Admission to Undergraduate Engineering Programs at NITs, IIITs, Other centrally funded Technical Institutions, Institutions funded by several participating State Governments, and several other Institutions shall involve the Joint Entrance Examination, iit jee 2013.
The iit jee 2013 will also be an eligibility test for the JEE (Advanced), which the candidate has to take if he/she is aspiring for admission to the undergraduate programmes offered by the IITs.
JEE(MAINS) SAMPLE QUESTIONS
SINGLE CORRECT CHOICE TYPE
1. Two large vertical and parallelmetal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. Aproton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then X is nearly
(A) 1 × 10.5 V (B) 1 × 10.7 V (C) 1 × 10.9 V (D) 1 × 10.10 V
2. A mixture of 2 moles of helium gas (atomic mass = 4 amu), and 1 mole of argon gas (atomic mass = 40 amu)is kept at 300 K in a container. The ratio of the rms speeds v (argon)
(A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16
3. A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2m and released from rest at t = 0. It then executes simple harmonicmotion with angular frequency rad/ s w = .p/3 Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45º as shown in the figure. Point P is at a horizontal distance of 10 cm from O. If the pebble hits the block at t = 1s, the value of v is(take g = 10 m/s2)
(A) 50m/ s (B) 51m/ s (C) 52m/ s (D) 53m/ s
4. 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
5.Athin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed w, as shown in thefigure. 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 remainswthroughout. Themagnitude of the torque (|t|) on the systemaboutO, as a function of time is best representedby which plot ?
6. In the determination of Youngs modulus Y by using Searles method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension = 0.25 mm in the length of the wire is observed.Quantities d and aremeasured using a screw gauge and amicrometer, respectively. They have the same pitch of 0.5mm. The number of divisions on their circular scale is 100. The contributions to themaximum probable error of the Y measurement
(A) due to the errors in the measurements of d and l are the same.
(B) due to the error in the measurement of d is twice that due to the error in the measurement of l.
(C) due to the error in the measurement of l is twice that due to the error in the measurement of d.
(D) due to the error in the measurement of d is four time that due to the error in the measurement of l.
7. Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of themagnitude of the electric field ( E(r))and the electric potential V(r) with the distancer from the centre, is best represented by which graph?
8. A bi-convex lens is formedwith two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R =14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
(A) 280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm
9. A small massm is attached to amassless string whose other end is fixed at P as shown in the figure. Themassis undergoing circular motion is the x-y plane with centre at O and constant angular speed w. If the angularmomentum of the system, calculated about O and P are denoted by Lo and Lp respectively, then
(A) Lo and Lp do not vary with time.
(B) Lo varies with time while Lp remains constant.
(C) Lo remains constant while Lp varies with time.
(D) Lo and Lp both vary with time.
10. Youngs 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
MULTIPLE CORRECT CHOICE TYPE
11. A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe.
(A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
(B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
(C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
(D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
12. A smallblock 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/s2)
(A) O= 45°
(B)O > 45° and a frictional force acts on the block towards P.
(C) O > 45° and a frictional force acts on the block towards Q.
(D) O< 45° and a frictional force acts on the block towards Q.
Ans. (A), (C)
(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the planex = a/2.
(B) The net electric flux crossing the plane y = +a/2 is more than the net electric flux crossing the plane y = a/2.
(C) The net electric flux crossing the entire region is q0
(D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane x = +a/2.
Ans. (A), (C), (D)
14. For the resistance network shown in the figure, choose the correct option(s).
(A) The current through PQ is zero.
(B) I1 = 3 A.
(C) The potential at S is less than that at Q.
(D) I2 = 2 A.
Ans. (A), (B), (C), (D)
15. Consider the motion of a positive point charge in a region where there are simultaneous uniform electric andmagnetic fields E = Eoj and B= Boj. At time t = 0, this charge has velocity v in the x-y plane, making anangle 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.
Ans. (C), (D)
INTEGER TYPE QUESTIONS
16. 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 atits start is :
(take the proton mass, mp = (5/3) × 1027 kg, h/e = 4.2 × 1015 J.s/C ; 1 fm = 1015 m)
17. A lamina is made by removing a small disc of diameter 2R froma bigger disc of uniform mass density and radius2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is IO andIP, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio IO and IP to the nearest integer
18. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a spherical cavity ofradius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric fieldat the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression. The value of k is
19. A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a shown in the figure. Both the cylinderand 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 12 N 0 aJ, then the value of N is :
20. A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop os side a (a << R) having two turns is placed with its center at a = 3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loopmakes an angle of 45° with respect to the z-axis. If the mutual inductance between the loops is given by, then the value of p is
SINGLE CORRECT CHOIC QUESTIONS
21.Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?
(A) HNO3, NO, NH4Cl, N2 (B) HNO3, NO, N2, NH4Cl
(C) HNO3, NH4Cl, NO, N2 (D) NO, HNO3, NH4Cl, N2
22. The number of aldol reaction (s) that occurs in the given transformation is :
23. For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs.1/V plot is shown below. The value of the van derWaals constant a (atm.liter2 mol)2 )) :
(A) 1.0 (B) 4.5 (C) 1.5 (D) 3.0
24.In allene (C3H4), the type(s) of hybridisation of the carbon atoms is (are) :
(A) sp and sp3 (B) sp and sp2 (C) only sp3 (D) sp2 and sp3
25. Acompound MP Xq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is
(A)MX (B)MX2 (C)M2X (D)M5X14
26. The number of optically active products obtained from the complete ozonolysis of the given compound is:
27. As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is :
(A) Tetraaquadiaminecobalt (III) chloride (B) Tetraaquadiamminecobalt (III) chloride
(C) Diaminetetraaquacoblat (III) chloride (D) Diamminetetraaquacobalt (III) chloride
28.The carboxyl functional group ( COOH) is present in
(A) picric acid (B) barbituric acid
(C) ascorbic acid (D) aspirin
29. The colour of light absorbed by an aqueous solution of CuSO4 is :
(A) organge-red (B) blue-green
(C) yellow (D) violet
MULTIPLE CORRECT CHOICE QUESTIONS
30. Which of the following molecules, in pure form, is (are) unstable at room temperature ?
31. Choose the correct reason(s) for the stability of the lyophobic colloidal particles.
(A) Preferential adsorption of ions on their surface from the solution.
(B) Preferential adsorption of solvent on their surface from the solution.
(C) Attraction between different particles having opposite charges on their surface.
(D) Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal
32. Which of the following halides react(s) withAgNO3(aq) to give a precipitate that dissolves in Na2S2O3(aq) ?
(A) HCl (B) HF (C)HBr (D)HI
33. An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively.What is hte value of 10[t ][1 ]
1/10t / 8 ?(log102 = 0.3)
34. When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is :
35. 29.2% (w/w) HCl stock solution has a density of 1.25 g mL1. The molecular weight of HCl is 36.5 g mol1. The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is :