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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
In the following statements __________
(i) Relation is a special case of function.
(ii) Function is special case of relation.
(iii) Both relation & function are same.
©
In the following statements __________
(i) Relation is a special case of function.
(ii) Function is special case of relation.
(iii) Both relation & function are same.
©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If cos(θ1) + cos(θ2) + cos(θ3) + cos(θ4) = 4, then the value of cot(
θ1
2
)
+ cot(
θ2
2
)
+ cot(
θ3
2
)
+ cot(
θ4
2
)
=
©
If cos(θ1) + cos(θ2) + cos(θ3) + cos(θ4) = 4, then the value of cot(
θ1
2
)
+ cot(
θ2
2
)
+ cot(
θ3
2
)
+ cot(
θ4
2
)
=
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
The tangent to the curve y = e2x at the point (0,1) meets the x - axis at __________
©
The tangent to the curve y = e2x at the point (0,1) meets the x - axis at __________
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Which of the following is not a root of f(x) = x311x2+36x36 ?
©
Which of the following is not a root of f(x) = x311x2+36x36 ?
©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Let u and v be two vectors. Then |u - v| = ||u| - |v|| if and only if
©
Let u and v be two vectors. Then |u - v| = ||u| - |v|| if and only if
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
π2
0
x+sinx
1+cosx
dx=
©
π2
0
x+sinx
1+cosx
dx=
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
The directrix of the parabola 2y2+25x = 0 is __________
©
The directrix of the parabola 2y2+25x = 0 is __________
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If
x2+5x+7
(x3)3
=
A
(x3)
+
B
(x3)2
+
C
(x3)3
, then 9A3B+C=
©
If
x2+5x+7
(x3)3
=
A
(x3)
+
B
(x3)2
+
C
(x3)3
, then 9A3B+C=
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
3x
19x
dx=
©
3x
19x
dx=
©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
The point to which the origin should be shifted so that the equation y26y4x+13 = 0 will not contain term in y and the constant term, is __________
©
The point to which the origin should be shifted so that the equation y26y4x+13 = 0 will not contain term in y and the constant term, is __________
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If on an average 9 mountain climbers out of 10 return safely, what is the probability that with 5 climbers out, at least 4 will return safely ?
©
If on an average 9 mountain climbers out of 10 return safely, what is the probability that with 5 climbers out, at least 4 will return safely ?
©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If S1 and S2 are two straight lines such that the reflection of S1 in S2 and the reflection of S2 in S1 coincide, the angle between S1 and S2 is equal to
©
If S1 and S2 are two straight lines such that the reflection of S1 in S2 and the reflection of S2 in S1 coincide, the angle between S1 and S2 is equal to
©
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The equation of the asymptotes of the hyperbola 2x2+5xy+2y211x7y4 = 0 is
©
The equation of the asymptotes of the hyperbola 2x2+5xy+2y211x7y4 = 0 is
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If f:RR is defined as f(x) = x[x]+3, xR, then f is
©
If f:RR is defined as f(x) = x[x]+3, xR, then f is
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
If the line y = 2x+c touches the curve x2+4y2 = 4, then c2=
©
If the line y = 2x+c touches the curve x2+4y2 = 4, then c2=
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
The equation of a circle which touches the x - axis and whose centre is (1,2) is __________
©
The equation of a circle which touches the x - axis and whose centre is (1,2) is __________
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Find the general solution of 3 sin4(θ)+cos4(θ) = 1
©
Find the general solution of 3 sin4(θ)+cos4(θ) = 1
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Calculate the area enclosed by the curves x2 = 2y, x2 = y
©
Calculate the area enclosed by the curves x2 = 2y, x2 = y
©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Eliminating a and b from the relation y = alogx+b, we get __________
©
Eliminating a and b from the relation y = alogx+b, we get __________
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If α,β,γ are the roots of x32x2+3x4 = 0 , then find αβ(α+β)
©
If α,β,γ are the roots of x32x2+3x4 = 0 , then find αβ(α+β)
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
Three dice are thrown. Given that they have a sum of 8, the probability that one of them is a four is __________
©
Three dice are thrown. Given that they have a sum of 8, the probability that one of them is a four is __________
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
The area of the parallelogram, whose diagonals are 2
^
i
^
j
+
^
k
and
^
i
+3
^
j
^
k
, is equal to __________ sq. units.
©
The area of the parallelogram, whose diagonals are 2
^
i
^
j
+
^
k
and
^
i
+3
^
j
^
k
, is equal to __________ sq. units.
©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
The general solution of the differential equation tan(y) dx + sec2(y)tan(x) dy = 0 is
©
The general solution of the differential equation tan(y) dx + sec2(y)tan(x) dy = 0 is
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
If P(3,2,4), Q(9,8,10) and R(5,4,6) are collinear, then the ratio in which R divides PQ is __________
©
If P(3,2,4), Q(9,8,10) and R(5,4,6) are collinear, then the ratio in which R divides PQ is __________
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
1+tanh(x2)
1tanh(x2)
=

©
1+tanh(x2)
1tanh(x2)
=

©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If a line drawn from a fixed point M(a,b) cuts the circle x2+y2 = k2 at C and D, then MC×MD is equal to __________
©
If a line drawn from a fixed point M(a,b) cuts the circle x2+y2 = k2 at C and D, then MC×MD is equal to __________
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
The number of ways of choosing a committee from four men and six women so that the committee includes atleast two men and exactly twice as many women as men is
©
The number of ways of choosing a committee from four men and six women so that the committee includes atleast two men and exactly twice as many women as men is
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
The equation of the line passing through the point of intersection of lines 2xy+2 = 0 and x+y+4 = 0 and the point (5,2) is __________
©
The equation of the line passing through the point of intersection of lines 2xy+2 = 0 and x+y+4 = 0 and the point (5,2) is __________
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
If f(x) = logx2(logx), then f(e) is equal to __________
©
If f(x) = logx2(logx), then f(e) is equal to __________
©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
The radius of the circle 2x2+2y23x+2y1 = 0 is _________ units.
©
The radius of the circle 2x2+2y23x+2y1 = 0 is _________ units.
©
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
If the value of
π2
0
sin4(x).cos2(x)
dx =
π
32
, then the value of
π2
0
cos4(x).sin2(x)
dx=
©
If the value of
π2
0
sin4(x).cos2(x)
dx =
π
32
, then the value of
π2
0
cos4(x).sin2(x)
dx=
©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
If the mean and standard deviation of a binomial distribution are 20 and 4 respectively, then the number of trials is _________
©
If the mean and standard deviation of a binomial distribution are 20 and 4 respectively, then the number of trials is _________
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
The angle between the tangents drawn from the point (1,4) to the parabola y2=4x is
©
The angle between the tangents drawn from the point (1,4) to the parabola y2=4x is
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If y =
(axb)
(x1)(x4)
has a turning point P(2,1), then the values of a and b are
©
If y =
(axb)
(x1)(x4)
has a turning point P(2,1), then the values of a and b are
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
If the bi - quadratic equation f(x) = x4+2x316x222x+7 = 0 has 2+3 as one of its roots, then which of the following is not a root of f(x) ?
©
If the bi - quadratic equation f(x) = x4+2x316x222x+7 = 0 has 2+3 as one of its roots, then which of the following is not a root of f(x) ?
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
If f:RR is defined as f(x) = (2020x2019)12019, xR, find (fofofof) (
2019
2020
)

©
If f:RR is defined as f(x) = (2020x2019)12019, xR, find (fofofof) (
2019
2020
)

©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
If f(x) = asinx+bcosx, f(0) = 4, f(0) = 3 and f(
π
2
)
= 5, then f(x)=
©
If f(x) = asinx+bcosx, f(0) = 4, f(0) = 3 and f(
π
2
)
= 5, then f(x)=
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
From 5 consonants and 5 vowels, how many words can be formed using 3 consonants and 2 vowels ?
©
From 5 consonants and 5 vowels, how many words can be formed using 3 consonants and 2 vowels ?
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The length of the perpendicular from (1,2) to the line 12x+5y+63 = 0 is __________
©
The length of the perpendicular from (1,2) to the line 12x+5y+63 = 0 is __________
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
If one end of the diameter of x2+y22x6y15 = 0 is (4,1), then the co-ordinates of the other end is
©
If one end of the diameter of x2+y22x6y15 = 0 is (4,1), then the co-ordinates of the other end is
©
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If the lengths of the sides of a triangle are 15, 20, 25 units. Find the circumradius of the triangle.
©
If the lengths of the sides of a triangle are 15, 20, 25 units. Find the circumradius of the triangle.
©
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
If the line y=mx is one of the bisectors of x2+4xyy2 = 0 ; then value of 2m=
©
If the line y=mx is one of the bisectors of x2+4xyy2 = 0 ; then value of 2m=
©
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
Number of unit vectors of the form a
^
i
+b
^
j
+c
^
k
, where a,b,c W is __________
©
Number of unit vectors of the form a
^
i
+b
^
j
+c
^
k
, where a,b,c W is __________
©
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
Statement-I: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point, are always perpendicular to each other.
Statement-II : Angle bisectors of two intersecting lines are always perpendicular to each other.
©
Statement-I: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point, are always perpendicular to each other.
Statement-II : Angle bisectors of two intersecting lines are always perpendicular to each other.
©
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Let R = (55+11)2n+1 and f=R[R], where [x] denotes the greatest integer less than or equal to x, then Rf=
©
Let R = (55+11)2n+1 and f=R[R], where [x] denotes the greatest integer less than or equal to x, then Rf=
©
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
If a = 1+2+4+ upto n terms, b = 1+3+9+ upto n terms and c = 1+5+25+ upto n terms, then Δ = |
a2b4c
222
2n3n5n
|
=

©
If a = 1+2+4+ upto n terms, b = 1+3+9+ upto n terms and c = 1+5+25+ upto n terms, then Δ = |
a2b4c
222
2n3n5n
|
=

©
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If the term independent of x in the expansion of (x
k
x2
)
10
is 405, then k=
©
If the term independent of x in the expansion of (x
k
x2
)
10
is 405, then k=
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
lim
x
(1+
2
x
)
3x
=

©
lim
x
(1+
2
x
)
3x
=

©
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The angle between the pair of tangents drawn from (1,3) to the circle x2+y22x+4y11 = 0
©
The angle between the pair of tangents drawn from (1,3) to the circle x2+y22x+4y11 = 0
©
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
Find the number of marked points on the plane, if when connected pairwise by line segments, the total number of line segments formed is 15.
©
Find the number of marked points on the plane, if when connected pairwise by line segments, the total number of line segments formed is 15.
©
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
(
1+cos(3θ)+isin(3θ)
1+cos(3θ)isin(3θ)
)
20
=
?
©
(
1+cos(3θ)+isin(3θ)
1+cos(3θ)isin(3θ)
)
20
=
?
©
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The angle between the lines with direction ratios (2,2,1) and (1,2,2) is __________
©
The angle between the lines with direction ratios (2,2,1) and (1,2,2) is __________
©
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
If f is a continuous real valued function, then the range of the function is __________
©
If f is a continuous real valued function, then the range of the function is __________
©
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If cosecθ+cotθ =
1
3
, then θ lies in the
©
If cosecθ+cotθ =
1
3
, then θ lies in the
©
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
If lx2+3xy2y25x+5y+k = 0 represents a pair of perpendicular lines, then
©
If lx2+3xy2y25x+5y+k = 0 represents a pair of perpendicular lines, then
©
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
If the curved surface area of right circular cylinder inscribed in a sphere of radius 22 cm is maximum then height of the cylinder will be
©
If the curved surface area of right circular cylinder inscribed in a sphere of radius 22 cm is maximum then height of the cylinder will be
©
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The index of the power of x occurring in the 5th term from the end in the expansion of (
x3
2
2
x2
)
12
is
©
The index of the power of x occurring in the 5th term from the end in the expansion of (
x3
2
2
x2
)
12
is
©
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If
d
dx
(
x4+x2+1
x2+x+1
)
= ax+b, then ab=
©
If
d
dx
(
x4+x2+1
x2+x+1
)
= ax+b, then ab=
©
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
xn1
x2n+4
dx=
©
xn1
x2n+4
dx=
©
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
a
a
ax
a+x
dx=
©
a
a
ax
a+x
dx=
©
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
A bag contains 5 blue and an unknown number x of red balls. Two balls are drawn at random. If the probability of both of them being blue is
5
14
, then the value of x is equal to
©
A bag contains 5 blue and an unknown number x of red balls. Two balls are drawn at random. If the probability of both of them being blue is
5
14
, then the value of x is equal to
©
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
For which value of nN, n! has 13 trailing zeros ?
©
For which value of nN, n! has 13 trailing zeros ?
©
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Evaluate A2+2I if A=[
10
12
]

©
Evaluate A2+2I if A=[
10
12
]

©
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
The difference between the greatest and least values of the function f(x) = x + sin2x on [
π
2
,
π
2
]
is
©
The difference between the greatest and least values of the function f(x) = x + sin2x on [
π
2
,
π
2
]
is
©
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
If y = Tan1(
4x
1+5x2
)
+ Tan1(
2+3x
32x
)
, then
dy
dx
=

©
If y = Tan1(
4x
1+5x2
)
+ Tan1(
2+3x
32x
)
, then
dy
dx
=

©
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
Two point A and B with co-ordinates (1,1) and (2,3) respectively are given. Then the locus of a point P so that the area of ΔPAB is 9 sq.units is given by ___________
©
Two point A and B with co-ordinates (1,1) and (2,3) respectively are given. Then the locus of a point P so that the area of ΔPAB is 9 sq.units is given by ___________
©
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The scalar product of the vector
a
=
^
i
+
^
j
+
^
k
with a unit vector along the sum of the vectors
b
= 2
^
i
+4
^
j
5
^
k
and
c
= λ
^
i
+2
^
j
+3
^
k
is equal to one. Then, λ=
©
The scalar product of the vector
a
=
^
i
+
^
j
+
^
k
with a unit vector along the sum of the vectors
b
= 2
^
i
+4
^
j
5
^
k
and
c
= λ
^
i
+2
^
j
+3
^
k
is equal to one. Then, λ=
©
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
1+tan2x
1tan2x
dx=
©
1+tan2x
1tan2x
dx=
©
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
If (a1,b1,c1), (a2,b2,c2) are the direction cosines of two lines making an angle θ with each other, then cosθ=
©
If (a1,b1,c1), (a2,b2,c2) are the direction cosines of two lines making an angle θ with each other, then cosθ=
©
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Solve ix23x2i = 0
©
Solve ix23x2i = 0
©
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
Find the least positive value of k, if the range of 15, 14, k, 25, 30, 35 is 23
©
Find the least positive value of k, if the range of 15, 14, k, 25, 30, 35 is 23
©
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
If [x] represents the greatest integer not greater than x, then [(1+
1
100000
)
100000
]
=

©
If [x] represents the greatest integer not greater than x, then [(1+
1
100000
)
100000
]
=

©
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
The range of the observations 20, 28, 40, 12, 30, 15, 50 is __________
©
The range of the observations 20, 28, 40, 12, 30, 15, 50 is __________
©
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
In ΔABC, A=30°+C and R(3+1)r = 0 where r is the inradius and R is the circumradius, then
©
In ΔABC, A=30°+C and R(3+1)r = 0 where r is the inradius and R is the circumradius, then
©
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
Find the solution of the differential equation given below
dy
dx
+y.cosec2(x)
= cosec2(x).cot(x)
©
Find the solution of the differential equation given below
dy
dx
+y.cosec2(x)
= cosec2(x).cot(x)
©
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
Find the rank of the matrix [
141
230
012
]

©
Find the rank of the matrix [
141
230
012
]

©
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter 3. Then, what is the probability that no accidents occur today ?
©
Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter 3. Then, what is the probability that no accidents occur today ?
©
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
The magnetic flux through a circuit of resistance R changes by an amount ΔØ in time Δt. Then the total quantity of electric charge Q, which is passing during this time through any point of the circuit is given by __________
©
The magnetic flux through a circuit of resistance R changes by an amount ΔØ in time Δt. Then the total quantity of electric charge Q, which is passing during this time through any point of the circuit is given by __________
©
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
Which of the following is not a unit of time ?
©
Which of the following is not a unit of time ?
©
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A thin rod of length L is magnetized and has magnetic moment M. The rod is then bent in a semicircular arc. The magnetic moment in the new shape is
©
A thin rod of length L is magnetized and has magnetic moment M. The rod is then bent in a semicircular arc. The magnetic moment in the new shape is
©
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
Two wires of equal diameters, lengths l1, l2 and having resistivities S1, S2 respectively are joined in series. The equivalent resistivity of the combination is ____________
©
Two wires of equal diameters, lengths l1, l2 and having resistivities S1, S2 respectively are joined in series. The equivalent resistivity of the combination is ____________
©
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
The first law of thermodynamics confirms the law of__________
©
The first law of thermodynamics confirms the law of__________
©
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
In an A.C. circuit, the current flowing is I = 5sin(100t
π
2
)
A and the potential difference is e = 200sin(100t). The power consumption is equal to ___________
©
In an A.C. circuit, the current flowing is I = 5sin(100t
π
2
)
A and the potential difference is e = 200sin(100t). The power consumption is equal to ___________
©
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
For television broadcasting, the frequency employed is normally in range__________
©
For television broadcasting, the frequency employed is normally in range__________
©
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
The displacement of a particle moving with uniform acceleration in time t is given by S=30t+5t2, its initial velocity is __________
©
The displacement of a particle moving with uniform acceleration in time t is given by S=30t+5t2, its initial velocity is __________
©
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A uniform chain of mass M and length L is lying on a smooth horizontal table, with half of its length hanging down. The work done is pulling the entire chain up the table is
©
A uniform chain of mass M and length L is lying on a smooth horizontal table, with half of its length hanging down. The work done is pulling the entire chain up the table is
©
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
When two identical capacitors are charged individually to different potentials and then connected in parallel, after disconnecting from the source, ___________
©
When two identical capacitors are charged individually to different potentials and then connected in parallel, after disconnecting from the source, ___________
©
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
The acceleration at the end of 2s, of a particle whose motion is represented by the equation S = 4t38t2+5t+4 is __________
©
The acceleration at the end of 2s, of a particle whose motion is represented by the equation S = 4t38t2+5t+4 is __________
©
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
232
90
Th
emits 6α and 4β particles and gets converted into a lead. The mass number and atomic number of lead is __________
©
232
90
Th
emits 6α and 4β particles and gets converted into a lead. The mass number and atomic number of lead is __________
©
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
Magnetic field dB to a current element at any point on its axis is __________
©
Magnetic field dB to a current element at any point on its axis is __________
©
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.
©
If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.
©
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
A wire of length 1 m and radius 2 mm is vertically clamped. The lower end is twisted through an angle of 45°. The angle of shear is ___________
©
A wire of length 1 m and radius 2 mm is vertically clamped. The lower end is twisted through an angle of 45°. The angle of shear is ___________
©
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
Which among the following has dimensions of charge ?
©
Which among the following has dimensions of charge ?
©
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A coil of area 10 m2 is placed in a uniform magnetic field of 0.3 k lb.m2, with its plane perpendicular to the field. The coil rotates at a uniform rate to complete the revolution in 8 s, find the average e.m.f. in the coil during intervals when the coil rotates from
i. 0° to 90° position
ii. 90° to 180° position
iii. 180° to 270° position
iv. 270° to 360° position
©
A coil of area 10 m2 is placed in a uniform magnetic field of 0.3 k lb.m2, with its plane perpendicular to the field. The coil rotates at a uniform rate to complete the revolution in 8 s, find the average e.m.f. in the coil during intervals when the coil rotates from
i. 0° to 90° position
ii. 90° to 180° position
iii. 180° to 270° position
iv. 270° to 360° position
©
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
The time taken by a force of 2 N to produce a change of momentum of 0.4 kg.m.s1 in a body is __________
©
The time taken by a force of 2 N to produce a change of momentum of 0.4 kg.m.s1 in a body is __________
©
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
When will a body of mass 20 kg moving at 15 m.s1, subjected to a retarding force of 100 N, come to rest ?
©
When will a body of mass 20 kg moving at 15 m.s1, subjected to a retarding force of 100 N, come to rest ?
©
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
The photoelectric threshold for a certain metal surface is 360 Å. If the metal surface is irradiated by a wavelength of 1100 Å, the kinetic energy of the emitted photoelectrons is
©
The photoelectric threshold for a certain metal surface is 360 Å. If the metal surface is irradiated by a wavelength of 1100 Å, the kinetic energy of the emitted photoelectrons is
©
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
A closed organ pipe and an open organ pipe of same length produce 2 beats/sec when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be
©
A closed organ pipe and an open organ pipe of same length produce 2 beats/sec when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be
©
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
The number of electric lines that emerge from a finite charge +q is __________
©
The number of electric lines that emerge from a finite charge +q is __________
©
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
In the following circuit, the equivalent resistance between A and B is
 

 
In the following circuit, the equivalent resistance between A and B is
 
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
An electron having charge 1.6×1019 C and mass 9×1031 kg is moving with 4×106 m.s1 speed in a magnetic field 2×101 T in a circular orbit. The force acting on electron and the radius of the circular orbit is __________
©
An electron having charge 1.6×1019 C and mass 9×1031 kg is moving with 4×106 m.s1 speed in a magnetic field 2×101 T in a circular orbit. The force acting on electron and the radius of the circular orbit is __________
©
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
The colour code for a resistance of 22 Ω±5% is __________
©
The colour code for a resistance of 22 Ω±5% is __________
©
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Kinetic energy of rotation of a flywheel of radius 2 m, mass 8 kg and angular speed 4 rad.s1 about an axis perpendicular to its plane and passing through its center is
©
Kinetic energy of rotation of a flywheel of radius 2 m, mass 8 kg and angular speed 4 rad.s1 about an axis perpendicular to its plane and passing through its center is
©
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
What is the pressure required to reduce the given volume of water by 1% ?
(Bulk modulus (K) = 2×108 N.m2)
©
What is the pressure required to reduce the given volume of water by 1% ?
(Bulk modulus (K) = 2×108 N.m2)
©
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A particle executes simple harmonic motion between x = A and x = +A. If it takes a time T1 to go from x = 0 to x =
A
2
and T2 to go from x =
A
2
to x = A. Then
©
A particle executes simple harmonic motion between x = A and x = +A. If it takes a time T1 to go from x = 0 to x =
A
2
and T2 to go from x =
A
2
to x = A. Then
©
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A mixture of Yellow light of wavelength 580 nm and blue light of wave length 450 nm is incident normally on an air film of thickness 2.9×104 mm. The colour of reflected light is
©
A mixture of Yellow light of wavelength 580 nm and blue light of wave length 450 nm is incident normally on an air film of thickness 2.9×104 mm. The colour of reflected light is
©
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in figure. The change in internal energy of the gas during the transition is
 

 
One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in figure. The change in internal energy of the gas during the transition is
 
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
W K Roentgen discovered __________
©
W K Roentgen discovered __________
©
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
A source is stationary and the observer is in motion along a line joining the source and the observer. If the frequency heard by the observer is 1% higher than the true frequency, the ratio of velocity of the observer and that of sound in air is :
©
A source is stationary and the observer is in motion along a line joining the source and the observer. If the frequency heard by the observer is 1% higher than the true frequency, the ratio of velocity of the observer and that of sound in air is :
©
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
Four projectiles are fired with the same velocities at angles 25°, 40°, 55° and 70° with the horizontal. The range of projectile will be largest for the one projected at angle __________
©
Four projectiles are fired with the same velocities at angles 25°, 40°, 55° and 70° with the horizontal. The range of projectile will be largest for the one projected at angle __________
©
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
A train is moving towards north. At one place it turns towards north-east. Here, we observe that :
©
A train is moving towards north. At one place it turns towards north-east. Here, we observe that :
©
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Minimum excitation potential of Bohr's first orbit of Hydrogen atom is__________
©
Minimum excitation potential of Bohr's first orbit of Hydrogen atom is__________
©
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
A system goes from A to B via two processes I and II as shown in the figure. If ΔU1 and ΔU2 are the changes in internal energies in the processes I and II respectively, then
 

 
A system goes from A to B via two processes I and II as shown in the figure. If ΔU1 and ΔU2 are the changes in internal energies in the processes I and II respectively, then
 
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be ___________
©
A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be ___________
©
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
Two thin circular discs A and B of radii 2 cm and 4 cm are in a liquid at the same depth. TA is the thrust on A and TB thrust on B. Then TA:TB =
©
Two thin circular discs A and B of radii 2 cm and 4 cm are in a liquid at the same depth. TA is the thrust on A and TB thrust on B. Then TA:TB =
©
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
For the reaction, 2H2(g) + O2(g)2H2O(g). At 300 K, ΔG and ΔH of water are 228.4 kJ.mol1 and 241.60 kJ.mol1 respectively. Then, calculate the value of change in entropy for the given reaction.
©
For the reaction, 2H2(g) + O2(g)2H2O(g). At 300 K, ΔG and ΔH of water are 228.4 kJ.mol1 and 241.60 kJ.mol1 respectively. Then, calculate the value of change in entropy for the given reaction.
©
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
Which of the following represents the structure of inorganic benzene ?
©
Which of the following represents the structure of inorganic benzene ?
©
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
Which of the following conclusions could not be derived from Rutherford's α -particle scattering experiment ?
©
Which of the following conclusions could not be derived from Rutherford's α -particle scattering experiment ?
©
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
Which of the following metal ions is colorless ?
©
Which of the following metal ions is colorless ?
©
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
Which of the following arrangements is correct regarding the three types of radii of an atom ?
©
Which of the following arrangements is correct regarding the three types of radii of an atom ?
©
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
Which of the following statements is not true for hydrogen ?
1) It exists as a diatomic molecule
2) It has one electron in the outermost shell
3) It can lose an electron to form a cation which can freely exist
4) It cannot form ionic compounds
©
Which of the following statements is not true for hydrogen ?
1) It exists as a diatomic molecule
2) It has one electron in the outermost shell
3) It can lose an electron to form a cation which can freely exist
4) It cannot form ionic compounds
©
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
When an iron rod is subjected towards an atmosphere having very high content of moisture, which of the process is predominant ?
©
When an iron rod is subjected towards an atmosphere having very high content of moisture, which of the process is predominant ?
©
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The correct statement among the following, regarding defects in solids is
1) Frenkel defect is favored by small difference in the sizes of cation and anion
2) Frenkel defect is a metal excess defect
3) Trapping of electron in the lattice leads to formation of F-CENTRE
4) Schottky defect has no effect on the physical property of solids
©
The correct statement among the following, regarding defects in solids is
1) Frenkel defect is favored by small difference in the sizes of cation and anion
2) Frenkel defect is a metal excess defect
3) Trapping of electron in the lattice leads to formation of F-CENTRE
4) Schottky defect has no effect on the physical property of solids
©
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
Which of the following metal is used as a catalyst in Haber's process of ammonia synthesis ?
©
Which of the following metal is used as a catalyst in Haber's process of ammonia synthesis ?
©
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
Find A in the reaction "ROH+A → Schiff's Base "
©
Find A in the reaction "ROH+A → Schiff's Base "
©
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
Match the following elements, given as hints to their first, second ionisation enthalpies and electron gain enthalpies.
Elements
ΔH1ΔH2ΔegH
i. Most reactive non metal
A.419305148
ii. Most reactive metal
B.16813374328
iii. Least reactive element
C.738145140
iv. Metal forming binary halide
D.23725251+48

©
Match the following elements, given as hints to their first, second ionisation enthalpies and electron gain enthalpies.
Elements
ΔH1ΔH2ΔegH
i. Most reactive non metal
A.419305148
ii. Most reactive metal
B.16813374328
iii. Least reactive element
C.738145140
iv. Metal forming binary halide
D.23725251+48

©
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
One mole of an organic compound A with the formula C3H8O reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. Then the compound A is
©
One mole of an organic compound A with the formula C3H8O reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. Then the compound A is
©
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Calculate the mass of AgCl precipitated, when 25 ml of 35% solution of AgNO3 and 25 ml of 11.6% solution of NaCl are mixed is __________
©
Calculate the mass of AgCl precipitated, when 25 ml of 35% solution of AgNO3 and 25 ml of 11.6% solution of NaCl are mixed is __________
©
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
The pressure exerted by a mixture of 3.2 g of methane and 4.4 g of CO2 contained in a 9 dm3 flask at 27°C is __________
©
The pressure exerted by a mixture of 3.2 g of methane and 4.4 g of CO2 contained in a 9 dm3 flask at 27°C is __________
©
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
The increasing order of acidic strength among the following compounds
I. Benzoic acid
II. 4 - Nitrobenzoic acid
III. 3,4 - Dinitrobenzoic acid
IV. 4 - Methoxybenzoic acid
©
The increasing order of acidic strength among the following compounds
I. Benzoic acid
II. 4 - Nitrobenzoic acid
III. 3,4 - Dinitrobenzoic acid
IV. 4 - Methoxybenzoic acid
©
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
O3 + 2KI(aq)→ ?
©
O3 + 2KI(aq)→ ?
©
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
During electro-osmosis of Fe(OH)3 sol, which of the following occurs ?
©
During electro-osmosis of Fe(OH)3 sol, which of the following occurs ?
©
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
The geometry of SF6 molecule is __________
©
The geometry of SF6 molecule is __________
©
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
Which among the following is a bactericidal antibiotic ?
©
Which among the following is a bactericidal antibiotic ?
©
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
The rate constant is same for 3 reactions of order I, II and III respectively, the unit of concentration being in moles / litre. If the concentration of reactant is unity, rates of reaction R1, R2, R3 will be __________
©
The rate constant is same for 3 reactions of order I, II and III respectively, the unit of concentration being in moles / litre. If the concentration of reactant is unity, rates of reaction R1, R2, R3 will be __________
©
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
When soap is dissolved in hard water, it's cleaning ability comes down. This is due to the formation of :
©
When soap is dissolved in hard water, it's cleaning ability comes down. This is due to the formation of :
©
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
Find the non-semiconductor element among the following.
©
Find the non-semiconductor element among the following.
©
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
10 g of a gas at STP occupies a volume of 2 L. At what temperature will the volume be doubled, if pressure & amount of gas remain constant
©
10 g of a gas at STP occupies a volume of 2 L. At what temperature will the volume be doubled, if pressure & amount of gas remain constant
©
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Increasing order of boiling points in the following compounds is :
 

Increasing order of boiling points in the following compounds is :

 
 
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
Predict the correct order of rate of diffusion of the following molecules.
©
Predict the correct order of rate of diffusion of the following molecules.
©
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt

For a first order reaction A55B2, the concentrations vs time plot is as shown. The half-life of the reaction is

For a first order reaction A55B2, the concentrations vs time plot is as shown. The half-life of the reaction is
 
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Calculate the mass percentage of 3 g of solute A dissolved in 18 g of water ?
©
Calculate the mass percentage of 3 g of solute A dissolved in 18 g of water ?
©
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Which of the following statements is true ?
1) 200ml of 0.2M NaOH has same number of moles of solute as 1000ml of 1M NaOH
2) 200ml of 1M NaOH has same number of moles as 1000ml of 0.2M NaOH
3) 100ml of 0.2M NaOH has same number of moles as 1000ml of 1M NaOH
4) 2000ml of 0.2M NaOH has same number of moles as 1000ml of 1M NaOH
©
Which of the following statements is true ?
1) 200ml of 0.2M NaOH has same number of moles of solute as 1000ml of 1M NaOH
2) 200ml of 1M NaOH has same number of moles as 1000ml of 0.2M NaOH
3) 100ml of 0.2M NaOH has same number of moles as 1000ml of 1M NaOH
4) 2000ml of 0.2M NaOH has same number of moles as 1000ml of 1M NaOH
©
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Which of the following metals cannot be obtained by auto-reduction of their compounds ?
©
Which of the following metals cannot be obtained by auto-reduction of their compounds ?
©
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
Which of the following is called "Lunar Caustic" ?
©
Which of the following is called "Lunar Caustic" ?
©
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Which of the following statements is true ?
1) Tertiary amines react with acid chlorides
2) N - Ethyl benzene sulphonamide is soluble in alkali
3) N, N - Diethyl benzene sulphonamide is soluble in alkali
4) Tertiary amines react with Hindberg's reagent
©
Which of the following statements is true ?
1) Tertiary amines react with acid chlorides
2) N - Ethyl benzene sulphonamide is soluble in alkali
3) N, N - Diethyl benzene sulphonamide is soluble in alkali
4) Tertiary amines react with Hindberg's reagent
©
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
The total number of σ and π bonds present in the following compound respectively are
 

 
The total number of σ and π bonds present in the following compound respectively are
 
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Which among the following is a correct statement based on Heisenberg’s uncertainty principle ?
1) It is impossible to determine exact position and exact momentum of an electron simultaneously
2) It is applicable to even macroscopic objects
3) It is possible to determine the exact position and momentum of an electron simultaneously
4) It is impossible to determine the exact position and momentum of macroscopic object simultaneously
©
Which among the following is a correct statement based on Heisenberg’s uncertainty principle ?
1) It is impossible to determine exact position and exact momentum of an electron simultaneously
2) It is applicable to even macroscopic objects
3) It is possible to determine the exact position and momentum of an electron simultaneously
4) It is impossible to determine the exact position and momentum of macroscopic object simultaneously
©
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
The product Q and R in the following reactions respectively are
 

 
The product Q and R in the following reactions respectively are
 
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
The fraction of voids occupied in inverse spinel compounds are __________
©
The fraction of voids occupied in inverse spinel compounds are __________
©
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Which among the following oxides is the most basic ?
©
Which among the following oxides is the most basic ?
©
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Total number of hydroxyIs (OH) groups in saccharic acid are :
©
Total number of hydroxyIs (OH) groups in saccharic acid are :
©
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
The formation of molecular orbitals can be described by the linear combination of atomic orbitals. Which one of the following correctly represents the formation of bonding molecular orbital from the atomic orbitals having wave functions ΨA and ΨB ?
©
The formation of molecular orbitals can be described by the linear combination of atomic orbitals. Which one of the following correctly represents the formation of bonding molecular orbital from the atomic orbitals having wave functions ΨA and ΨB ?
©
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
The number of isomers of C5H12 is :
©
The number of isomers of C5H12 is :
©
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Which of the following does not exist ?
©
Which of the following does not exist ?
©
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