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Frequently Asked IIT-JEE Latest Exam Pattern - IIT-JEE Sample Question with Solutions Page 33

(#M40027956) IIT-JEE QUESTION 2012 question Keep an EYE

The function f : [0, 3] [1, 29], defined by f(x) = 2x^3 -– 15x^2 + 36x + 1, is
(A) one-one and onto (B) onto but not one-one
(C) one-one but not onto (D) neither one-one nor onto

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(#M40027953) IIT-JEE QUESTION 2012 question Keep an EYE

The point P is the intersection of the straight line joining the points Q(2,3,5) and R(1, –1, 4) with the plane
5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1,4) to QR, then the length of the
line segment PS is

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(#M40027943) IIT-JEE QUESTION 2012 question Keep an EYE

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a //Both the cylinder
and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the
magnetic field at the point P is given by N/12 MICRO aJ, then the value of N is

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(#M40027941) IIT-JEE QUESTION 2012 question Keep an EYE

A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge.
It makes a closest approach of 10 fm to the nucleus. The de Brogle wavelength (in units of fm) of the proton at
its start is

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(#M40027940) IIT-JEE QUESTION 2012 question Keep an EYE

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and
magnetic fields j ˆ E  E0

and j ˆ B  B0

. At time t = 0, this charge has velocity v
 in the x-y plane, making an
angle  with x-axis. Which of the following option(s) is(are) correct for time t > 0 ?
(A) If  = 0°, the charge moves in a circular path in the x-z plane.
(B) If  = 0°, the charge undergoes helical motion with constant pitch along the y-axis.
(C) If  = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
(D) If  = 90°, the charge undergoes linear but accelerated motion along the y-axis.

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(#M40027939) IIT-JEE QUESTION 2012 question Keep an EYE

Asmall block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle  with the horizontal. A
horizontal force of 1 N on the block through its center of mass as shown in the figure. The block remains
stationary if (take g = 10 m/s^2)

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(#M40027937) IIT-JEE QUESTION 2012 question Keep an EYE

Young’s double slit experiment is carried out by using green, red and blue light, one color at time. The fringe
widths recorded are G, R and B, respectively. Then
(A) G > B > R (B)B > G > R (C)R > B > G (D)R > G > B

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(#M40027936) IIT-JEE QUESTION 2012 question Keep an EYE

A small massm is attached to amassless string whose other end is fixed at P as shown in the figure. Themass
is undergoing circular motion is the x-y plane with centre at O and constant angular speed . If the angular
momentum of the system, calculated about O and P are denoted by O L

and P L

respectively, then

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(#M40027934) IIT-JEE QUESTION 2012 question Keep an EYE

Athin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed w,At time, t = 0, a small insect starts from O and moves with constant speed v with respect to the rod
towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains
throughout. Themagnitude of the torque (| 
|) on the systemaboutO, as a function of time is best represented
by which plot ?

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(#M40027933) IIT-JEE QUESTION 2012 question Keep an EYE

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal
black surfaces and have very high thermal conductivity. The first and third plates aremaintained at temperatures
2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

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