IIT JEE Question Paper, Sample/Model Question Papers With Solutions

IIT JEE Question Paper

  • IIT JEE Sample model papers with solutions are provided here for the candidates who are preparing for the IIT written exam which is conducted in two section; JEE Main & JEE Advanced.
  • The exam is conducted for the admission in different engineering programs like B.Tech, B.E, B.Arch and B.Planning beneath the direction of Ministry of Human Resource Development (MHRD). This entrance Exam organized each year by one of the different IITs, using a round robin rotation pattern.
  • Candidates can take a look below to prepare through some Sample papers; some IIT JEE Model Question Papers with Solutions are provided below by the team of recruitmentlauncher.com

IIT JEE Model Question Papers With Solutions:

1. Let z = x + iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation 3 3 zz zz 350 + = is

  1. 48
  2. 32
  3. 40
  4. 80

Sol. (1.)

2. The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is

  1. 3110
  2. 2910
  3. 2110
  4. 2710

 Sol. (4.)

3. The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

  1. 55
  2. 66
  3. 77
  4. 88

 Sol. (3.)

4. Tangents drawn from the point P (1, 8) to the circle x2 + y2 − 6x − 4y − 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is

  1. x2+ y2+ 4x − 6y + 19 = 0
  2. x2 + y2 − 4x − 10y + 19 = 0
  3. x2 + y2− 2x + 6y − 29 = 0
  4. x2 + y2 − 6x − 4y + 19 = 0

Sol. (2.)

5. Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are: outer circle (0, 0) left inner circle (−a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, −a). The y-coordinate of the centre of mass of the ink in this drawing is

  1. a 10
  2. a 8
  3. a 12
  4. a 3

Sol. (1.)

 6. Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?

  1. 4
  2. 3
  3. 2
  4. 1

Sol. (3.)

7. A student performed the experiment of determination of focal length of a concave mirror by u – v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

  1. (42, 56)
  2. (48, 48)
  3. (66, 33)
  4. (78, 39)

 Sol. (3& 4.)

8. If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

  1. linear momentum of the system does not change in time
  2. kinetic energy of the system does not change in time
  3. angular momentum of the system does not change in time
  4. potential energy of the system does not change in time

Sol. (1.)

9. Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is

  1. Nylon
  2. Poly(vinyl chloride)
  3. Cellulose
  4. Natural Rubber

Sol. (4.)

10. The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)6 is

  1. 0
  2. 2.84
  3. 4.90
  4. 5.92

 Sol. (1.)

11. XeF4 and XeF6 are expected to be

  1. oxidizing
  2. reducing
  3. unreactive
  4. strongly basic

 Sol. (1.)

12. A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.

Sol. 5

13. 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

  1. 30° for both the colours
  2. greater for the violet colour
  3. greater for the red colour
  4. equal but not 30° for both the colours

Sol. (1.)

14. 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).

  1. If d = λ, the screen will contain only one maximum
  2. If λ < d < 2λ, at least one more maximum (besides the central maximum) will be observed on the screen
  3. 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
  4. 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

 Sol. (1.) & (2.)

15. Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of

  1. nitrogen
  2. oxygen
  3. carbon dioxide
  4. argon

Sol. (2.)

16. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

  1. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
  2. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
  3. No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
  4. No potential difference appears between the two cylinders when same charge density is given to both the cylinders.

Sol. (1.)

17. 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,

  1. x < f
  2. f < x < 2f
  3. x = 2f
  4. x > 2f

Sol. (2.)

18. The number of structural isomers for C6H14 is

  1. 3
  2. 4
  3. 5
  4. 6

Sol. (3.)

19. Extraction of zinc from zinc blende is achieved by

  1. electrolytic reduction
  2. roasting followed by reduction with carbon
  3. roasting followed by reduction with another metal
  4. roasting followed by self-reduction

 Sol. (2.)

20. If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is

  1. 200
  2. 225
  3. 400
  4. 446

Sol. (4.)

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