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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Let f : R → R , g : R → R be differentiable functions such that (fog) (x) = x . If f (x) = 2x + cos x + sin2 x , then the value of
99
Σ
n=1
 g (1 + (2n - )π) is
Let f : R → R , g : R → R be differentiable functions such that (fog) (x) = x . If f (x) = 2x + cos x + sin2 x , then the value of
99
Σ
n=1
 g (1 + (2n - )π) is
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If f : [1 , ∞) [1 , ∞] is defined by f (x) =
1+√1+4log2x
2
 then f−1 (3) =
If f : [1 , ∞) [1 , ∞] is defined by f (x) =
1+√1+4log2x
2
 then f−1 (3) =
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If α and β are the greatest divisors of n(n2−1) and 2n(n2+2) respectively for all n ∊ N then αβ =
If α and β are the greatest divisors of n(n2−1) and 2n(n2+2) respectively for all n ∊ N then αβ =
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Let A =
[
1
6
−
1
3
−
1
6
−
1
3
2
3
1
3
−
1
6
1
3
1
6
]
. If A2016l+A2017m + A2018n =
1
α
 A , for every l , m , n ∊ N , then the value of α is
Let A =
[
1
6
−
1
3
−
1
6
−
1
3
2
3
1
3
−
1
6
1
3
1
6
]
. If A2016l+A2017m + A2018n =
1
α
 A , for every l , m , n ∊ N , then the value of α is
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Let l , m , n ∊ R and A =
[
1rr2l
rr21m
r21rn
]
. Then the set of all real values of r for which the rank of is 3, is
Let l , m , n ∊ R and A =
[
1rr2l
rr21m
r21rn
]
. Then the set of all real values of r for which the rank of is 3, is
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The following system of equations
x + y + z = 9
2x + 5y + 7x = 52
x + 7y + 11z = 77
has
The following system of equations
x + y + z = 9
2x + 5y + 7x = 52
x + 7y + 11z = 77
has
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Z is a complex number such that |Z| ≤ 2 and −
π
3
 ≤ amp Z ≤
π
3
. The area of the region formed by locus of Z is
Z is a complex number such that |Z| ≤ 2 and −
π
3
 ≤ amp Z ≤
π
3
. The area of the region formed by locus of Z is
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The points in the argand plane given by
Z1 = - 3 + 5i , Z2 = - 1 + 6i , Z3 = - 2 + 8i , Z4 = - 4 + 7i from a
The points in the argand plane given by
Z1 = - 3 + 5i , Z2 = - 1 + 6i , Z3 = - 2 + 8i , Z4 = - 4 + 7i from a
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
When n = 8 , (√3+i)n + (√3−i)n =
When n = 8 , (√3+i)n + (√3−i)n =
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
If 2 cis
7π
5
 is one of the values of z
1
5
 , then z =
If 2 cis
7π
5
 is one of the values of z
1
5
 , then z =
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
The set of real values of x for which the inequality |x - 1| + |x + 1| < 4 always holds aood is
The set of real values of x for which the inequality |x - 1| + |x + 1| < 4 always holds aood is
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If the roots of the equation x2 + x + a = 0 exceed a , then
If the roots of the equation x2 + x + a = 0 exceed a , then
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If the roots of the equation √
x
1−x
 + √
1−x
x
 =
5
2
 are p and q (p > q) and the roots of the equation (p + q) x4 - pqx2 +
p
q
 = 0 are α , β , γ , δ , then (Σα)2 - Σ αβ + αβγδ =
If the roots of the equation √
x
1−x
 + √
1−x
x
 =
5
2
 are p and q (p > q) and the roots of the equation (p + q) x4 - pqx2 +
p
q
 = 0 are α , β , γ , δ , then (Σα)2 - Σ αβ + αβγδ =
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The equation x5−5x3+5x2 - 1 = 0 has three equal roots. If α , β are the other two roots of this equation, then α + β + αβ =
The equation x5−5x3+5x2 - 1 = 0 has three equal roots. If α , β are the other two roots of this equation, then α + β + αβ =
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
If all possible numbers are formed by using the digits 1. 2. 3. 5, 7 without repetition and they are arranged in descending order, then the rank of the number 327 is
If all possible numbers are formed by using the digits 1. 2. 3. 5, 7 without repetition and they are arranged in descending order, then the rank of the number 327 is
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
If a is the number of all even divisors and b is the number of all odd divisors of the number 10800 , then 2a + 3b =
If a is the number of all even divisors and b is the number of all odd divisors of the number 10800 , then 2a + 3b =
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
If the coefficient of x5 in the expansion of (ax2+
1
bx
)13 is equal to the coefficient of x−5 in the expansion of (ax−
1
bx2
)13 , then ab =
If the coefficient of x5 in the expansion of (ax2+
1
bx
)13 is equal to the coefficient of x−5 in the expansion of (ax−
1
bx2
)13 , then ab =
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
For n ∊ N. in the expansion (4√x−3+a4√x5)n , the sum of all binomial coefficients lies between 200 and 400 and the term independent of x is 448. Then the value of a is
For n ∊ N. in the expansion (4√x−3+a4√x5)n , the sum of all binomial coefficients lies between 200 and 400 and the term independent of x is 448. Then the value of a is
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
if
x4+x3+2x2−2x+1
x3+x2
 = P (x) +
A
x
+
B
x2
+
C
x+1
 then A + B + C =
if
x4+x3+2x2−2x+1
x3+x2
 = P (x) +
A
x
+
B
x2
+
C
x+1
 then A + B + C =
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If A (n) = sinnα+cosnα , then A (1) A (4) + A (2) A (5) =
If A (n) = sinnα+cosnα , then A (1) A (4) + A (2) A (5) =
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
When
sin9θ
cos27θ
 +
sin3θ
cos9θ
 +
sinθ
cos3θ
 = k (tan 27 θ - tan θ) is defined , then k =
When
sin9θ
cos27θ
 +
sin3θ
cos9θ
 +
sinθ
cos3θ
 = k (tan 27 θ - tan θ) is defined , then k =
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If x =
∞
Σ
n=0
cos2nθ , y =
∞
Σ
n=0
sin2nθ , z =
∞
Σ
n=0
cos2nθsin2nθ and 0 < θ <
π
2
 , then
If x =
∞
Σ
n=0
cos2nθ , y =
∞
Σ
n=0
sin2nθ , z =
∞
Σ
n=0
cos2nθsin2nθ and 0 < θ <
π
2
 , then
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Number of solutions of the equation sin x - sin 2x + sin 3x = 2 cos2 x - 2 cos x in (0 , π) is :
Number of solutions of the equation sin x - sin 2x + sin 3x = 2 cos2 x - 2 cos x in (0 , π) is :
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
2 tan−1
1
5
 + sec−1
5√2
7
 + 2 tan−1
1
8
 =
2 tan−1
1
5
 + sec−1
5√2
7
 + 2 tan−1
1
8
 =
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If cosh x =
√14
3
 , sinh x = cos θ and - π < θ < -
π
2
 then sin θ =
If cosh x =
√14
3
 , sinh x = cos θ and - π < θ < -
π
2
 then sin θ =
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
In Δ ABC , if a = 5 and tan
A−B
2
 =
1
4
 tan
A+B
2
 , then √a2−b2 =
In Δ ABC , if a = 5 and tan
A−B
2
 =
1
4
 tan
A+B
2
 , then √a2−b2 =
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In a triangle ABC , if A = 2B and the sides opposite to the angles A , B , C are α + 1 , α - 1 and α respectively then α =
In a triangle ABC , if A = 2B and the sides opposite to the angles A , B , C are α + 1 , α - 1 and α respectively then α =
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
In Δ ABC right angled at A. the circum radius. inradius and radius of the excircle opposite to A are respectively in the ratio 2 : 5 : λ , then the roots of the equation x2 - (λ - 5) x + (λ - 6) = 0 are
In Δ ABC right angled at A. the circum radius. inradius and radius of the excircle opposite to A are respectively in the ratio 2 : 5 : λ , then the roots of the equation x2 - (λ - 5) x + (λ - 6) = 0 are
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Let 3
→
i
+
→
j
−
→
k
 be the position vector of a point B. Let A be a point on the line which is passing through B and parallel to the vector 2
→
i
−
→
j
+2
→
k
 . If |
−
BA
| = 18 , then the position vector of A is
Let 3
→
i
+
→
j
−
→
k
 be the position vector of a point B. Let A be a point on the line which is passing through B and parallel to the vector 2
→
i
−
→
j
+2
→
k
 . If |
−
BA
| = 18 , then the position vector of A is
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
The vector that is parallel to the vector 2
→
i
−2
→
j
−4
→
k
 and coplanar with the vectors
→
i
+
→
j
 and
→
j
+
→
k
 is
The vector that is parallel to the vector 2
→
i
−2
→
j
−4
→
k
 and coplanar with the vectors
→
i
+
→
j
 and
→
j
+
→
k
 is
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
A line L is passing through the points whose position vector is
→
i
+2
→
j
−3
→
k
 and parallel to the vector 2
→
i
+
→
j
+2
→
k
. A plane π is passing through the points
→
i
+
→
j
+
→
k
 ,
→
i
−
→
j
−
→
k
 and parallel to the vector
→
i
−2
→
j
. Then the point where this plane π meets the line L is
A line L is passing through the points whose position vector is
→
i
+2
→
j
−3
→
k
 and parallel to the vector 2
→
i
+
→
j
+2
→
k
. A plane π is passing through the points
→
i
+
→
j
+
→
k
 ,
→
i
−
→
j
−
→
k
 and parallel to the vector
→
i
−2
→
j
. Then the point where this plane π meets the line L is
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
If the position vectors of three points A, B , C respectively are
→
i
+2
→
j
+
→
k
 , 2
→
i
−
→
j
+2
→
k
 and
→
i
+
→
j
+2
→
k
 , then the perpendicular distance of the point C from the line AB is
If the position vectors of three points A, B , C respectively are
→
i
+2
→
j
+
→
k
 , 2
→
i
−
→
j
+2
→
k
 and
→
i
+
→
j
+2
→
k
 , then the perpendicular distance of the point C from the line AB is
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
The volume of a tetrahedron whose vertices are 4
→
i
+5
→
j
+
→
k
 , −
→
j
+
→
k
 , 3
→
i
+9
→
j
+4
→
k
 and −2
→
i
+4
→
j
+4
→
k
 is (in cubic units)
The volume of a tetrahedron whose vertices are 4
→
i
+5
→
j
+
→
k
 , −
→
j
+
→
k
 , 3
→
i
+9
→
j
+4
→
k
 and −2
→
i
+4
→
j
+4
→
k
 is (in cubic units)
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If the vectors
→
b
,
→
c
,
→
d
 bxJ are not coplanar. then, the vector (
→
a
×
→
b
) × (
→
a
×
→
b
) + (
→
a
×
→
c
) × (
→
d
×
→
b
) + (
→
a
×
→
d
) × (
→
b
×
→
c
) is
If the vectors
→
b
,
→
c
,
→
d
 bxJ are not coplanar. then, the vector (
→
a
×
→
b
) × (
→
a
×
→
b
) + (
→
a
×
→
c
) × (
→
d
×
→
b
) + (
→
a
×
→
d
) × (
→
b
×
→
c
) is
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
x1,x2 , ..... xn are n observations with mean
−
x
 and standard deviation a Match the items of List-I with those of List-II

x1,x2 , ..... xn are n observations with mean
−
x
 and standard deviation a Match the items of List-I with those of List-II

Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
The variance of 50 observations is 7. If each observation is multiplied by 6 and then 5 is subtracted from it. then the variance of the new data is
The variance of 50 observations is 7. If each observation is multiplied by 6 and then 5 is subtracted from it. then the variance of the new data is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
Two dice are thrown and two coins are tossed simultaneously. The probability of getting prime numbers on both the dice along with a head and a tail on the two coins is
Two dice are thrown and two coins are tossed simultaneously. The probability of getting prime numbers on both the dice along with a head and a tail on the two coins is
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
5 persons entered a lift cabin on the ground floor of a 7 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all the 5 persons leaving the cabin at different floors, is
5 persons entered a lift cabin on the ground floor of a 7 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all the 5 persons leaving the cabin at different floors, is
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A company produces 10.000 items per day. On a particular day 2500 items were produced on machine A. 3500 on machine B and 4000 on machine C. The probability that an item produced by the machines A. B, C to be defective is respectively 2%, 3% and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C. is
A company produces 10.000 items per day. On a particular day 2500 items were produced on machine A. 3500 on machine B and 4000 on machine C. The probability that an item produced by the machines A. B, C to be defective is respectively 2%, 3% and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C. is
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
A random variable A"takes the values 1.2.3 and 4 such that 2P (X = 1) = 3P (X = 2) = P (X = 3) = 5P (X = 4). If σ2 4). If µ is the variance and mean of X then σ2+µ2 =
A random variable A"takes the values 1.2.3 and 4 such that 2P (X = 1) = 3P (X = 2) = P (X = 3) = 5P (X = 4). If σ2 4). If µ is the variance and mean of X then σ2+µ2 =
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
Ail executive in a company makes on an average 5 telephone calls per hour at a cost of Rs.2 per cell. The probability that in any hour the cost of the calls exceeds a sum of Rs.4 is
Ail executive in a company makes on an average 5 telephone calls per hour at a cost of Rs.2 per cell. The probability that in any hour the cost of the calls exceeds a sum of Rs.4 is
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
A quadrilateral ABCD is divided by the diagonal AC into two triangles of equal areas. If A, B, C are respectively (3.4), (-3,6), (-5.1). then the locus of D is
A quadrilateral ABCD is divided by the diagonal AC into two triangles of equal areas. If A, B, C are respectively (3.4), (-3,6), (-5.1). then the locus of D is
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
By rotating the coordinate axes in the positive direction about the origin by an angle a.if the point (1.2) is transformed to (
3√3−1
2√2
 ,
√3+3
2√2
) in new coordinate system then α =
By rotating the coordinate axes in the positive direction about the origin by an angle a.if the point (1.2) is transformed to (
3√3−1
2√2
 ,
√3+3
2√2
) in new coordinate system then α =
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
Let a ≠ 0 , b ≠ 0 , c be three real numbers and L (p , q) =
ap+bq+c
√a2+b2
 , for all p , q ∊ R . If L (
2
3
,
1
3
) + L (
1
3
,
2
3
) + L (2 , 2) = 0 , then the line ax + by + x = 0 always passes through the fixed point
Let a ≠ 0 , b ≠ 0 , c be three real numbers and L (p , q) =
ap+bq+c
√a2+b2
 , for all p , q ∊ R . If L (
2
3
,
1
3
) + L (
1
3
,
2
3
) + L (2 , 2) = 0 , then the line ax + by + x = 0 always passes through the fixed point
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
The incentre of the triangle formed by the straight line having 3 as X - intercept and 4 as Y - intercept, together with the coordinate axes, is
The incentre of the triangle formed by the straight line having 3 as X - intercept and 4 as Y - intercept, together with the coordinate axes, is
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The equation of the straight line in the normal form which is parallel to the lines x + 2y + 3 = 0 and x + 2y + 8 = 0 and dividing the distance between these two lines hi the ratio 1 : 2 internally is
The equation of the straight line in the normal form which is parallel to the lines x + 2y + 3 = 0 and x + 2y + 8 = 0 and dividing the distance between these two lines hi the ratio 1 : 2 internally is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
A pair of straight lilies is passing through the point (1,1). One of the lines makes an angle 0 with the positive direction of X-axis and the other makes the same angle with the positive direction of I-axis. If the equation of the pair of straight lines is
x2 - (a + 2) xy + y2 + a (x + y - 1) = 0 , a ≠ - 2 , then the value of θ is
A pair of straight lilies is passing through the point (1,1). One of the lines makes an angle 0 with the positive direction of X-axis and the other makes the same angle with the positive direction of I-axis. If the equation of the pair of straight lines is
x2 - (a + 2) xy + y2 + a (x + y - 1) = 0 , a ≠ - 2 , then the value of θ is
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If the pair of lines 6x2+xy−y2=0 and 3x2−axy−y2=0 a>0 have a common line, then a=
If the pair of lines 6x2+xy−y2=0 and 3x2−axy−y2=0 a>0 have a common line, then a=
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If the chord L = y - mx - 1 = 0 of the circle S = 2+y2 - 1 = 0 touches the circle S1 = x2+y2 - 4x + 1 = 0 then the possible points for which L = 0 is a chord of contact of S = 0 are
If the chord L = y - mx - 1 = 0 of the circle S = 2+y2 - 1 = 0 touches the circle S1 = x2+y2 - 4x + 1 = 0 then the possible points for which L = 0 is a chord of contact of S = 0 are
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
If y + c = 0 is a tangent to the circle x2+y2 - 6x - 2y + 1 = 0 at (a , 4) then
If y + c = 0 is a tangent to the circle x2+y2 - 6x - 2y + 1 = 0 at (a , 4) then
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the circles given by S = x2+y2 - 14x + 6y + 33 = 0 and S' = x2+y2−a2 = 0 (a ∊ N) have 4 common tangents, then the possible number of circles S' = 0 is
If the circles given by S = x2+y2 - 14x + 6y + 33 = 0 and S' = x2+y2−a2 = 0 (a ∊ N) have 4 common tangents, then the possible number of circles S' = 0 is
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The center of the circle passing through the point (1, 0) and cutting the circles x2+y2 - 2x + 4y + 1 = 0 and x2+y2 + 6x - 2y + 1 = 0 orthogonally is
The center of the circle passing through the point (1, 0) and cutting the circles x2+y2 - 2x + 4y + 1 = 0 and x2+y2 + 6x - 2y + 1 = 0 orthogonally is
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
Hie equation of the tangent at the point (0. 3) on the circle which cuts the circles x2+y2 - 2x + 6y = 0 , x2+y2 - 4x - 2y + 6 = 0 and x2+y2 - 12x + 2y + 3 = 0 orthogonally is
Hie equation of the tangent at the point (0. 3) on the circle which cuts the circles x2+y2 - 2x + 6y = 0 , x2+y2 - 4x - 2y + 6 = 0 and x2+y2 - 12x + 2y + 3 = 0 orthogonally is
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If two tangents to the parabola y2 = 8x meet the tangent at its vertex in M and N such that MN = 4. then the locus of the point of intersection of those two tangents is
If two tangents to the parabola y2 = 8x meet the tangent at its vertex in M and N such that MN = 4. then the locus of the point of intersection of those two tangents is
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Three normals are drawn from the point (c. 0) to the curve y2 = x. If one of the normals is X-axis, then the value of x for which the other two normals are perpendicular to each other is
Three normals are drawn from the point (c. 0) to the curve y2 = x. If one of the normals is X-axis, then the value of x for which the other two normals are perpendicular to each other is
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
If the normal drawn at one end of the latus rectum of the ellipse b2x2+a2y2 = a2b2 with eccentricity 'e' passes through one end of the minor axis, then.
If the normal drawn at one end of the latus rectum of the ellipse b2x2+a2y2 = a2b2 with eccentricity 'e' passes through one end of the minor axis, then.
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
A variable tangent to the ellipse
x2
a2
+
y2
b2
 = 1 makes intercepts on both the axes. The locus of the middle point of the portion of the tangent between the coordinate axes is
A variable tangent to the ellipse
x2
a2
+
y2
b2
 = 1 makes intercepts on both the axes. The locus of the middle point of the portion of the tangent between the coordinate axes is
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If the eccentricity of a conic satisfies the equation 2x3 + 10x - 13 = 0 , then that conic is
If the eccentricity of a conic satisfies the equation 2x3 + 10x - 13 = 0 , then that conic is
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Assertion (A): If (-1.3.2) and (5.3.2) are respectively the orthocentre and circumcentre of a triangle, then (3. 3. 2) is its centroid.
Reason (R): Centroid of the triangle divides the line segment joining the orthocentreand the circumcentre in the ratio 1 : 2
Which one of the following is true?
Assertion (A): If (-1.3.2) and (5.3.2) are respectively the orthocentre and circumcentre of a triangle, then (3. 3. 2) is its centroid.
Reason (R): Centroid of the triangle divides the line segment joining the orthocentreand the circumcentre in the ratio 1 : 2
Which one of the following is true?
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
The lines whose direction cosines are given by the relations al + bm + cn = 0 and mn + nl + lm = 0 are
The lines whose direction cosines are given by the relations al + bm + cn = 0 and mn + nl + lm = 0 are
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
If The plane passing through The points (1 , 2 , 3) , (2 , 3 , 1) and (3 , 1 , 2) is ax + by + cz = 1 then a + 2b + 3c =
If The plane passing through The points (1 , 2 , 3) , (2 , 3 , 1) and (3 , 1 , 2) is ax + by + cz = 1 then a + 2b + 3c =
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
x→−∞
3|x|−x
|x|−2x
 -
lim
x→0
log(1+x3)
sin3x
 =
lim
x→−∞
3|x|−x
|x|−2x
 -
lim
x→0
log(1+x3)
sin3x
 =
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
if f (x) =
{
x−2
|x−2|
+a		x<2
x−2
|x−2|
+b		x>2

is continuous at x = 2, then a + b =
if f (x) =
{
x−2
|x−2|
+a		x<2
x−2
|x−2|
+b		x>2

is continuous at x = 2, then a + b =
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
If f (x) = {
x2log(cosx)
log(1+x2)
x≠0
0x=0
 then f is
If f (x) = {
x2log(cosx)
log(1+x2)
x≠0
0x=0
 then f is
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Match the items given in List-A with those of the items of List-B

Match the items given in List-A with those of the items of List-B

Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
It y =
(sin−1x)2
2
 , then (1−x2) y2−xy1 =
It y =
(sin−1x)2
2
 , then (1−x2) y2−xy1 =
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
If the relative errors in the base radius and the height of a cone are same and equal to 0.02. then the percentage error in the volume of that cone is
If the relative errors in the base radius and the height of a cone are same and equal to 0.02. then the percentage error in the volume of that cone is
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The normal at a point 0 to the curve x = a (1 + cos θ) , y = a sin θ always passes through the fixed point
The normal at a point 0 to the curve x = a (1 + cos θ) , y = a sin θ always passes through the fixed point
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
Let f (x) be continuous on [0. 6] and differentiable on (0.6). Let f (0) = 12 and f (6) = - 4. If g (x) =
f(x)
x+1
 , then for some La grange’s constant c ∊ (0 , 6) , g ' (c) =
Let f (x) be continuous on [0. 6] and differentiable on (0.6). Let f (0) = 12 and f (6) = - 4. If g (x) =
f(x)
x+1
 , then for some La grange’s constant c ∊ (0 , 6) , g ' (c) =
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
If (α , β) and (γ , δ) where α < γ , are the turning points of f (x) = 2x3−15x2 + 36x - 8 then α - γ - β + δ =
If (α , β) and (γ , δ) where α < γ , are the turning points of f (x) = 2x3−15x2 + 36x - 8 then α - γ - β + δ =
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
The height of a cylinder of the greatest volume that can be inscribed in a sphere of radius 3 is
The height of a cylinder of the greatest volume that can be inscribed in a sphere of radius 3 is
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
∫
dx
(ex+e−x)2
 =
∫
dx
(ex+e−x)2
 =
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
π
2
∫
0
dx
1+(tanx)√2018
 =
π
2
∫
0
dx
1+(tanx)√2018
 =
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
If ∫
x
(x2+1)(x−1)
 dx = A log |x2 + 1 | + B tan−1 x + C log |x - 1| + d , then A + B + C =
If ∫
x
(x2+1)(x−1)
 dx = A log |x2 + 1 | + B tan−1 x + C log |x - 1| + d , then A + B + C =
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
π
2
∫
0
cos3x
sinx+cosx
 dx =
π
2
∫
0
cos3x
sinx+cosx
 dx =
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
3
∫
0
 (2 + x2) dx =
3
∫
0
 (2 + x2) dx =
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Hie area enclosed (in square units) by the curve y = x4−x2 , the X-axis and the vertical lines passing through the two minimum points of the curve is
Hie area enclosed (in square units) by the curve y = x4−x2 , the X-axis and the vertical lines passing through the two minimum points of the curve is
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The differential equation corresponding to the family of circles having centres on X-axis and passing through the origin is
The differential equation corresponding to the family of circles having centres on X-axis and passing through the origin is
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The general solution of the differential equation (x2 + xy) y ' = y2 is
The general solution of the differential equation (x2 + xy) y ' = y2 is
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
At any point on a curve, the slope of the tangent is equal to the stun of abscissa and the product of ordinate and abscissa of that point. If the curve passes through (0. 1). then the equation of the curve is
At any point on a curve, the slope of the tangent is equal to the stun of abscissa and the product of ordinate and abscissa of that point. If the curve passes through (0. 1). then the equation of the curve is
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Assertion (A): When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.
Reason (R) : Energy can change from one form to another but die total energy is alwaysconserved.
Which of the following is true?
Assertion (A): When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.
Reason (R) : Energy can change from one form to another but die total energy is alwaysconserved.
Which of the following is true?
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
A gas satisfies the relation PV
5
3
 = K where P is pressure, V is volume and K is constant. The dimensions of constant K are
A gas satisfies the relation PV
5
3
 = K where P is pressure, V is volume and K is constant. The dimensions of constant K are
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A car moves in positive Y - direction with velocity 'v' proportional to distance travelled y as v (y) α yB , where β is a positive constant. The car covers a distance L with average velocity < v > proportional to L AS < v > α L
1
3
. The constant β is given as
A car moves in positive Y - direction with velocity 'v' proportional to distance travelled y as v (y) α yB , where β is a positive constant. The car covers a distance L with average velocity < v > proportional to L AS < v > α L
1
3
. The constant β is given as
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
Consider a particle moving along the positive direction ofX-axis. The velocity of the particleis given by v = α √x (α is a positive constant). At time = 0. if the particle is located at x = 0. the time dependence of the velocity and the acceleration of the particle are respectively.
Consider a particle moving along the positive direction ofX-axis. The velocity of the particleis given by v = α √x (α is a positive constant). At time = 0. if the particle is located at x = 0. the time dependence of the velocity and the acceleration of the particle are respectively.
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector
→
r
 = 3t2
^
i
+2t
^
j
+
^
k
 at t = 2 sec. are, respectively
The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector
→
r
 = 3t2
^
i
+2t
^
j
+
^
k
 at t = 2 sec. are, respectively
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
Two objects are located at height 10m above the ground. At some point of time, the objects are thrown with initial velocity 2√2m∕s at an angle 45∘ and 135∘ with the positive X -axis, respectively. Assuming g=10m∕s2, the velocity vectors will be perpendicular to each other at time is equal to
Two objects are located at height 10m above the ground. At some point of time, the objects are thrown with initial velocity 2√2m∕s at an angle 45∘ and 135∘ with the positive X -axis, respectively. Assuming g=10m∕s2, the velocity vectors will be perpendicular to each other at time is equal to
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
String AB of unstretched length L is stretched by applying a force F at the mid-point C such that the segments AC and BC make an angle ‘ θ ’with AB as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio K. The force is given by

String AB of unstretched length L is stretched by applying a force F at the mid-point C such that the segments AC and BC make an angle ‘ θ ’with AB as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio K. The force is given by
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A block of mass 5 kg is kept against an accelerating wedge with a wedge angle of 45° to the horizontal. The co-efficient of friction between the block and the wedge is µ = 0.4. What is the minimum absolute value of the acceleration of the wedge to keep the block steady. Assume g = 10 m/s2

A block of mass 5 kg is kept against an accelerating wedge with a wedge angle of 45° to the horizontal. The co-efficient of friction between the block and the wedge is µ = 0.4. What is the minimum absolute value of the acceleration of the wedge to keep the block steady. Assume g = 10 m/s2

Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
All object moves along the circle with normal acceleration proportional to tα , where t is the time and α is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to
All object moves along the circle with normal acceleration proportional to tα , where t is the time and α is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
A ball of mass 1kg moving along X -direction collides elastically with a stationary ball of mass m. The first ball (mass =1kg ) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle 30∘ with the X -axis, then the value of ' m ' must be
A ball of mass 1kg moving along X -direction collides elastically with a stationary ball of mass m. The first ball (mass =1kg ) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle 30∘ with the X -axis, then the value of ' m ' must be
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A machine gun can fire 200 bullets min. If 35 g bullets are fired at a speed of 750 m s. the average force exerted by the gun on the bullets is.
A machine gun can fire 200 bullets min. If 35 g bullets are fired at a speed of 750 m s. the average force exerted by the gun on the bullets is.
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
A solid sphere of radius R makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle θ. If the radius of gyration is k. then its acceleration is
A solid sphere of radius R makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle θ. If the radius of gyration is k. then its acceleration is
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
A particle of mass 'm' is attached to four springs with spring constant k , k , 2k and 2k as shown in the figure. Four springs are attached to the four comers of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

A particle of mass 'm' is attached to four springs with spring constant k , k , 2k and 2k as shown in the figure. Four springs are attached to the four comers of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
The ratio of the height above the surface of earth to the depth below the surface of earth, for gravitational accelerations to be the same (assuming small heights), is
The ratio of the height above the surface of earth to the depth below the surface of earth, for gravitational accelerations to be the same (assuming small heights), is
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
A steel rod has radius 50mm and length 2m. It is stretched along its length with a force of 400kN. This causes an elongation of 0.5mm. Find the (approximate) Young's modulus of steel from this information.
A steel rod has radius 50mm and length 2m. It is stretched along its length with a force of 400kN. This causes an elongation of 0.5mm. Find the (approximate) Young's modulus of steel from this information.
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
Consider a vessel filled with a liquid upto height H. The bottom of the vessel lies in the X-Y plane passing through the origin. The density of the liquid varies with Z-axis as ρ (z) = ρ0 [2−(
z
H
)2]. If P1 and P2 are the pressures at the bottom surface and top surface of the liquid, the magnitude of (P1−P2) is :
Consider a vessel filled with a liquid upto height H. The bottom of the vessel lies in the X-Y plane passing through the origin. The density of the liquid varies with Z-axis as ρ (z) = ρ0 [2−(
z
H
)2]. If P1 and P2 are the pressures at the bottom surface and top surface of the liquid, the magnitude of (P1−P2) is :
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A one mole of ideal gas goes through a process in which pressure varies with volume V as P = 3 - g (
V
V0
)2 , where V0 is a constant. The maximum attainable temperature by the ideal gas during this process is
(All quantities are in SI unitsand R is gas constant)
A one mole of ideal gas goes through a process in which pressure varies with volume V as P = 3 - g (
V
V0
)2 , where V0 is a constant. The maximum attainable temperature by the ideal gas during this process is
(All quantities are in SI unitsand R is gas constant)
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
The internal energy of the air. in a room of volume F. at temperature T and with outside pressure P increasing linearly with time, varies as
The internal energy of the air. in a room of volume F. at temperature T and with outside pressure P increasing linearly with time, varies as
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
The efficiency of carnot engine is q when its hot and cold reservoirs are maintained at temperature T1 and T2 , respectively. To increase the efficiency to 1.5 η , the increase in temperature (ΔT) of the hot reservoir by keeping the cold one constant at T2 is
The efficiency of carnot engine is q when its hot and cold reservoirs are maintained at temperature T1 and T2 , respectively. To increase the efficiency to 1.5 η , the increase in temperature (ΔT) of the hot reservoir by keeping the cold one constant at T2 is
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
Ail ail' bubble rises from the bottom of a water tank of height 5 m. If the initial volume of the bubble is 3 mm3 . What will be its volume as it reaches the surface. Assume that its temperature does not change.
[g = 9.8 m/s2 , 1 atm = 105 Pa , density of water = 1 gm/cc]
Ail ail' bubble rises from the bottom of a water tank of height 5 m. If the initial volume of the bubble is 3 mm3 . What will be its volume as it reaches the surface. Assume that its temperature does not change.
[g = 9.8 m/s2 , 1 atm = 105 Pa , density of water = 1 gm/cc]
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
Two harmonic travelling waves are described by the equations y1 = a sin (kx - ωt) and y2 = a sin (- kx + ωt + Φ) . The amplitude of the superposed wave is
Two harmonic travelling waves are described by the equations y1 = a sin (kx - ωt) and y2 = a sin (- kx + ωt + Φ) . The amplitude of the superposed wave is
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
Where should an object be placed on the axis of a convex lens of focal length 8 cm so as to achieve magnification of - 4 ? (Distances are measured from optic centre of the lens)
Where should an object be placed on the axis of a convex lens of focal length 8 cm so as to achieve magnification of - 4 ? (Distances are measured from optic centre of the lens)
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
A converging minor is placed on the right hand side of a converging lens as shown in the figure. The focal length of the mirror and the lens are 20 cm and 15 cm respectively. The separation between the lens and the mirror is 40 cm and their principal axes coincide. A point source is placed on the principal axis at a distance V’ to the left of the lens. If the final beam comes out parallel to the principal axis, then the value of 'd' is:

A converging minor is placed on the right hand side of a converging lens as shown in the figure. The focal length of the mirror and the lens are 20 cm and 15 cm respectively. The separation between the lens and the mirror is 40 cm and their principal axes coincide. A point source is placed on the principal axis at a distance V’ to the left of the lens. If the final beam comes out parallel to the principal axis, then the value of 'd' is:

Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
Interference fringes are obtained in a Young double slit experiment using beam of light consisting two wavelengths 500 nm and 600 nm. Bright fringes due to both wavelengths coincide at 2.5 mm from the central maximum. If the separation between the slitsis 3 mm. then the distance between the screen and plane of the slits is
Interference fringes are obtained in a Young double slit experiment using beam of light consisting two wavelengths 500 nm and 600 nm. Bright fringes due to both wavelengths coincide at 2.5 mm from the central maximum. If the separation between the slitsis 3 mm. then the distance between the screen and plane of the slits is
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
A point charge of 50 µC is placed in the XY plane at a location with radius vector
−
r0
 = 2
^
i
+3
^
j
 m. The electric field strength and its magnitude at a point with radius vector
−
r
 = 8
^
i
−5
^
j
 m is (∊0 = 8.85 × 10−12C2 / N - m2)
A point charge of 50 µC is placed in the XY plane at a location with radius vector
−
r0
 = 2
^
i
+3
^
j
 m. The electric field strength and its magnitude at a point with radius vector
−
r
 = 8
^
i
−5
^
j
 m is (∊0 = 8.85 × 10−12C2 / N - m2)
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
Hie work done to assemble the three chaises in a configuration as shown in the figure below is

Hie work done to assemble the three chaises in a configuration as shown in the figure below is

Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
Consider the following two circuits
[A] : 20 bulbs are connected in series to a power supply line
[B] : 20 bulbs identical to [A] are connected in a parallel circuit to an identical powersupply line
Consider the following two circuits
[A] : 20 bulbs are connected in series to a power supply line
[B] : 20 bulbs identical to [A] are connected in a parallel circuit to an identical powersupply line
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
A tapered bar of length I and end diameters D1 and D2 is made of a material of electrical resistivity ρ. The electrical resistance of the bar is
A tapered bar of length I and end diameters D1 and D2 is made of a material of electrical resistivity ρ. The electrical resistance of the bar is
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
Two circular loops L1 and L2 of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop L1 is R1 and that of L2 is R2. The distance between the centres of the loops is √3R1. The magnetic field at the centre of L2 shall be zero if
Two circular loops L1 and L2 of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop L1 is R1 and that of L2 is R2. The distance between the centres of the loops is √3R1. The magnetic field at the centre of L2 shall be zero if
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A non-conducting thin disc of radius R rotates about its axis with an angular velocity ω. The surface chaise density on the disc varies with the distance r from the center as σ (r) = σ0[1+(
r
R
)β] , where σ0 and β pare constants. If the magnetic induction at the center is B = (
9
10
) µ0σ0 ωR , the value of β is :
A non-conducting thin disc of radius R rotates about its axis with an angular velocity ω. The surface chaise density on the disc varies with the distance r from the center as σ (r) = σ0[1+(
r
R
)β] , where σ0 and β pare constants. If the magnetic induction at the center is B = (
9
10
) µ0σ0 ωR , the value of β is :
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A bar magnet of magnetic moment M is placed at a distance D with its axis along positive X-axis. Likewise, second bar magnet of magnetic moment is placed at a distance 2D on positive Y-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the orisin is |
→
B
| = α [
µ0M
4πD3
] . The value of a must be
(Assume D ≫ l where l is the length of magnets)

A bar magnet of magnetic moment M is placed at a distance D with its axis along positive X-axis. Likewise, second bar magnet of magnetic moment is placed at a distance 2D on positive Y-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the orisin is |
→
B
| = α [
µ0M
4πD3
] . The value of a must be
(Assume D ≫ l where l is the length of magnets)

Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A wire loop enclosing a semi-circle of radius 'R' is located on the boundary of a uniform magnetic field of induction
→
B
. At time t = 0 , the loops is set into rotation with velocity 'ω' about its axis '0', coinciding with a line of vector
→
B
 on the boundary as shown in the figure. The emf induced in the loop is

A wire loop enclosing a semi-circle of radius 'R' is located on the boundary of a uniform magnetic field of induction
→
B
. At time t = 0 , the loops is set into rotation with velocity 'ω' about its axis '0', coinciding with a line of vector
→
B
 on the boundary as shown in the figure. The emf induced in the loop is

Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
In the circuit given below, the capacitor C is charged by closing the switch S1 and opening the switch S2. After charging, the switch S1 is opened and S2 is closed, then the maximum current in the circuit
 
In the circuit given below, the capacitor C is charged by closing the switch S1 and opening the switch S2. After charging, the switch S1 is opened and S2 is closed, then the maximum current in the circuit

Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
A 100 W electric bulb produces electromagnetic radiation with electric field amplitude of
2V
m
 at a distance of 10 m. Assuming it as a point source, estimate the efficiency of the bulb.
A 100 W electric bulb produces electromagnetic radiation with electric field amplitude of
2V
m
 at a distance of 10 m. Assuming it as a point source, estimate the efficiency of the bulb.
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
At an incident radiation frequency of v1 , which is greater than the threshold frequency, the stopping potential for a certain metal is V1 . At frequency 2v1 the stopping potential is 3 V1. If the stopping potential at frequency 4 v1 is n V1 , then n is
At an incident radiation frequency of v1 , which is greater than the threshold frequency, the stopping potential for a certain metal is V1 . At frequency 2v1 the stopping potential is 3 V1. If the stopping potential at frequency 4 v1 is n V1 , then n is
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
Tlie de Broglie wavelength of an electron of kinetic energy 9eV is (take h = 4 × 10−15 eV . sec , e = 3 × 1010 cm/sec and the mass me of electron as mec2 = 0.5 MeV)
Tlie de Broglie wavelength of an electron of kinetic energy 9eV is (take h = 4 × 10−15 eV . sec , e = 3 × 1010 cm/sec and the mass me of electron as mec2 = 0.5 MeV)
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
An active nucleus decays to one-third (
1
3
) in 20 His. The fraction of original activityremaining after 80 His is
An active nucleus decays to one-third (
1
3
) in 20 His. The fraction of original activityremaining after 80 His is
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Consider an amplifier circuit wherein a transistor is used in common emitter mode. The change in collector current and base current respectively are 4 mA and 20 µA when a signal of 40 mV is added to the base-emitter voltage. If the load resistance is 10 kΩ, then power gain in the circuit is
Consider an amplifier circuit wherein a transistor is used in common emitter mode. The change in collector current and base current respectively are 4 mA and 20 µA when a signal of 40 mV is added to the base-emitter voltage. If the load resistance is 10 kΩ, then power gain in the circuit is
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
The output 'F' of the logic circuit given below is

The output 'F' of the logic circuit given below is

Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A carrier wave of peak voltage 20 V is used to transmit a message signal. For getting a modulation index of 60%, the peak voltage of the modulating signal is
A carrier wave of peak voltage 20 V is used to transmit a message signal. For getting a modulation index of 60%, the peak voltage of the modulating signal is
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The energy of an electron in the 3rd orbit of H-atom (in J) is approximately.
The energy of an electron in the 3rd orbit of H-atom (in J) is approximately.
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The wavelength (in m) of a particle of mass 11.043 × 10−36 kg moving with a velocity of 6.0 × 107 ms−1 is
The wavelength (in m) of a particle of mass 11.043 × 10−36 kg moving with a velocity of 6.0 × 107 ms−1 is
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
Covalent bond length of chlorine molecule is 1.98 A. Covalent radius (in
0
A
) of chlorine atom is
Covalent bond length of chlorine molecule is 1.98 A. Covalent radius (in
0
A
) of chlorine atom is
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
The covalency of Al in [AlCl(H2O)5]2+ is
The covalency of Al in [AlCl(H2O)5]2+ is
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
The correct order of bond angles of the given compounds is
The correct order of bond angles of the given compounds is
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The molecular orbital theory supports paramagnetic behaviour of
The molecular orbital theory supports paramagnetic behaviour of
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
Which of the following represents van der Waal’s equation for n moles of the gas?
Which of the following represents van der Waal’s equation for n moles of the gas?
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
Hie kinetic energy in J of 1 mole of N2 at 27°C is (R = 8.314 J mol−1K−1)
Hie kinetic energy in J of 1 mole of N2 at 27°C is (R = 8.314 J mol−1K−1)
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
In the titration of I2 (aq) by S2O32− (aq) using the starch indicator, the end point is indicated by
In the titration of I2 (aq) by S2O32− (aq) using the starch indicator, the end point is indicated by
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
When 10 g of 90% pure limestone is heated, the approximate volume (in L) of CO2 liberated at STP is
When 10 g of 90% pure limestone is heated, the approximate volume (in L) of CO2 liberated at STP is
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
liberated at STP is 1.5 O2(g) ⇌ O3(g) is 3 × 10−29 . Standard fi ee energy change (in KJ mol−1 ; log 3 = 0.47)
liberated at STP is 1.5 O2(g) ⇌ O3(g) is 3 × 10−29 . Standard fi ee energy change (in KJ mol−1 ; log 3 = 0.47)
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
Fora reaction 2A(g) ⇌ 2B(g) + C(g) , Kc = 3.75 × 10−6 at 1069 K. The approximate value of Kp for this reaction at the same temperature is
(R = 0.082 L bar mol−1K−1)
Fora reaction 2A(g) ⇌ 2B(g) + C(g) , Kc = 3.75 × 10−6 at 1069 K. The approximate value of Kp for this reaction at the same temperature is
(R = 0.082 L bar mol−1K−1)
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
The degree of dissociation of 0.1N CH3COOH is (given Ka = 1 × 10−5) approximately
The degree of dissociation of 0.1N CH3COOH is (given Ka = 1 × 10−5) approximately
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
Match the reactants in List-I with the products in List-II

The correct answer is
Match the reactants in List-I with the products in List-II

The correct answer is
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
When sodium (Na) metal is dissolved in liquid ammonia (NH3), it imparts a blue color to the solution. This blue coloration is due to
When sodium (Na) metal is dissolved in liquid ammonia (NH3), it imparts a blue color to the solution. This blue coloration is due to
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
Identify the correct statements from the following
a) In orthoboric acid, boron is in planar geometry
b) In BCl3,NH3 , boron has tetrahedral geometry
c) Aqueous solution of borax is acidic
Identify the correct statements from the following
a) In orthoboric acid, boron is in planar geometry
b) In BCl3,NH3 , boron has tetrahedral geometry
c) Aqueous solution of borax is acidic
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Si reacts with CH3Cl at 573 K in the presence of Cu powder to form methyl substituted chlorosilanes. Among the given methyl substituted chlorosilanes, whose yield is minimum?
Si reacts with CH3Cl at 573 K in the presence of Cu powder to form methyl substituted chlorosilanes. Among the given methyl substituted chlorosilanes, whose yield is minimum?
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
When vegetation is burnt in the absence of oxygen, which of the following will be formed?
When vegetation is burnt in the absence of oxygen, which of the following will be formed?
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
IUPAC name for the following compound is

IUPAC name for the following compound is

Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
What are the products formed in the reaction given below?
Ph - CH2 - CH = CH - CH3
1)‌O3
→
2)‌Z‌n+H2O
 ?
What are the products formed in the reaction given below?
Ph - CH2 - CH = CH - CH3
1)‌O3
→
2)‌Z‌n+H2O
 ?
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The major product obtained in the reaction of isobutyl benzene with acetic anhydride in the presence of anhydrous AlCl3 is
The major product obtained in the reaction of isobutyl benzene with acetic anhydride in the presence of anhydrous AlCl3 is
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
A compound is formed by elements of X. Y and Z. Atoms of Z (anions) make fee lattice. Atoms of X (cations) occupy all the octahedral voids. Atoms of Y (cations) occupy
1
3
 rd of the tetrahedral voids. The formula of the compound is
A compound is formed by elements of X. Y and Z. Atoms of Z (anions) make fee lattice. Atoms of X (cations) occupy all the octahedral voids. Atoms of Y (cations) occupy
1
3
 rd of the tetrahedral voids. The formula of the compound is
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
A litre of sea water (which weighs 1030 g) contains 6 × 10−3 g of dissolved oxygen. The concentration of dissolved oxygen in ppm is
A litre of sea water (which weighs 1030 g) contains 6 × 10−3 g of dissolved oxygen. The concentration of dissolved oxygen in ppm is
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
At 300 K. a one litre solution of sucrose (molecular weight: 342) was prepared by dissolving 40 g of sucrose. What is the approximate osmotic pressure (in kPa) of solution at the same temperature?
(R = 8.314 × 106cm3 Pa K−1mol−1)
At 300 K. a one litre solution of sucrose (molecular weight: 342) was prepared by dissolving 40 g of sucrose. What is the approximate osmotic pressure (in kPa) of solution at the same temperature?
(R = 8.314 × 106cm3 Pa K−1mol−1)
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
The EMF of a galvanic cell consisting of two hydrogen electrodes is 0.17 V. If the solution of one of the electrodes has [H+] = 10−3 M . the pH at the other electrode is?
The EMF of a galvanic cell consisting of two hydrogen electrodes is 0.17 V. If the solution of one of the electrodes has [H+] = 10−3 M . the pH at the other electrode is?
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
If the rate constants of a reaction at 500 K and 700 K are 0.002 s−1 and 0.06 s−1 respectively, the value of K−1 activation energy is
(R = 8.314 J mol−1K−1 , log 3 = 0.477)
If the rate constants of a reaction at 500 K and 700 K are 0.002 s−1 and 0.06 s−1 respectively, the value of K−1 activation energy is
(R = 8.314 J mol−1K−1 , log 3 = 0.477)
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
The following graph is obtained for physisorption of a gas as a function of pressure at different temperatures

The correct order of temperatures is
The following graph is obtained for physisorption of a gas as a function of pressure at different temperatures

The correct order of temperatures is
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Identify the correct set of sulphide ores from the following
Identify the correct set of sulphide ores from the following
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Identify the reactions in which N2 is liberated
(a) (NH4)2SO4 + NaOH →
(b)
NH3
excess
 + Cl2 →
(c) (NH4)2Cr2O7
Δ
→
(d) NH4NO3
Δ
→
(e) NH4Cl(aq) + NaNO2(aq) →
Identify the reactions in which N2 is liberated
(a) (NH4)2SO4 + NaOH →
(b)
NH3
excess
 + Cl2 →
(c) (NH4)2Cr2O7
Δ
→
(d) NH4NO3
Δ
→
(e) NH4Cl(aq) + NaNO2(aq) →
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
What are X and Y, respectively in the following reactions?
Au + aqua regia → AuCl−+H2O + X
Pt + aqua regia → PtCl62−+H2O + Y
What are X and Y, respectively in the following reactions?
Au + aqua regia → AuCl−+H2O + X
Pt + aqua regia → PtCl62−+H2O + Y
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Which of the following sets correctly represent the increasing paramagnetic property of the ion?
Which of the following sets correctly represent the increasing paramagnetic property of the ion?
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
Which of the following molecules / ions can exhibit isomerism?
A) Tetrahedral : NiCl2Br22−
B) Square planar : Pt(NH3)2Cl2
C) Octahedral : Co(NH3)3Cl3
D) Square planar : Pd(NH3)3Br+
E) Octahedral : Co(en)33+
where, en = 1,2 - di amino ethane
Which of the following molecules / ions can exhibit isomerism?
A) Tetrahedral : NiCl2Br22−
B) Square planar : Pt(NH3)2Cl2
C) Octahedral : Co(NH3)3Cl3
D) Square planar : Pd(NH3)3Br+
E) Octahedral : Co(en)33+
where, en = 1,2 - di amino ethane
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
The formation of terylene (or decron) from ethylene glycol and terephthalic acid is
The formation of terylene (or decron) from ethylene glycol and terephthalic acid is
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Which of the following carbohydrates has a glycosidic linkage?
Which of the following carbohydrates has a glycosidic linkage?
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
Identify an antioxidant, an antiseptic, and an antibiotic respectively from the following
Equanil
(A)
Chloramphenicol
(B)
Bitlhionol
(C)
Aspartame
(D)
Dimetapp
(E)
Butylated‌hydroxytoluene
(F)
Identify an antioxidant, an antiseptic, and an antibiotic respectively from the following
Equanil
(A)
Chloramphenicol
(B)
Bitlhionol
(C)
Aspartame
(D)
Dimetapp
(E)
Butylated‌hydroxytoluene
(F)
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
The major product (P) formed in the following reaction is

The major product (P) formed in the following reaction is

Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
The product (P) of the below reaction is

The product (P) of the below reaction is

Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
Hie products A, B and C in the following reaction sequence are

Hie products A, B and C in the following reaction sequence are

Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
Identify A and B in the following reaction

Identify A and B in the following reaction

Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Which product of the following reactions fails to give carbyl amine test?
Which product of the following reactions fails to give carbyl amine test?
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