OJEE 2017 Question Paper LE B.Tech (B.Sc)

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OJEE 2017
Question Paper · LE
B.Tech (B.Sc)
EXAM YEAR TYPE SUBJECT

OJEE 2017 Question Paper LE B.Tech (B.Sc)

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BSC-LATERAL ENTRY-60 QUESTION

1. The time dependence of a physical quantity P is given by = , where α is a constant
and t is time. Then constant α is

m
(a) dimensionless (b) dimension of (c) dimension of P (d) dimension of

m . c o
. cotravelling in the same direction with velocities v and v (v > v ). When sem
e m s behind car B, the driver of the car A applies the brakes producinglaa
2. Two cars A and B are A B A B

a s a g
the car A is at a distance

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uniform retardation a, there will be no collision when
( ) ( ) ( ) ( )
(a) < (b) = (c) ≥ (d) ≤

3. A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre
of cavity is at a distance R/2 from the centre of the sphere. A point mass m is placed inside the
cavity at a distance R/4 from the centre of the sphere. The gravitational pull between the sphere

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and point mass m is

(c) .
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las
(a) (b) (d)

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4. The kinetic energy K of a particle moving along a circle of radius R depends on the distance
covered s as K = as2, where a is a constant. The force acting on the particle is
/
(a) 2 (b) 2 1+ (c) 2 (d) 2

m
c. o
5. Steam is passed into 22 g of water at 200C. The mass of water that will be present when the

m
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water acquires a temperature of 900C (latent heat of steam is 540 cal/g) is

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(a) 24.8 g (b) 24 g (c) 36.6 g
l a s
(d)

s g
la 6. Hot food cools from 94 C to 86 C in 2 min when the room temperature
a
ag 0 0
0 0
is 20 C. How long 0

would the food take to cool from 71 C to 69 C?
(a) 12 s (b) 25 s (c) 16 s (d) 42s

m . c
c. o se m
m a
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7. A wire of length L and radius r fixed at one end and a force F applied to the other end produces
an extension l. The extension produced in another wire of the same material of length 2L and radius
2r by a force 2F, is

(a) l (b) 2l (c) 4l (d)

8. The length of a sonometer wire AB is 110 cm. Where should the two bridges be placed from A
to divide the wire in three segments whose fundamental frequencies are in the ratios of 1 : 2 : 3.
(a) 30 cm, 90 cm (b) 60 cm, 90 cm (c) 40 cm, 70 cm (d) None of these

9. Four charges equal to –Q are placed at the four corners of a square and a charge q is at its centre.
If the system is in equilibrium, the value of q is

(a) − 1 + 2√2 (b) 1 + 2√2 (c) − 1 + 2√2 (d) 1 + 2√2

10. Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same
direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A?
(Assume that µ o= 4π×10-7 H)
(a) 1.5 × 10-5 N (b) 2 × 10-5 N (c) 4 × 10-5 N (d) 3.2 × 10-5 N

11. The armature of a DC motor has resistance of 20 Ώ. It draws a current of 1.5 A when run by
220 V of DC. The value of peak emf induced in it will be
(a) 150 V (b) 170 V (c) 190 V (d) 180 V

12. A parallel plate capacitor is charged and then disconnected from the charging battery. If the
plates are now moved farther apart by pulling at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases

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13. For maintaining sustained chain reaction, which of the following is required
(a) Protons (b) Electrons (c) Neutrons (d) Positrons

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14. A Si and a Ge diode has identical physical dimensions. The band gap of Si is larger than that

m is larger than that in Si. . co
of Ge. An identical reverse bias is applied across the diodes.
(a) The reverse current inoGe
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em in Si is larger than that in Ge. l a s
s
lacurrent is identical in the two diodes a g
(b) The reverse current

a g
(c) The reverse
(d) The relative magnitude of the reverse current cannot be determined from the given data only

15. In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude A
and wavelength λ. In another experiment with the same set up, the two slits are sources of equal
amplitude A and wavelength λ but are incoherent. The ratio of the intensity of light at the mid-

m
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point of the screen in the first case to that of second case is

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(a) 2 : 1 (b) 1: 2 (c) 3 : 4 (d) 4 : 3

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16.
a
Eka silico and Eka-aluminium are known as: g
a) gallium and germenium b) germanium and gallium
c) indium and silicon d) zinc and arsenic

17. Which of the following order is wrong with respect to the properties mentioned?

m
a) Al3+< Li+ <Mg2+ <Na+ (ionic radius)

m c. o
c. o c) Al O < MgO < Na O < K O (basic nature)
b) I < Br < F < Cl (electron affinity)

e m
em (increasing order of density)a s
2 3 2 2

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d) Li <Na < K < Rb <Cs

ag 18. In which of the following the central atom has least number of lone pair of electron(s)?
a) XeF4 b) ClO3¯
c) IO2¯ d) I3¯

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19. The ion which is not tetrahedral in shape is:
a) NH4+ b) ClO4¯
c) NiCl42¯ d) PtCl42¯

20. Which compound has maximum O─N─O bond angle?
a) NO2 b) NO2+
c) NO3¯ d) NO2¯
21. Ka1, Ka2 and Ka3 are the respective ionization constant for the following reactions

H 2S HS + H+

HS S2 + H+

H 2S S2 + 2 H+

The correct relationship between Ka1, Ka2 and Ka3 is
a) Ka1 x Ka2 = Ka3 b) Ka1 + Ka2 = Ka3
c) Ka1 / Ka2 = Ka3 d) Ka2 / Ka1 = Ka3

22. Which of the following alcohol will react fastest with conc. HCl ?

23. The enantiomer of the following molecule (P) on reaction with NaOAc followed by
hydrolysis with NaOH gives the compound
H
CH3

C2 H5 (P)
Br

H H H H
CH3 OH C2 H5 OAc
a) b) c) d)
C2 H5 C2 H5 H 3C OH C2 H5 CH 3
OH CH 3

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24. The conversion of acetophenone to acetanilide is best accomplished by using which
reaction as one of the key step.
a) Hofmann rearrangement b) Curtius rearrangement
c) Beckman rearrangement d) Lossen rearrangement

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25. Green chemistry means such reactions which

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a) are related to depletion of ozone layer

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c)aproduces colour during reaction
b) study the reaction in green plants

d) reduce the use and production of hazardous chemicals
26. An unknown organic compound (X) C8H10O3 on acetylation with CH3COCl/Py forms
acetyl derivative of X whose M.W. is 280. X on treatment with CH2N2 gives a compound
Y having M. W. 182. The number of phenolic hydroxyls and alcoholic hydroxyls in the
compound X will respectively be:

o m
c
Acetaldehyde can directly be converted into .ethyl acetate by which one of the following
a) 1,3 b) 3,1 c) 2,1 d) 1,2

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27.
reactions
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a) Cannizzaro reaction
a b) Tischenko reaction
c) Baeyer Villiger oxidation reaction d) Claisen ester condensaation
reaction
28. The number of radial nodes in 3s and 2p orbital respectively are
a) 2 and 0 b) 1 and 2 c) 0 and 2 d) 2 and 1

m
29. 0.004 M solution of Na2SO4 is isotonic with 0.01 M solution of glucose at same

m a) 85% c. d)o75%
temperature. Degree of dissociation of Na2SO4 is

c.30.o A 50 mL solution of pH = 1 is mixed with equal volume of solutionsofem
b) 25% c) 50%

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pH = 2. The pH of

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the resultant solution will be nearly
a) 0.76 b) 2.26 c) 1.26 d) 1.76

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31. If , are roots of the equation + + 1 = 0 then the equation whose roots are
, will be
a) + +1=0
b) − +1=0
c) + −1=0
d) − −1=0
32. If ⌊ ⌋ represents the greatest integer less than or equal to x, then the function ( ) =
⌊ + 1⌋ − ⌊ − 1⌋ is
a) not continuous in the interval (-1,1).
b) continuous but not differentiable in the interval (-1,1).
c) differentiable in the interval (-1,1).
d) strictly increasing in the interval (-1,1).
33. If the pair of equation + + = 0 and + + = 0 have a common root then
a) =
b) ( − )( + + 1) = 0
c) ( − )( + − 1) = 0
d) ( + )( + + 1) = 0
34. If cos 8 cos 4 cos 2 cos = − 1 16 , then the value of will be
a) 16
b) − 15
c) − 16
d) 15
35. In the sitting arrangement for ten girls and ten boys around a round table with twenty
identical chairs, the number of arrangements that no two girls will sit together is
a) 3 × (10)!
b) 2 × (10)!
c) (10)!
d) 5 × (10)!

36. If , , are three real numbers satisfying the pair of conditions + + = 0 and
+ + =0
( − ) +( − ) +( − ) >0 then the system of equations + + =0
+ + =0
will represent
a) the straight line = = .
b) the straight line +1 = −1= .
c) the straight line =− = .
d) the straight line − 1 = = + 1.

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37. The value of lim (1 + 2 ) will be
→
a) −
b) 1
c)
d) 1
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38. The value of the integral ∫ log|tan 2 | will be
a) 0
.c e m
m
c) e− log 2
b) 1
l a s
l a s log 2 ag
ag 39. If angle between the unit vectors ⃗ , ⃗ is
d)
⃗. ⃗ ⃗. ⃗
4 then the value of ⃗. ⃗ ⃗. ⃗
is

a) 0
b) 1
c) 1 2
d) 1
√2

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40. If ⃗ , ⃗ , ⃗ are position vectors of the points A, B, C and O is the origin, then the
vector ⃗ × ⃗ + ⃗ × ⃗ + ⃗ × ⃗ is c
.triangle ABC
b) a vector perpendicular to thesplane
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e of the triangle ABC
a) a vector parallel to the plane of the

g a
lthe plane of the triangle OBC
d) a vector perpendicularato the plane of the triangle OAB
c) a vector perpendicular to

41. The line ⃗ = ̂+ ̂+ + ̂− ̂+ lies in the plane
a) ⃗ ∙ ̂+2 ̂+ = 4.

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b) ⃗ ∙ ̂−2 ̂+ =4

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c) ⃗∙ ̂+2 ̂− =4

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d) ⃗ ∙ ̂ + 2 ̂ + = −4

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42. Let be the sum of first terms of the A.P. having first term and common difference

g
. Then be the n term of th
a
a a) an A.P. with first term and common difference .
b) an A.P. with first term be and common difference + .
c) an G.P. with first term and common ratio .
d) none of the above.

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43. The line of interaction of the pair of planes, ⃗ ∙ ̂ + 2 ̂ + 3 = 0 and ⃗ ∙ 3 ̂ + 2 ̂ + =
0 is equally inclined to the axes
a) ̂ , ̂
b) ̂ ,
c) ̂ ,
d) ̂ , ̂ ,
44. The equation of a sphere that have points ⃗ , ℎ⃗ as the extreme points of one diameter is
⃗ ⃗
a) ⃗− ∙ ⃗− =0

b) ( ⃗ − ⃗) ∙ ⃗ − ℎ⃗ = 0
c) ⃗ − 3 ⃗ ∙ ⃗ − 3ℎ⃗ = 0
d) ( ⃗ − 2 ⃗) ∙ ⃗ − 2ℎ⃗ = 0

45. If = and =( )
then the value of x at which =0
a) −
b)
c) –
d)

46. Which of the following statement is not true in general?
a) (AB) A is a tautology, for any B.
b) A implies B if and only if B implies A.
c) A is a tautology if and only if A is a contradiction.
d) (AB)A is not a contradiction, for any B always.

47. All points (x,y) satisfying the differential equation = 0 belong to
a) The perimeter of a closed curve centered at origin.
b) The area bounded by a circle centered at origin.
c) Any one of the infinite number of straight line in XY plane.
d) The area bounded by a circle not centered at origin.

48. The differential equation formed by the primitive lx + my = n is
a) = −l/m

b) = k/n, where k is any constant
c) = − m⁄n

d) =0

49. The differential equation 3 + 5x( ) + 4y = 5x-4 has degree and order
a) 1,2.

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b) 1,3.
c) 2,2.
d) 3,2.

50. Conditional probability P(A|B) is undefined only when

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a) A is a certain event

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b) P(B)=0

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c) P(A)=0

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d) B is a certain event.

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51. g l binary representation of the decimal number 39 is a
a a) 101111
The

b) 100111
c) 101011
d) 111011

52. The plane containing the origin and passing through the line of intersection of the planes
2x + 2y − 4z = 2 and 3x + 9y − 3z = 12 is

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a) 3x+y=7z

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b) x+3y=4z

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c) 2x+3y=5z
d) 3x+2y+7z=0

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53. The general solution of the differential equation y = 5xp + 3e , where p = is
a) y = 5x + 3e
b) y = 5c + 3e
c) y = 5xc + 3xe
d) y = 5xc + 3e
where c is a constant.

54. The parabolas = 2( + 1) and = −2( − 1) has

m
c. o
a) x axis as one common tangent.

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b) Two common tangents = 0 and + = 0

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c) Two common tangents 3 = 0 and 2 = 3

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d) No common tangent

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a 55. The equation 5x − 5y + 3x + 3y = 4 represents
a) A parabola
b) A pair of straight lines
c) A hyperbola
d) An ellipse

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56. Mean and Standard deviation of a sample of 15 positive numbers are 15 and 3 respectively.
The sum of squares of the numbers is
a) (225+10)6
b) (225+11)9
c) (225+9)15
d) (225+9)11
57. The value of the integral ∫ 3x dx is
a) 3
b) -3
c) 1
d) 0
58. State which of the following is not true:
a) Addition of two real numbers is always commutative.
b) Multiplication of two integers is commutative.
c) Perpendicularity in the set of straight lines is not an equivalence relation.
d) Parallelism in the set of straight lines is not an equivalence relation.
59. The sphere 5x + 5y + 5z + 10x + 10y − 10z = 40 has center
a) (1,1,1)
b) (−1, −1,1)
c) (1,1, −1)
d) (1, −1,1)
60. For a natural number (> 2), the number ( + 1)( − 1) is not always divisible by
a) 6
b) 2
c) 7
d) 3

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