gas. The temperature of the gas when the bubble

is at the bottom is T0, the height of the liquid is H and the

atmospheric pressure is P0 (Neglect surface tension). As the bubble moves upwards, besides the buoyancy force the following

forces are acting on it

A) Only the force of gravity

B) The force due to gravity and the force due to the pressure of the liquid

C) The force due to gravity, the force due to the pressure of the

liquid and the force due to viscosity of the liquid

D) The force due to gravity and the force due to viscosity of the

liquid

39. A small spherical monoatomic ideal gas bubble (λ = 5/3) is

trapped inside a liquid of density ρl(see figure). Assume that the

bubble does not exchange any heat with the liquid. The bubble

contains n moles of gas. The temperature of the gas when the bubble

is at the bottom is T0, the height of the liquid is H and the

atmospheric pressure is P0 (Neglect surface tension). When the gas bubble is at height y from the bottom, its temperature

is

A)  T0 ( P0+ Pgh) / P0 + P1gy) 2/5

B)   T0 (P0 + ρlg(H-y)P0 + ρlgH)2/5

C) T0 ( P0 + ρlgH P0 + ρlgy )3/5

D) T0 ( P0 + ρlg(H-y) P0 + ρlgH )3/5

40.  A small spherical monoatomic ideal gas bubble (λ = 5/3) is

trapped inside a liquid of density ρl(see figure). Assume that the

bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension). The buoyancy force acting on the gas bubble is (Assume R is the

universal gas constant)

A) ρlnRgT0( P0 + ρlgH )2/5/ ( P0 + ρlgy )7/5

B) ρlnRgT0/ ( P0 + ρlgH )2/5 [P0 + ρlg(H-y) ]3/5

C) ρlnRgT0( P0 + ρlgH )3/5 / ( P0 + ρlgy )8/5

D)  ρlnRgT0/ ( P0 + ρlgH )2/5 [P0 + ρlg(H-y) ]2/5

41. In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr Model of atom is exactly valid The quantum number of n of the state finally populated in He+ ions is

A)2

B)3

C)4

D)5

42. In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr Model of atom is exactly valid The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is

A) 6.5 x 10-7m

B) 5.6 x 10-7m

C) 4.8 x 10-7m

D) 4.0 x 10-7m

43. In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr Model of atom is exactly valid The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is

A) 1/4

B)1/2

C)1

D)2

44. A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at

A. Assume that collisions between the block and the incline are

totally inelastic (g = 10 m/s2) The speed of the block at point B immediately after it strikes the

second incline is

A) m/s

B) m/s

C) √30 m/s

D) √15 m/s

45. A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at

A. Assume that collisions between the block and the incline are totally inelastic (g = 10 m/s2) The speed of the block at point C, immediately before it leaves the

second incline is

A) √120

B) √105

C) √90

D) √75

46. A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at

A. Assume that collisions between the block and the incline are

totally inelastic (g = 10 m/s2) If collision between the block and the incline is completely elastic,

then the vertical (upward) component of the velocity of the block at

point B, immediately after it strikes the second incline is

A) √30 m/s

B)   √15 m/s

C)  0 m/s

D) -  √15 m/s

47. Hyperconjugation involves overlap of the following orbitals

A) σ-σ

B) σ-p

C) p-p

D) π-π