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IIT JEE Question Paper with Solutions

Paper 1

Q. Given that the abundances of isotopes ⁵⁴Fe, ⁵⁶Fe and ⁵⁷Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is
(A) 55.85
(B) 55.95
(C) 55.75
(D) 56.05

Q. The term that corrects for the attractive forces present in a real gas in the vander Waals equation is
(A) nb
(B) an²/V²
(C) -an²/V²
(D) -nb

Paper 2

Q. The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)₆ is
(A) 0
(B) 2.84
(C) 4.90
(D) 5.92

Q. Among the following, the state function(s) is (are)
(A) Internal energy
(B) Irreversible expansion work
(C) Reversible expansion work
(D) Molar enthalpy

IIT JEE 2008 Question Paper with Solutions

Paper 1

Q. 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

Q. Let a and b be 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 n and b are of the same sign and c is of sign opposite to that of a.

Paper 2

Q. A particle P starts from the point z_o=1 + 2i, where i = v-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z₁. From z₁the particle moves v2 units in the direction of
the vector i + j and then it moves through an angle /2 in anticlockwise direction on a
circle with centre at origin, to reach a point z₂ . The point z₂ is given by
(A) 6 + 7i
(B) -7 + 6i
(C) 7 + 6i
(D) -6 + 7i

Q. An experiment has 10 equally likely outcomes. Let A and B be two non-empty-events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is
(A) 2, 4 or 8
(B) 3, 6 or 9
(C) 4 or 3
(D) 5 or 10

IIT JEE 2007 Question Paper with Solutions

Paper 1

Q. A resistance of 2 ohm is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 ohm, is connected across the other gap. When these resistances arc inter changed, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is :
(A) 3 ohm
(B) 4 ohm
(C) 5 ohm
(D) 6 ohm

Q. In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin Then,
(A) x<f
(B) f<x<2f
(C) x=2f
(D) x>2f

Paper 2

Q. In the experiment to determine the speed of sound using a resonance column,
(A) prongs of the tuning fork are kept in a vertical plane.
(B) prangs of the tuning fork are kept in a horizontal plane.
(C) in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air.
(D) in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air.

Q. A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of + 0.01 mm. Take g = 9.8 m/s² (exact). The Young’s modulus obtained from the reading is
(A) (2.0 ± 0.3) x 10¹¹ N/m²
(B) (2.0 ± 0.2) x 10¹¹ N/m²
(C) (2.0 ± 0.1) x 10¹¹ N/m²
(D) (2.0 ± 0.05) x 10¹¹ N/m²

Resources:

IIT-JEE 2009 (including solutions) : Paper 1 (328kb) | Paper 2 (306kb)
IIT-JEE 2008 (including solutions) : Paper 1 (385kb) | Paper 2 (432kb)
IIT-JEE 2007 (including solutions) : Paper 1 (298kb) | Paper 2 (306kb)
IIT-JEE 2006 (including solutions) : Paper 1 (871kb)
IIT-JEE 2005 (including solutions) : Paper 1 (1.19mb)
IIT-JEE 2004 : Paper 1 (1.62mb) | Solutions (1.04mb)
IIT-JEE 2003 : Paper 1 (1.34mb) | Solutions (794kb)
IIT-JEE 2002 : Paper 1 (1.51mb) | Solutions (797kb)
IIT-JEE 1997 : Paper 1 (490kb)

Note : Papers are in PDF Format, which requires Adobe Reader to run.

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