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**Note**: Please be patient while the PDF loads completely, it depends on your internet connection purely. ) Tags : AIEEE,2003,Paper,Exam,Chemistry,Maths,Physics,IIT,JEE,IIT JEE,Joint Entrance Examination, iit jee solved question paper with answers and detailed solutions, online question paper free,important questions,aieee exam paper, jee mains, iit jee papers.AIEEE−2012−2
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1. The equation e
sin x
– e
–sin x
– 4 = 0 has
(1) infinite number of real roots (2) no real roots
(3) exactly one real root (4) exactly four real roots
1. 2
Sol. e
sin x
– e
–sin x
= 4 e
sin x
= t
t –
1
t
= 4
t
2
– 4t – 1 = 0 t =
4 16 4
2
± +
t =
4 2 5
2
±
t = 2 ± 5
e
sin x
= 2 ± 5 –1 ≤ sin x ≤ 1
1
e
≤ e
sin x
≤ e
e
sin x
= 2 + 5 not possible
e
sin x
= 2 – 5 not possible ∴ hence no solution
2. Let
ˆ aˆ and b be two unit vectors. If the vectors
ˆ ˆ c = aˆ + 2b and d = 5aˆ − 4b
are perpendicular to each other,
then the angle between ˆ aˆ and b is
(1)
6
π
(2)
2
π
(3)
3
π
(4)
4
π
2. 3
Sol. c ⋅ d = 0
2 2
5 a + 6a ⋅b − 8 b = 0
1
6a b 3 a b
2
⋅ = ⋅ =
(a b)
3
π
⋅ =
3. A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas
to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the
radius of the balloon decreases 49 minutes after the leakage began is
(1)
9
7
(2)
7
9
(3)
2
9
(4)
9
2
3. 3
Sol. v =
4 2
r
3
π
After 49 minutes volume = 4500π – 49 (72π) = 972π
4
3
πr
3
= 972π r
3
= 729 r = 9
v =
4
3
πr
3 dv 4 2 dr
3r
dt 3 dt
= π 72π = 4π
2 dr
r
dt
dr 72 2
dt 4 9 9 9
= =
⋅ ⋅
4. Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + …… + (361 + 380 +
400) is 8000.
Statement 2: ( ( ) )
n
3 3 3
k 1
k k 1 n
=
− − = for any natural number n.
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
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(4) Statement 1 is true, statement 2 is false
4. 2
Sol. Statement 1 has 20 terms whose sum is 8000
And statement 2 is true and supporting statement 1.
k
th
bracket is (k – 1)
2
+ k(k – 1) + k
2
= 3k
2
– 3k + 1.
5. The negation of the statement “If I become a teacher, then I will open a school” is
(1) I will become a teacher and I will not open a school
(2) Either I will not become a teacher or I will not open a school
(3) Neither I will become a teacher nor I will open a school
(4) I will not become a teacher or I will open a school
5. 1
Sol. ~(~p ∨ q) = p ∧ ~q
6. If the integral
5tanx
tanx − 2dx = x + a ln |sin x – 2 cos x| + k, then a is equal to
(1) –1 (2) –2 (3) 1 (4) 2
6. 4
Sol.
5tanx 5sinx
dx dx
tanx 2 sinx 2cos x
=
− −
2(cos x 2sinx) (sinx 2cos x)
dx
sinx 2cos x
+ + −
− =
cos x 2sinx
2 dx dx k
sin x 2cos x+
+ +
− = 2 log |sin x – 2 cos x| + x + k ∴ a = 2
7. Statement 1: An equation of a common tangent to the parabola y
2
=16 3x and the ellipse 2x
2
+ y
2
= 4 is
y = 2x + 2 3 .
Statement 2: If the line y = mx +
4 3
m
, (m ≠ 0) is a common tangent to the parabola
y
2
= 16 3x and the ellipse 2x
2
+ y
2
= 4, then m satisfies m
4
+ 2m
2
= 24.
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4) Statement 1 is true, statement 2 is false
7. 2
Sol. y
2
= 16 3x
2 2
x y
1
2 4
+ =
y = mx +
4 3
m
is tangent to parabola
which is tangent to ellipse c
2
= a
2m
2
+ b
2
2
48
m
= 2m
2
+ 4 m
4
+ 2m
2
= 24 m
2
= 4
8. Let A =
1 0 0
2 1 0
3 2 1
. If u1 and u2 are column matrices such that Au1 =
1
0
0
and Au2 =
0
1
0
, then u1 + u2 is
equal to
(1)
1
1
0−
(2)
1
1
1−
−
(3)
1
1
0−−
(4)
1
1
1−
−
8. 4
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Sol. A =
1 0 0
2 1 0
3 2 1
Let u1 =
a
b
c
; u2 =
d
e
f
Au1 = 1
1 1
0 u 2
0 1
= −
Au2 =
0
1
0
u2 =
0
1
2
−
u1 + u2 =
1
1
1
−
−
9. If n is a positive integer, then ( ) ( )
2n 2n
3 +1 − 3 −1 is
(1) an irrational number (2) an odd positive integer
(3) an even positive integer (4) a rational number other than positive integers
9. 1
Sol. ( ) ( ) ( ) ( ) ( ) ( )
n n
2n 2n 2 2 n n
3 1 3 1 3 1 3 1 4 2 3 4 2 3
+ − − = + − − = + − −
= ( ) ( )
n n
n
2 2 3 2 3
+ − −
= { }
n n n n n 1 n n 2 n n n n 1 n n 2
2 C0 2 C12 3 C2 2 3 C0 2 C12 3 C2 2 3 +
−
+
−
+ ⋅ ⋅⋅⋅⋅− −
−
+
−
− ⋅ ⋅⋅⋅⋅
=
n 1 n n 1 n n 3 n 1
2 C12 3 C3 2 3 3 2 3
+ − − +
+ + ⋅⋅⋅⋅ =
(some integer)
Which is irrational
10. If 100 times the 100
th
term of an AP with non zero common difference equals the 50 times its 50
th
term,
then the 150
th
term of this AP is
(1) –150 (2) 150 times its 50
th
term
(3) 150 (4) zero
10. 4
Sol. 100(T100) = 50(T50) 2[a + 99d] = a + 49d a + 149d = 0 T150 = 0
11. In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to
(1)
5
6
π
(2)
6
π
(3)
4
π
(4)
3
4
π
11. 2
Sol. 3 sin P + 4 cos Q = 6 …… (1)
4 sin Q + 3 cos P = 1 …… (2)
From (1) and (2) ∠P is obtuse.
(3 sin P + 4 cos Q)
2
+ (4 sin Q + 3 cos P)
2
= 37
9 + 16 + 24 (sin P cos Q + cos P sin Q) = 37
24 sin (P + Q) = 12
sin (P + Q) =
1
2
P + Q =
5
6
π
R =
6
π
12. An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is
(1) x – 2y + 2z – 3 = 0 (2) x – 2y + 2z + 1 = 0
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(3) x – 2y + 2z – 1 = 0 (4) x – 2y + 2z + 5 = 0
12. 1
Sol. Equation of plane parallel to x – 2y + 2z – 5 = 0 is x – 2y + 2z + k = 0 …… (1)
perpendicular distance from O(0, 0, 0) to (1) is 1
k
1+ 4 + 4
= 1 |k| = 3 k = ±3 ∴ x – 2y + 2z – 3 = 0
13. If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and
(2, 4) in the ratio 3 : 2, then k equals
(1)
29
5
(2) 5 (3) 6 (4)
11
5
13. 3
Sol. Point p =
6 2 12 2
,
5 5+ +
p =
8 14
,
5 5
8 14
p ,
5 5
lies on 2x + y = k
16 14
k
5 5
+ = k =
30
5
= 6
14. Let x1, x2, ……, xn be n observations, and let x be their arithematic mean and σ
2
be their variance.
Statement 1: Variance of 2×1, 2×2, ……, 2xn is 4 σ
2
.
Statement 2: Arithmetic mean of 2×1, 2×2, ……, 2xn is 4x .
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4) Statement 1 is true, statement 2 is false
14. 4
Sol. σ
2
=
2 2
i i
x x
n n
− Variance of 2×1, 2×2, ….., 2xn =
( )
2 2
i i
2x 2x
n n
−
=
2 2
i i
x x
4
n n
−
= 4σ
2
Statement 1 is true.
A.M. of 2×1, 2×2, ……, 2xn =
2 1 2 n 1 2 n
x 2x 2x x x x
2 2x
n n
+ + ⋅ ⋅⋅⋅ +
+ + ⋅⋅⋅⋅ +
=
=
Statement 2 is false.
15. The population p(t) at time t of a certain mouse species satisfies the differential equation
dp(t)
dt
= 0.5 p(t)
– 450. If p(0) = 850, then the time at which the population becomes zero is
(1) 2 ln 18 (2) ln 9 (3)
1
ln18
2
(4) ln 18
15. 1
Sol.
d(p(t)) 1
dt 2
= p(t) – 450
d(p(t)) p(t) 900
dt 2
−
=
d(p(t))
2 dt
p(t) 900
=
−
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2 ln |p(t) – 900| = t + c
t = 0 2 ln 50 = 0 + c c = 2 ln 50
∴ 2 ln |p(t) – 900| = t + 2 ln 50
P(t) = 0 2 ln 900 = t + 2 ln 50
t = 2 (ln 900 – ln 50) =
900
2ln
50
= 2 ln 18.
16. Let a, b ∈ R be such that the function f given by f(x) = ln |x| + bx
2
+ ax, x ≠ 0 has extreme values at x = –1
and x = 2.
Statement 1: f has local maximum at x = –1 and at x = 2.
Statement 2: a =
1
2
and b =
1
4
−
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4) Statement 1 is true, statement 2 is false
16. 2
Sol. f′(x) =
1
x
+ 2b x + a
f has extremevalues and differentiable
f′(–1) = 0 a – 2b = 1
f′(2) = 0 a + 4b =
1
2
− a =
1
2
, b =
1
4
−
f′′(–1), f′′(2) are negative. f has local maxima at –1, 2
17. The area bounded between the parabolas x
2
=
y
4
and x
2
= 9y, and the straight line y = 2 is
(1) 20 2 (2)
10 2
3
(3)
20 2
3
(4) 10 2
17. 3
Sol. Required area
A =
2 2
0 0
y 5 y
2 3 y dy 2 dy
2 2
−
=
=
2
3 / 2
3 / 2
0
y 10 20 2
5 2 0
3 / 2 3 3
= − =
O
y = 2
x
2
=
9
4
x
2
= 9y
18. Assuming the balls to be identical except for difference in colours, the number of ways in which one or
more balls can be selected from 10 white, 9 green and 7 black balls is
(1) 880 (2) 629 (3) 630 (4) 879
18. 4
Sol. Number of ways of selecting one or more balls from 10 white, 9 green, and 7 black balls
= (10 + 1)(9 + 1)(7 + 1) – 1 = 11 × 10 × 8 – 1 = 879.
19. If f: R → R is a function defined by f(x) = [x]
2x 1
cos
2−
π, where [x] denotes the greatest integer
function, then f is
(1) continuous for every real x (2) discontinuous only at x = 0
(3) discontinuous only at non-zero integral values of x (4) continuous only at x = 0
19. 1
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Sol. f(x) =
2x 1 1
x cos x cos x
2 2−
π = −
π
= [x] sin π x is continuous for every real x.
20. If the lines
x 1 y 1 z 1 x 3 y k z
and
2 3 4 1 2 1
− + − − −
= = = = intersect, then k is equal to
(1) –1 (2)
2
9
(3)
9
2
(4) 0
20. 3
Sol. Any point on
x 1 y 1 z 1
2 3 4
− + −
= = = t is (2t + 1, 3t – 1, 4t + 1)
And any point on
x 3 y k z
1 2 1
− −
= = = s is (s + 3, 2s + k, s)
Given lines are intersecting t =
3
2
− and s = –5 ∴ k =
9
2
21. Three numbers are chosen at random without replacement from {1, 2, 3, …… 8}. The probability that their
minimum is 3, given that their maximum is 6, is
(1)
3
8
(2)
1
5
(3)
1
4
(4)
2
5
21. 2
Sol. Let A be the event that maximum is 6.
B be event that minimum is 3
P(A) =
5
2
8
3
C
C
(the numbers < 6 are 5)
P(B) =
5
2
8
3
C
C
(the numbers > 3 are 5)
P(A ∩ B) =
2
1
8
3
C
C
Required probability is
2
1
5
2
B P(A B) C 2 1
P
A P(A) C 10 5∩
= = = =
.
22. If z ≠ 1 and
2
z
z −1
is real, then the point represented by the complex number z lies
(1) either on the real axis or on a circle passing through the origin
(2) on a circle with centre at the origin
(3) either on the real axis or on a circle not passing through the origin
(4) on the imaginary axis
22. 1
Sol. Let z = x + iy ( x ≠ 1 as z ≠ 1)
z
2
= (x
2
– y
2
) + i(2xy)
2
z
z −1
is real its imaginary part = 0
2xy (x – 1) – y(x
2
– y
2
) = 0
y(x
2
+ y
2
– 2x) = 0
y = 0; x
2
+ y
2
– 2x = 0
∴ z lies either on real axis or on a circle through origin.
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23. Let P and Q be 3 × 3 matrices with P ≠ Q. If P
3
= Q
3
and P
2Q = Q
2
P, then determinant of
(P
2
+ Q
2
) is equal to
(1) –2 (2) 1 (3) 0 (4) –1
23. 3
Sol. P
3
= Q
3
P
3
– P
2Q = Q
3
– Q
2
P
P
2
(P – Q) = Q
2
(Q – P)
P
2
(P – Q) + Q
2
(P – Q) = O
(P
2
+ Q
2
)(P – Q) = O |P
2
+ Q
2
| = 0
24. If g(x) =
x
0
cos4t dt, then g(x + π) equals
(1)
g(x)
g(π)
(2) g(x) + g(π) (3) g(x) – g(π) (4) g(x) . g(π)
24. 2 or 4
Sol. g(x) =
x
0
cos4t dt g′(x) = cos 4x g(x) =
sin4x
k
4
+ g(x) =
sin4x
4
[ g(0) = 0]
g(x + π) = g(x) + g(π) = g(x) – g(π) ( g(π) = 0)
25. The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through
the point (2, 3) is
(1)
10
3
(2)
3
5
(3)
6
5
(4)
5
3
25. 1
Sol. Let (h, k) be centre.
(h – 1)
2
+ (k – 0)
2
= k
2 h = 1
(h – 2)
2
+ (k – 3)
2
= k
2 k =
5
3
∴ diameter is 2k =
10
3
k
k
(h, k)
(2, 3)
(1, 0)
26. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z
⊆ X and Y ∩ Z is empty, is
(1) 5
2
(2) 3
5
(3) 2
5
(4) 5
3
26. 2
Sol. Y ⊆ X, Z ⊆ X
Let a ∈ X, then we have following chances that
(1) a ∈ Y, a ∈ Z
(2) a ∉ Y, a ∈ Z
(3) a ∈ Y, a ∉ Z
(4) a ∉ Y, a ∉ Z
We require Y ∩ Z = φ
Hence (2), (3), (4) are chances for ‘a’ to satisfy Y ∩ Z = φ.
∴ Y ∩ Z = φ has 3 chances for a.
Hence for five elements of X, the number of required chances is 3 × 3 × 3 × 3 × 3 = 3
5
27. An ellipse is drawn by taking a diameter of the circle (x – 1)
2
+ y
2
= 1 as its semiminor axis and a
diameter of the circle x
2
+ (y – 2)
2
= 4 as its semi-major axis. If the centre of the ellipse is the origin and
its axes are the coordinate axes, then the equation of the ellipse is
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(1) 4x
2
+ y
2
= 4 (2) x
2
+ 4y
2
= 8 (3) 4x
2
+ y
2
= 8 (4) x
2
+ 4y
2
= 16
27. 4
Sol. Semi minor axis b = 2
Semi major axis a = 4
Equation of ellipse =
2 2
2 2
x y
a b
+ = 1
2 2
x y
16 4
+ = 1
x
2
+ 4y
2
= 16.
28. Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4) Statement 1 is true, statement 2 is false
28. 2
Sol. f(x) = 7 – 2x; x < 2
= 3; 2 ≤ x ≤ 5
= 2x – 7; x > 5
f(x) is constant function in [2, 5]
f is continuous in [2, 5] and differentiable in (2, 5) and f(2) = f(5)
by Rolle’s theorem f′(4) = 0
∴ Statement 2 and statement 1 both are true and statement 2 is correct explanation for statement 1.
29. A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a
triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ
is
(1)
1
4
− (2) –4 (3) –2 (4)
1
2
−
29. 3
Sol. Equation of line passing through (1, 2) with slope m is y – 2 = m(x – 1)
Area of ∆OPQ =
2
(m 2)
2 m
−
∆ =
2 m 4 4m
2m
+ −
∆ =
m 2
2
2 m
+ −
∆ is least if
m 2
2 m
= m
2
= 4 m = ±2 m = –2
30. Let ABCD be a parallelogram such that AB = q,AD = p
and ∠BAD be an acute angle. If r
is the vector
that coincides with the altitude directed from the vertex B to the side AD, then r
is given by
(1)
( )
( )
3 p q
r 3q p
p p
⋅
= −
⋅
(2)
p q
r q p
p p⋅
= − + ⋅
(3)
p q
r q p
p p⋅
= − ⋅
(4)
( )
( )
3 p q
r 3q p
p p
⋅
= − +
⋅
30. 2
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Sol. AE
= vector component of q on p
AE
=
( )
( )
p q
p
p q
⋅
⋅
∴ From ∆ABE; AB +BE = AE
( )
( )
p q p
q r
p q
⋅
+ =
⋅
( )
( )
p q
r q p
p p
⋅
= − +
⋅
A B
D C
E
r
q
p
31. A wooden wheel of radius R is made of two semicircular parts (see figure); The two
parts are held together by a ring made of a metal strip of cross sectional area S
and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so
that its temperature rises by ∆T and it just steps over the wheel. As it cools down to
surrounding temperature, it presses the semicircular parts together. If the
coefficient of linear expansion of the metal is α, and its Youngs’modulus is Y, the
force that one part of the wheel applies on the other part is :
(1) 2πSYα∆T (2) SYα∆T (3) πSYα ∆T (4) 2SYα ∆T
31. 4
Sol. If temperature increases by ∆T,
Increase in length L, ∆L = Lα∆T
∴
L
T
L
∆
= α∆
Let tension developed in the ring is T.
∴
T L
Y Y T
S L
∆
= = α∆
∴ T = SYα∆T
From FBD of one part of the wheel,
F = 2T
F
T T
Where, F is the force that one part of the wheel applies on the other part.
∴ F = 2SYα∆T
32. The figure shows an experimental plot for discharging of a
capacitor in an R-C circuit. The time constant τ of this circuit
lies between:
(1) 150 sec and 200 sec (2) 0 and 50 sec
(3) 50 sec and 100 sec (4) 100 sec and 150 sec
32. 4
Sol. For discharging of an RC circuit,
t / V V0e
− τ
=
So, when
V0 V
2
=
0 t /
0
V
V e
2
− τ
=
1 t t
ln
2 ln2
= − τ =
τ
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From graph when
V0 V
2
= , t = 100 s ∴
100
144.3 sec
ln2
τ = =
33. In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of
distance from the centre. The graph which would correspond to the above will be
R r
E
R r
E
R r
E
R r
E
(1) (2) (3) (4)
33. 3
Sol. inside
3
0
1 Q
E r
4 R
= πε
outside
3
0
1 Q
E r
4 r πε
∴
r
R
E
34. An electromagnetic wave in vacuum has the electric and magnetic fields E
and B
, which are always
perpendicular to each other. The direction of polarization is given by X
and that of wave propagation by
k
. Then :
(1) X
||B
and k || B×E
(2) X || E and k || E×B
(3) X || B and k || E×B
(4) X || E and k || B×E
34. 3
Sol. Direction of polarization is parallel to magnetic field,
∴ X ||B
and direction of wave propagation is parallel to E×B
∴ K ||
E×B
35. If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between
t = Os to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the
pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ‘b’as the constant of
proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:
(1)
0.693
b
(2) b (3)
1
b
(4)
2
b
35. 4
Sol. As retardation = bv
∴ retarding force = mbv
∴ net restoring torque when angular displacement is θ is given by
= – mg sinθ + mbv
∴ Iα = – mg sinθ + mbv
where, I = m
2
∴
2
2
d g bv
sin
dt
θ
= α = − θ +θ
mbv
v
mg
for small damping, the solution of the above differential equation will be
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bt
2
0e sin(wt )
−
∴ θ = θ + φ
∴ angular amplitude will be =
bt
2 .e
−
θ
According to question, in τ time (average life–time),
angular amplitude drops to
1
e
value of its original value (θ)
∴
6
0 2
0e
e
τ
θ −
= θ
6
1
2
τ
=
∴
2
b
τ =
36. Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4.
Then the number of spectral lines in the emission spectra will be
(1) 2 (2) 3 (3) 5 (4) 6
36. 4
Sol. Number of spectral lines from a state n to ground state is
n(n 1)
6
2
−
= = .
37. A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of
force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an
aluminium plate is placed near to the coil, it stops. This is due to :
(1) development of air current when the plate is placed.
(2) induction of electrical charge on the plate
(3) shielding of magnetic lines of force as aluminium is a paramagnetic material.
(4) electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.
37. 4
Sol. Oscillating coil produces time variable magnetic field. It cause eddy current in the aluminium plate which
causes anti–torque on the coil, due to which is stops.
38. The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The
value of ‘g’and ‘R'(radius of earth) are 10 m/s
2
and 6400km respectively. The required energy for this
work will be ;
(1) 6.4 x 10
11
Joules (2) 6.4 x 10
8
Joules (3) 6.4 x 10
9
Joules (4) 6.4 x 10
10
Joules
38. 4
Sol. To launch the spaceship out into free space, from energy conservation,
GMm
E 0
R
−
+ =
2
GMm GM
E mR mgR
R R
= =
=
= 6.4 x 10
10
J
39. Helium gas goes through a cycle ABCDA (consisting of two isochoric and
two isobaric lines) as shown in figure. Efficiency of this cycle is nearly:
(Assume the gas to be close to ideal gas)
(1) 15.4% (2) 9.1%
(3) 10.5% (4) 12.5%
2P0
P0
V0 2V0
A D
B C
39. 1
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Sol. Work done in complete cycle = Area under P–V graph
= P0V0
from A to B, heat given to the gas
= v 0 0 0
3 3 3
nC T n R T V P P V
2 2 2
∆ = ∆ = ∆ =
from B to C, heat given to the system
p
5
nC T n R T
2
= ∆ =
∆
0 0 0
5
(2P ) V 5P V
2
= ∆ =
from C to D and D to A, heat is rejected.
efficiency, η =
work done by gas
100
heat given to the gas
×
0 0
0 0 0 0
P V
15.4%
3
P V 5P V
2
η = =
+
40. In Young’s double slit experiment, one of the slit is wider than other, so that the amplitude of the light from
one slit is double of that from other slit. If Im be the maximum intensity, the resultant intensity I when they
interfere at phase difference φ is given by
(1)
m
I
(4 5cos )
9
+ φ (2)
m 2
I
1 2cos
3 2φ
+
(3)
m 2
I
1 4cos
5 2φ
+
(4)
m 2
I
1 8cos
9 2φ
+
40. 4
Sol. Let A1 = A0, A2 = 2A0
If amplitude of resultant wave is A then
2 2 2 A A1 A2 2A1A2 = + + cosφ
For maximum intensity,
2 2 2 Amax = A1 + A2 + 2A1A2
∴
2 2 2
1 2 1 2
2 2 2
max 1 2 1 2
A A A 2A A cos
A A A 2A A
+ + φ
=
+ +
2 2
0 0 0 0
2 2
0 0 0 0
A 4A 2(A )(2A )cos
A 4A 2(A )(2A )
+ + φ
=
+ +
2
m
I 5 4cos 1 8cos ( / 2)
I 9 9
+ φ + φ
= =
41. A liquid in a beaker has temperature θ(t) at time t and θ0 is temperature of surroundings, then according
to Newton’s law of cooling the correct graph between loge (θ – θ0) and t is
(1) (2) (3) (4)
41. 1
Sol. According to Newtons law of cooling.
0
d
( )
dt
θ
∝ − θ − θ
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0
d
k( )
dt
θ
= − θ − θ
0
d
k dt
θ
= −
θ − θ ln(θ – θ0) = –kt + c
Hence the plot of ln(θ – θ0) vs t should be a straight line with negative slope.
42. A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F0e
–bt
in the x
direction. Its speed v(t) is depicted by which of the following curves?
(1) (2)
(3) (4)
42. 3
Sol.
bt F F0e
−
=
F F0 bt
a e
m m
−
= =
dv F0 bt
e
dt m
−
=
t
bt
0
F
dv e dt
m
−
=
t
bt
0
F 1
v e
m b
− −
=
F bt
v e
mb
−
=
v = 0 at t = 0
and
F
v as t
mb
→ → ∞
So, velocity increases continuously and attains a maximum value of
F
v as t
mb
= → ∞ .
43. Two electric bulbs marked 25W – 220V and 100W – 220V are connected in series to a 440Vsupply.
Which of the bulbs will fuse?
(1) both (2) 100 W (3) 25 W (4) neither
43. 3
Sol. Resistances of both the bulbs are
2 2
1
1
V 220
R
P 25
= =
2 2
2
2
V 220
R
P 100
= =
Hence R1 > R2
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When connected in series, the voltages divide in them in the ratio of their resistances. The voltage of 440
V devides in such a way that voltage across 25 w bulb will be more than 220 V.
Hence 25 w bulb will fuse.
44. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference
applied across it. If the percentage errors in the measurement of the current and the voltage difference
are 3% each, then error in the value of resistance of the wire is
(1) 6% (2) zero (3) 1% (4) 3%
44. 1
Sol.
V
R
i
=
R V i
R V i
∆ ∆ ∆
= +
V
100 3
V
∆
× =
V
0.03
V
∆
=
Similarly,
i
0.03
i
∆
=
Hence
R
0.06
R
∆
=
So percentage error is
R
100 6%
R
∆
× =
45. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy
can throw the same stone up to will be
(1) 20 2 m (2) 10 m (3) 10 2 m (4) 20 m
45. 4
Sol. maximum vertical height =
2
u
10m
2g
=
Horizontal range of a projectile =
2
u sin2
g
θ
Range is maximum when θ = 45
0
Maximum horizontal range =
2
u
g
Hence maximum horizontal distance = 20 m.
46. This question has statement 1 and statement 2. Of the four choices given after the statements, choose
the one that best describes the two statements
Statement 1 : Davisson – germer experiment established the wave nature of electrons.
Statement 2 : If electrons have wave nature, they can interfere and show diffraction.
(1) Statement 1 is false, Statement 2 is true
(2) Statement 1 is true, Statement 2 is false
(3) Statement 1 is true, Statement 2 is the correct explanation for statement 1
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.
46. 3
Sol. Davisson – Germer experiment showed that electron beams can undergo diffraction when passed
through atomic crystals. This shows the wave nature of electrons as waves can exhibit interference and
diffraction.
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47. A thin liquid film formed between a U-shaped wire and a light slider supports a
weight of 1.5 x10
–2N (see figure). The length of the slider is 30 cm and its weight
negligible. The surface tension of the liquid film is
(1) 0.0125 Nm
–1
(2) 0.1 Nm
–1
(3) 0.05 Nm
–1
(4) 0.025 Nm
–1
w
FILM
47. 4
Sol. The force of surface tension acting on the
slider balances the force due to the weight.
F = 2T = w
2T(0.3) = 1.5 x 10
–2
T = 2.5 x 10
–2 N/m
F = 2Tl
w
48. A charge Q is uniformly distributed over the surface of non conducting disc of radius R. The disc rotates
about an axis perpendicular to its plane and passing through its centre with an angular velocity ω. As a
result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both
the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the
disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure
B
R
B
R
B
R
B
R
(1) (2) (3) (4)
48. 1
Sol. Consider ring like element of disc of radius r and thickness dr.
If σ is charge per unit area, then charge on the element
dq = σ(2πr dr)
current ‘i’ associated with rotating charge dq is
(dq)w
i w r dr
2
= = σ
π
Magnetic field dB at center due to element
0 0
i dr
dB
2r 2
µ µ σω
= =
R
0
net
0
B dB dr
2
µ σω
= =
0 R
2
µ σω
=
dr
r
0 2
net
Q
B Q R
2 R
µ ω
= = σπ π
So if Q and w are unchanged then
net
1
B
R
∝
Hence variation of Bnet with R should be a rectangular hyperbola as represented in (1).
49. Truth table for system of four NAND gates as shown in figure is
A
B
Y
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A B Y
0
0
1
1
0
1
0
1
0
1
1
0
A B Y
0
0
1
1
0
1
0
1
0
0
1
1
A B Y
0
0
1
1
0
1
0
1
1
1
0
0
A B Y
0
0
1
1
0
1
0
1
1
0
0
1
(1) (2) (3) (4)
49. 1
Sol.
A B y y1 y2 y
0 0 1 1 1 0
0 1 1 1 0 1
1 0 1 0 1 1
1 1 0 1 1 0
50. A radar has a power of 1 Kw and is operating at a frequency of 10 GHz. It is located on a mountain top of
height 500 m. The maximum distance upto which it can detect object located on the surface of the earth
(Radius of earth = 6.4 x 10
6 m) is
(1) 80 km (2) 16 km (3) 40 km (4) 64 km
50. 1
Sol. Maximum distance on earth where object can be
detected is d, then
2 2 2
(h + R) = d + R
2 2
d = h + 2Rh
since h << R, d
2
= 2hR
6
d = 2(500)(6.4 ×10 ) = 80 km
R
d h
R
51. Assume that a neutron breaks into a proton and an electron. The energy released during this process is
(Mass of neutron = 1.6725 x 10
–27
kg; mass of proton = 1.6725 x 10
–27
kg; mass of electron = 9 x 10
–31
kg)
(1) 0.73 MeV (2) 7.10 MeV (3) 6.30 MeV (4) 5.4 MeV
51. 1
Sol. m p e n ∆ = (m + m ) − m
= 9 x 10
–31
kg.
Energy released = (9 x 10
–31
kg)c
2
joules
31 8 2
13
9 10 (3 10 )
MeV
1.6 10
−
−
× × ×
=
×
= 0.73 MeV.
52. A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of
500 K It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same
exhaust (sink) temperature must be
(1) efficiency of Carnot engine cannot be made larger than 50%
(2) 1200 K (3) 750 K (4) 600 K
52. 3
Sol.
40 500 TS
100 500
−
= , TS = 300 K
600 T 300
100 T
−
= T = 750 K
53. This question has statement 1 and statement 2. Of the four choices given after the statements, choose
the one that best describes the two statements.
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If two springs S1 and S2 of force constants k1 and k2, respectively, are stretched by the same force, it is
found that more work is done on spring S1 than on spring S2.
Statement 1 : If stretched by the same amount, work done on S1, will be more than that on S2
Statement 2 : k1 < k2
(1) Statement 1 is false, Statement 2 is true
(2) Statement 1 is true, Statement 2 is false
(3) Statement 1 is true, Statement 2 is the correct explanation for statement 1
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.
53. 1
Sol. F = K1S1 = K2 S2
W1 = FS1, W2 = FS2
K1S1
2
> K2S2
2
S1 > S2
K1 < K2
W ∝ K
W1 < W2
54. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are
such that they make complete circles in the same time t. The ratio of their centripetal acceleration is
(1) m1r1 : m2r2 (2) m1 : m2 (3) r1 : r2 (4) 1 : 1
54. 3
Sol. a ∝ r
55. A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically
in water so that half of it is in water. The fundamental frequency of the air-column is now
(1) f (2)
f
2
(3)
3f
4
(4) 2f
55. 1
Sol. f0 =
v
2
fC =
v
2
56. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1cm
thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At
what distance (from lens) should object be shifted to be in sharp focus on film?
(1) 7.2 m (2) 2.4 m (3) 3.2 m (4) 5.6 m
56. 4
Sol. Case I: u = –240cm, v = 12, by Lens formula
1 7
f 80
=
Case II: v = 12 –
1 35
3 3
= (normal shift =
2 1
1
3 3
− = )
f =
7
80
u = 5.6
57. A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we
calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will
be given by (n is an integer)
(1)
2 2 2
1 2
2 2 2
1 2
(m m ) n h
2m m r
+
(2)
2 2
2
1 2
n h
2(m + m )r
(3)
2 2
2
1 2
2n h
(m + m )r
(4)
2 2
1 2
2
1 2
(m m )n h
2m m r
+
57. 4
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Sol. r1 =
2
1 2
m r
m + m
; r2 =
1
1 2
m r
m + m
(I1 + I2)ω =
nh
n
2
=
π
K.E =
1
2
(I1 + I2) ω
2
=
2 2
1 2
2
1 2
n (m m )
2m m r
+
58. A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30
and match with 29 divisions of the main scale. The angle of the prism from the above data
(1) 58.59
o
(2) 58.77
o
(3) 58.65
o
(4) 59
o
58. 3
Sol. L.C =
1
60
Total Reading = 585 +
9
60
= 58.65
59. This question has statement 1 and statement 2. Of the four choices given after the statements, choose
the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this
uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the
surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
Statement 1 : When a charge q is taken from the centre to the surface of the sphere, its potential energy
changes by
0
qp
3ε
Statement 2 : The electric field at a distance r(r < R) from the centre of the sphere is
0
r
3
ρ
ε
(1) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.
(2) Statement 1 is true, Statement 2 is false
(3) Statement 1 is false, Statement 2 is true
(4) Statement 1 is true, Statement 2 is the correct explanation for statement 1
59. 3
Sol.
3
0
1 4
E dA r
3
⋅ = ρ× πε
E =
0
r
3
ρ
ε
Statement 2 is correct
∆PE = (Vsur – Vcent)q =
2
0
q
R
6
− ρ
ε
Statement 1 is incorrect
60. Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a
constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp, rd and rα.
Which one of the following relations is correct?
(1)
p d
r r r α = = (2)
p d
r r r α = < (3)
d p
r r r α > > (4)
d p
r r r α = >
60. 2
Sol. r =
2mK
Bq
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r ∝
m
q
rα = rp < rd
61. Which among the following will be named as dibromidobis(ethylene diamine)chromium(III) bromide ?
(1) C ( )
3 3
r en Br
(2) C ( )
2 2
r en Br Br
(3) C ( ) 4
r en Br
−
(4) ( ) C 2 r en Br Br
61. 2
Sol. C ( )
2 2
r en Br Br
– dibromido bis (ethylene diamine)chromium(III) bromide
62. Which method of purification is represented by the following equation :
( ) ( ) ( ) ( ) ( )
523K 1700K
T 2 4 2
i s + 2I g →TiI g →Ti s + 2I g
(1) zone refining (2) cupellation (3) Poling (4) Van Arkel
62. 4
Sol. Van Arkel method
( ) ( ) ( )
523K
T 2 4
i s + 2I g →TiI g
( ) ( ) ( )
1700 K
T 4 2
iI g →Ti s + 2I g
63. Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius
of the lithium will be :
(1) 75 pm (2) 300 pm (3) 240 pm (4) 152 pm
63. 4
Sol. For BCC, 3a = 4r
3 351
r 152pm
4
×
= =
64. The molecule having smallest bond angle is :
(1) NCl3 (2) AsCl3 (3) SbCl3 (4) PCl3
64. 3
Sol. As the size of central atom increases lone pair bond pair repulsions increases so, bond angle
decreases
65. Which of the following compounds can be detected by Molisch’s test ?
(1) Nitro compounds (2) Sugars (3) Amines (4) Primary alcohols
65. 2
Sol. Molisch’s Test : when a drop or two of alcoholic solution of α–naphthol is added to sugar solution and
then conc. H2SO4 is added along the sides of test tube, formation of violet ring takes place at the junction
of two liquids.
66. The incorrect expression among the following is :
(1)
system
total
G
T
S
∆
= −
∆
(2) In isothermal process
f
reversible
i
V
w nRTln
V
= −
(3)
0 0 H T S
lnK
RT
∆ − ∆
= (4)
0 G /RT K e
−∆
=
66. 3
Sol. ∆G° = –RTln K and ∆ = ∆ − ∆
0 0 0 G H T S
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67. The density of a solution prepared by dissolving 120 g of urea (mol. Mass = 60 u ) in 1000g of water is
1.15 g/mL. The molarity of this solution is :
(1) 0.50 M (2) 1.78 M (3) 1.02 M (4) 2.05 M
67. 4
Sol. Total weight of solution = 1000 + 120 = 1120 g
Molarity =
120 1000
2.05M
60 1120 /1.15
× =
68. The species which can best serve as an initiator for the cationic polymerization is :
(1) LiAlH4 (2) HNO3 (3) AlCl3 (4) BuLi
68. 3
Sol. lewis acids can initiate the cationic polymerization.
69. Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?
(1) NaNO3 (2) KClO3 (3) CaCO3 (4) NH4NO3
69. 3
Sol. CaCO3 → 2
Basic Acidic
CaO + CO
70. The standard reduction potentials for Zn
2+
/ Zn, Ni
2+
/ Ni, and Fe
2+
/ Fe are –0.76, –0.23 and –0.44 V
respectively. The reaction X + Y
2+ → X
2+
+ Y will be spontaneous when :
(1) X = Ni, Y = Fe (2) X = Ni, Y = Zn (3) X = Fe, Y = Zn (4) X = Zn, Y = Ni
70. 4
Sol. Zn + Fe
+2 → Zn
+2
+ Fe
Fe + Ni
+2 → Fe
2+
+ Ni
Zn + Ni
2+ → Zn
+2
+ Ni
All these are spontaneous
71. According to Freundlich adsorption isotherm, which of the following is correct ?
(1)
x 0 P
m
∝ (2)
x 1
p
m
∝ (3)
x 1/ n
p
m
∝
(4) All the above are correct for different ranges of pressure
71. 4
Sol.
x 0 P
m
∝ is true at extremely high pressures
x 1
p
m
∝ ;
x 1/ n
p
m
∝ are true at low and moderate pressures
72. The equilibrium constant (KC) for the reaction N2(g) + O2(g) → 2NO(g) at temperature T is 4 x 10
–4
. The
value of KC for the reaction, NO(g) → ½ N2(g) + ½ O2(g) at the same temperature is :
(1) 0.02 (2) 2.5 x 10
2
(3) 4 x 10
–4
(4) 50.0
72. 4
Sol.
4 N2 O2 2NO KC 4 10
−
+ = ×
1
2 2 C
C
1 1 1
NO N O K
2 2 K
+ =
1
C
4
1
K 50
4 10
−
= =
×
73. The compressibility factor for a real gas at high pressure is :
(1) 1 + RT/pb (2) 1 (3) 1 + pb/RT (4) 1–pb/RT
73. 3
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Sol. At high pressure Z =
Pb
1
RT
+
74. Which one of the following statements is correct ?
(1) All amino acids except lysine are optically active
(2) All amino acids are optically active
(3) All amino acids except glycine are optically active
(4) All amino acids except glutamic acid are optically active
74. 3
Sol.
CH2
NH2
COOH
Glycine
75. Aspirin is known as :
(1) Acetyl salicylic acid (2) Phenyl salicylate
(3) Acetyl salicylate (4) Methyl salicylic acid
75. 1
Sol.
O
COOH
C
O
CH3
Aspirin
Acetyl salicylic acid
76. Ortho–Nitrophenol is less soluble in water than p– and m– Nitrophenols because :
(1) o–Nitrophenol is more volatile in steam than those of m – and p–isomers
(2) o–Nitrophenol shows Intramolecular H–bonding
(3) o–Nitrophenol shows Intermolecular H–bonding
(4) Melting point of o–Nitrophenol is lower than those of m–and p–isomers.
76. 2
Sol.
N
O
O
H
O
Intramolecular H–bonding decreases water solubility.
77. How many chiral compounds are possible on monochlorination of 2–methyl butane ?
(1) 8 (2) 2 (3) 4 (4) 6
77. 2
Sol. ( ) H3C − CH2 − CH CH3 − CH3
on monochlorination gives
( ) ( )
( )
2 2 3 3
I
Achiral
H C Cl − CH − CH CH − CH ( ) ( )
( )
3 3 3
II
Chiral
H C − CH Cl − CH CH − CH
H3C CH2 C
CH3
Cl
CH3
CH2 CH
CH2
H3C CH3
Cl
(IV)
chiral
(III)
Achiral
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78. Very pure hydrogen (99.9%) can be made by which of the following processes ?
(1) Reaction of methane with steam
(2) Mixing natural hydrocarbons of high molecular weight
(3) Electrolysis of water
(4) Reaction of salt like hydrides with water
78. 3
Sol. Highly pure hydrogen is obtained by the electrolysis of water.
79. The electrons identified by quantum numbers n and l :
(a) n = 4, l = 1 (b) n = 4, l = 0 (c) n = 3, l = 2 (d) n = 3 , l = 1
Can be placed in order of increasing energy as :
(1) (c) < (d) < (b) < (a) (2) (d) < (b) < (c) < (a) (3) (b) < (d) < (a) < (c) (4) (a) < (c) < (b) < (d)
79. 2
Sol. (a) (n + l) = 4 + 1 = 5 (b) (n + l) = 4 + 0 = 4 (c) (n + 1) = 3 + 2 = 5 (d) (n + 1) = 3 + 1 = 4
80. For a first order reaction, (A) → products, the concentration of A changes from 0.1 M to 0.025 M in 40
minutes. The rate of reaction when the concentration of A is 0.01 M is :
(1) 1.73 x 10
–5 M/ min (2) 3.47 x 10
–4 M/min
(3) 3.47 x 10
–5 M/min (4) 1.73 x 10
–4 M/min
80. 2
Sol. =
2.303 0.1
k log
40 0.025
=
0.693
k
20
For a F.O.R., rate=k[A]; rate =
0.693 2 4
10 3.47 10 M/min.
20
− −
× = ×
81. Iron exhibits + 2 and +3 oxidation states. Which of the following statements about iron is incorrect ?
(1) Ferrous oxide is more basic in nature than the ferric oxide.
(2) Ferrous compounds are relatively more ionic than the corresponding ferric compounds
(3) Ferrous compounds are less volatile than the corresponding ferric compounds.
(4) Ferrous compounds are more easily hydrolysed than the corresponding ferric compounds.
81. 4
Sol. FeO → More basic, more ionic, less volatile
82. The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of this acid is :
(1) 3 x 10
–1
(2) 1 x 10
–3
(3) 1 x 10
—5
(4) 1 x 10
–7
82. 3
Sol.
3 1 H Ka a
.C 10 K .10
+ − − = =
Ka = 10
–5
83. Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of
mono substituted alky halide ?
(1) Tertiary butyl chloride (2) Neopentane
(3) Isohexane (4) Neohexane
83. 2
Sol.
H3C C
CH3
CH3
CH3
H3C C
CH3
CH3
CH2 Cl
Neopentane
Mol. wt = 72u
only one compound
mono chlorination
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84. Kf
for water is 1.86K kg mol
–1
. If your automobile radiator holds 1.0 kg of water, how many grams of
ethylene glycol (C2H6O2) must you add to get the freezing point of the solution lowered to –2.8°C ?
(1) 72g (2) 93g (3) 39g (4) 27g
84. 2
Sol. Tf Kf ∆ = .m
wt 1000
2.8 1.86
62 1000
= × ×
Wt = 93g
85. What is DDT among the following :
(1) Greenhouse gas (2) A fertilizer
(3) Biodegradable pollutant (4) Non–biodegradable pollutant
85. 4
Sol. DDT – non–biodegradable pollutant.
86. The increasing order of the ionic radii of the given isoelectronic species is :
(1) Cl
–
, Ca
2+
, K
+
, S
2–
(2) S
2–
, Cl
–
, Ca
2+
, K
+
(3) Ca
2+
, K
+
, Cl
–
, S
2–
(4) K
+
, S
2–
, Ca
2+
, Cl
–
86. 3
Sol. For isoelectronic species, as the z/e decreases, ionic radius increases
87. 2–Hexyne gives trans–2–Hexene on treatment with :
(1) Pt/H2 (2) Li/NH3 (3) Pd/BaSO4 (4) LiAlH4
87. 2
Sol.
H3C CH2 CH2 C C CH3
C C
H7C3
H CH3
H
2-Hexyne
Li/NH3
Birch reduction
Trans-2-Hexene
88. Iodoform can be prepared from all except :
(1) Ethyl methyl ketone (2) Isopropyl alcohol
(3) 3–Methyl – 2– butanone (4) Isobutyl alcohol
88. 4
Sol. Iodoform is given by 1) methyl ketones R-CO-CH3
2) alcohols of the type R-CH(OH)CH3
where R can be hydrogen also
H3C C
O
C2H5
H3C CH
CH3
OH
H3C C
O
CH
CH3
CH3
Isopropyl alchol
ethyl methyl ketone
3-methyl 2-butanone
can give Iodoform Test
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H3C CH
CH3
CH2 OH
Isobutyl alcohol
can't give
89. In which of the following pairs the two species are not isostructural ?
(1)
2 CO3 3
and NO
− −
(2) PC 4 4
l and SiCl
+
(3) PF5 and BrF5 (4)
3 A 6 6
lF and SF
−
89. 3
Sol. (1)
2 2 CO3 & NO3 Sp
− − → hybridized, Trigonal planar
(2)
3 PC 4 4
l & SiCl Sp
+ → hybridized, Tetrahedral
(3) PF5 → Sp
3
d hybridized, Trigonal bipyramidal
BrF5 → Sp
3
d
2
hybridized, square pyramidal
(4)
3 3 2 A 6 6
lF &SF Sp d
− → hybridized, octahedral
90. In the given transformation, which of the following is the most appropriate reagent ?
CH
HO
CHCOCH3
CH
HO
CHCH2CH3
Reagent
(1)
( )
NH2NH2
,OH
−
(2) Zn − Hg/HCl (3) Na 3
,Liq.NH (4) NaBH4
90. 1
Sol. ZnHg/Hcl can’t be used due to the presence of acid sensitive group i.e. OH
CH
HO
CH C
O
CH3 CH
Cl
CH CH2 CH3
Zn-Hg/HCl
and Na/Liq. NH3 and NaBH4 convert – CO – into – CH(OH)–
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1. 2 2. 3 3. 3 4. 2
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9. 1 10. 4 11. 1 12. 1
13. 3 14. 4 15. 1 16. 3
17. 3 18. 4 19. 1 20. 3
21. 2 22. 1 23. 3 24. 2 or 4
25. 1 26. 2 27. 4 28. 2
29. 3 30. 2
31. 4 32. 4 33. 3 34. 3
35. 4 36. 4 37. 4 38. 4
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43. 3 44. 1 45. 4 46. 3
47. 4 48. 1 49. 1 50. 1
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55. 1 56. 4 57. 4 58. 3
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61. 2 62. 4 63. 4 64. 3
65. 2 66. 3 67. 4 68. 3
69. 3 70. 4 71. 4 72. 4
73. 3 74. 3 75. 1 76. 2
77. 2 78. 3 79. 2 80. 2
81. 4 82. 3 83. 2 84. 2
85. 4 86. 3 87. 2 88. 4
89. 3 90. 1