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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Let C be the set of all real numbers.
Statement I: The function f:(−‌
π
2
,‌
π
2
)→C defined by f(x)=sec‌x+tan‌x is a one - one function.
Statement II: The function f:[0,∞)→C defined by f(x)=x2 is a one - one function.
Let C be the set of all real numbers.
Statement I: The function f:(−‌
π
2
,‌
π
2
)→C defined by f(x)=sec‌x+tan‌x is a one - one function.
Statement II: The function f:[0,∞)→C defined by f(x)=x2 is a one - one function.
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
Let C be the set of all real numbers. Let f:C→C be a function defined by
f(x)={
2x−5if‌x<−3
x+2if−3≤x<5
3x+1if‌x≥5

The correct match is
Let C be the set of all real numbers. Let f:C→C be a function defined by
f(x)={
2x−5if‌x<−3
x+2if−3≤x<5
3x+1if‌x≥5

The correct match is
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If A+B=[
212
120
022
],AB=[
122
110
121
] then A2+B(A+B)=
If A+B=[
212
120
022
],AB=[
122
110
121
] then A2+B(A+B)=
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
A, P,B are 3×3 matrices. If |−B|=5,|BAT|=15,|PTAP|=−27, then one of the values of |P| is
A, P,B are 3×3 matrices. If |−B|=5,|BAT|=15,|PTAP|=−27, then one of the values of |P| is
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If A is a 3×3 matrix and |A|=‌
1
2
 then ∣A−1(Adj(AdjA))−1=
If A is a 3×3 matrix and |A|=‌
1
2
 then ∣A−1(Adj(AdjA))−1=
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Let x=α,y=β,z=γ be the unique solution of the system of simultaneous linear equations 2x+3y−2z+4=0,3x−4y+3z+5=0,kx−2y+z+3=0. If α=−2 then k=
Let x=α,y=β,z=γ be the unique solution of the system of simultaneous linear equations 2x+3y−2z+4=0,3x−4y+3z+5=0,kx−2y+z+3=0. If α=−2 then k=
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If the point (x,y) satisfies the equation ‌
x+i(x−2)
3+i
−i=‌
2y+i(1−3y)
i−3
, then x+y=
If the point (x,y) satisfies the equation ‌
x+i(x−2)
3+i
−i=‌
2y+i(1−3y)
i−3
, then x+y=
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If cos‌α+cos‌β+cos‌γ=0 and sin‌α+sin‌β+sin‌γ=0 then cos‌2‌α+cos‌2‌β+cos‌2‌γ=
If cos‌α+cos‌β+cos‌γ=0 and sin‌α+sin‌β+sin‌γ=0 then cos‌2‌α+cos‌2‌β+cos‌2‌γ=
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
One of the values of (−32i)‌
2
5
 is
One of the values of (−32i)‌
2
5
 is
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
If the quadratic equations x2−7x+3c=0 and x2+x−5c=0 have a common root, then for non-zero real value of c the sign of the expression x2−3x+c is
If the quadratic equations x2−7x+3c=0 and x2+x−5c=0 have a common root, then for non-zero real value of c the sign of the expression x2−3x+c is
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Let f(x)=‌
6x2−18x+21
6x2−18x+17
. If m is the maximum value of f(x) and f(x)>n‌∀x∈C Then 14m−7n=
Let f(x)=‌
6x2−18x+21
6x2−18x+17
. If m is the maximum value of f(x) and f(x)>n‌∀x∈C Then 14m−7n=
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If α,β,γ are the roots of the equation x3+x2+x+r=0 and α3+β3+γ3=5, then r=
If α,β,γ are the roots of the equation x3+x2+x+r=0 and α3+β3+γ3=5, then r=
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If ‌
5
2
 is the sum of two roots of the equation 6x6−25x5+31x4−31x2+25x−6=0 then the sum of all non-real roots of the equation is
If ‌
5
2
 is the sum of two roots of the equation 6x6−25x5+31x4−31x2+25x−6=0 then the sum of all non-real roots of the equation is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If 1+√2 and 2−i are the roots of the equation x4+bx3+cx2+dx+e=0 where b,c, d,e are rational numbers, then the roots of the equation bx2+cx+d=0 are
If 1+√2 and 2−i are the roots of the equation x4+bx3+cx2+dx+e=0 where b,c, d,e are rational numbers, then the roots of the equation bx2+cx+d=0 are
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
Let the transformed equation of 2x4−8x3+3x2−1=0 so that the term containing the cubic power of x is absent be 2x4+bx2+cx+d=0. Then b=
Let the transformed equation of 2x4−8x3+3x2−1=0 so that the term containing the cubic power of x is absent be 2x4+bx2+cx+d=0. Then b=
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
a, b, c are three particular speakers among the 10 speakers of a meeting. The number of ways of arranging all the 10 speakers on the dias in a row so that all the three speakers a,b,c do not sit together is
a, b, c are three particular speakers among the 10 speakers of a meeting. The number of ways of arranging all the 10 speakers on the dias in a row so that all the three speakers a,b,c do not sit together is
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
The exponent of 6 in 72! is
The exponent of 6 in 72! is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If the 4‌th ‌ term in the expansion of (‌
x
2
−‌
2y
3
)6 is −20, then xy=
If the 4‌th ‌ term in the expansion of (‌
x
2
−‌
2y
3
)6 is −20, then xy=
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
If ∫‌
x+3
(x−1)2(2x−1)
dx=‌
A
x−1
+B‌log(2x−1)+C‌log(x−1)+K then A+B+C=
If ∫‌
x+3
(x−1)2(2x−1)
dx=‌
A
x−1
+B‌log(2x−1)+C‌log(x−1)+K then A+B+C=
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If ‌
x2+7
(x2+1)(x−2)
=‌
A
x−2
+‌
Bx+C
x2+1
, then the determinant of the matrix (
AB
C‌
2
5
) is
If ‌
x2+7
(x2+1)(x−2)
=‌
A
x−2
+‌
Bx+C
x2+1
, then the determinant of the matrix (
AB
C‌
2
5
) is
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
If tan‌15∘ and tan‌30∘ are the roots of the equation x2+px+q=0, then pq=
Options:
If tan‌15∘ and tan‌30∘ are the roots of the equation x2+px+q=0, then pq=
Options:
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If cos‌x+cos‌y=p,sin‌x+sin‌y=q, then cos(‌
x−y
2
)=
If cos‌x+cos‌y=p,sin‌x+sin‌y=q, then cos(‌
x−y
2
)=
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If A+B+C=‌
3π
2
 then 4‌sin‌A‌sin‌B‌sin‌C+cos‌2‌A+cos‌2‌B+cos‌2‌C=
If A+B+C=‌
3π
2
 then 4‌sin‌A‌sin‌B‌sin‌C+cos‌2‌A+cos‌2‌B+cos‌2‌C=
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
‌
e4x+e−4x+14
4(ex−e−x)2
=
‌
e4x+e−4x+14
4(ex−e−x)2
=
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If tanh‌x=‌
1
2
 then sinh‌2‌x−sech2x=
If tanh‌x=‌
1
2
 then sinh‌2‌x−sech2x=
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
In triangle ABC, if A is acute, C is obtuse, sin‌A=‌
3√3
14
,a=3 and b=5, then c=
In triangle ABC, if A is acute, C is obtuse, sin‌A=‌
3√3
14
,a=3 and b=5, then c=
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
If ∆ denotes the area of triangle ABC, then (b‌sin‌C+c‌sin‌B)(b‌cos‌C+c‌cos‌B)=
If ∆ denotes the area of triangle ABC, then (b‌sin‌C+c‌sin‌B)(b‌cos‌C+c‌cos‌B)=
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
Let A be the area of in-circle and A1,A2,A3 be the areas of ex-circles of a triangle. If A1=4,A2=9,A3=16, then A=
Let A be the area of in-circle and A1,A2,A3 be the areas of ex-circles of a triangle. If A1=4,A2=9,A3=16, then A=
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
If 3i−5j+2k,7i+2j−4k,i−3j+4k and −7i−17j+16k are position vectors of the points A,B,C and D respectively, then the angle between AB and CD is
If 3i−5j+2k,7i+2j−4k,i−3j+4k and −7i−17j+16k are position vectors of the points A,B,C and D respectively, then the angle between AB and CD is
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
If A(2i+j−k),B(λi+5j+4k),C(−4i+3j+2k) and D(−i−2j+3k) are four points in space such that AB=xAC+yAD for some real numbers x≠0,y≠0 then 17(λ+9)=
If A(2i+j−k),B(λi+5j+4k),C(−4i+3j+2k) and D(−i−2j+3k) are four points in space such that AB=xAC+yAD for some real numbers x≠0,y≠0 then 17(λ+9)=
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Let a plane P has the points i,j and i+j+k. Let L be the line through the point A and parallel to the vector i−j+k. If the plane P and line L intersect at a point B(0,3,2) and the distance from A to B is 3 units, then equations of the normal to the plane P through A are
Let a plane P has the points i,j and i+j+k. Let L be the line through the point A and parallel to the vector i−j+k. If the plane P and line L intersect at a point B(0,3,2) and the distance from A to B is 3 units, then equations of the normal to the plane P through A are
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
Let a=i+j+k and b be two vectors such that a⋅b=1,cos(a,b)=‌
1
3
 and the components of b w.r.t (i,j,k) be integers. Then the number of possible vectors that represent b is
Let a=i+j+k and b be two vectors such that a⋅b=1,cos(a,b)=‌
1
3
 and the components of b w.r.t (i,j,k) be integers. Then the number of possible vectors that represent b is
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
Let π1 be the plane passing through the point 2i−j+k and perpendicular to the vector ai+2j−3k and π2 be the plane passing through the point i+2j−k and perpendicular to the vector i−2j+k. If θ is the angle between the planes π1 and π2 and cos‌θ=−√‌
3
7
, then the integral value of a is
Let π1 be the plane passing through the point 2i−j+k and perpendicular to the vector ai+2j−3k and π2 be the plane passing through the point i+2j−k and perpendicular to the vector i−2j+k. If θ is the angle between the planes π1 and π2 and cos‌θ=−√‌
3
7
, then the integral value of a is
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If a and b are two vectors such that a=2i+2j+pk,|b|=7,a⋅b=4 and |a×b|=5√17 then p=
If a and b are two vectors such that a=2i+2j+pk,|b|=7,a⋅b=4 and |a×b|=5√17 then p=
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
The mean deviation from the mean of the discrete data 1,3,4,7,11,18,29,47,78 is
The mean deviation from the mean of the discrete data 1,3,4,7,11,18,29,47,78 is
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is
When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
Let A,B,C be three pairwise independent events of a random experiment. If P(B∪C)=‌
1
2
,P(A)>0,P(B)=b and P(C)=c, then P((B∩C)∣A)=
Let A,B,C be three pairwise independent events of a random experiment. If P(B∪C)=‌
1
2
,P(A)>0,P(B)=b and P(C)=c, then P((B∩C)∣A)=
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of 4 . If p is the conditional probability that number 4 has appeared atleast once, then 3p+2=
Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of 4 . If p is the conditional probability that number 4 has appeared atleast once, then 3p+2=
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
In a random experiment of throwing 5 coins, the number of heads is defined as a random variable. The mean of the random variable is
In a random experiment of throwing 5 coins, the number of heads is defined as a random variable. The mean of the random variable is
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
The variance of a Poisson variate X is 2 . Then P(X≥3)=
The variance of a Poisson variate X is 2 . Then P(X≥3)=
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If the perimeter of a triangle is 20 and two of its vertices are (−5,0) and (6,0), then the locus of the third vertex is
If the perimeter of a triangle is 20 and two of its vertices are (−5,0) and (6,0), then the locus of the third vertex is
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The transformed equation of 3x2+4xy+y2−8x−4y−4=0 is f(X,Y)=aX2+2hXY+bY2+c=0 when the origin is shifted to a new point by the translation of axes. Then f(1,1)=
The transformed equation of 3x2+4xy+y2−8x−4y−4=0 is f(X,Y)=aX2+2hXY+bY2+c=0 when the origin is shifted to a new point by the translation of axes. Then f(1,1)=
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
If the line 2x−3y+4=0 divides the line segment joining the points A(−2,3) and B(3,−2) in the ratio m:n, then the point which divides AB in the ratio −4m:3n is
If the line 2x−3y+4=0 divides the line segment joining the points A(−2,3) and B(3,−2) in the ratio m:n, then the point which divides AB in the ratio −4m:3n is
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
If the lines L1≡2x+y+3=0,L2≡kx+2y−3=0‌‌ and L3≡3x−2y+1=0 are concurrent then the cosine of the acute angle between the lines L2=0 and 2x−5y+7=0 is
If the lines L1≡2x+y+3=0,L2≡kx+2y−3=0‌‌ and L3≡3x−2y+1=0 are concurrent then the cosine of the acute angle between the lines L2=0 and 2x−5y+7=0 is
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
If Q is the image of the point P(1,1) with respect to the straight line x+y+1=0, then the length of the perpendicular drawn from Q to the line 3x−4y+3=0 is
If Q is the image of the point P(1,1) with respect to the straight line x+y+1=0, then the length of the perpendicular drawn from Q to the line 3x−4y+3=0 is
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The centroid of the triangle formed by the lines x−3y+3=0,x+3y+3=0, x+y−1=0 is
The centroid of the triangle formed by the lines x−3y+3=0,x+3y+3=0, x+y−1=0 is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If the slope of one of the lines represented by 5x2+‌
40
3
xy+ky2=0 is 3 , then the angle between the pair of lines is
If the slope of one of the lines represented by 5x2+‌
40
3
xy+ky2=0 is 3 , then the angle between the pair of lines is
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If a line L is common to the pairs of lines 6x2−xy−12y2=0 and 15x2+14xy−8y2=0, then the combined equation the other two lines is
If a line L is common to the pairs of lines 6x2−xy−12y2=0 and 15x2+14xy−8y2=0, then the combined equation the other two lines is
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If L is a line passing through the point (−1,1) and parallel to the common line of the pairs of lines 6x2−xy−12y2=0 and 15x2+14xy−8y2=0, then the equation of pair of lines joining the origin to the points of intersection of the curve 2x2−xy−y2+x−y=0 and the line L is
If L is a line passing through the point (−1,1) and parallel to the common line of the pairs of lines 6x2−xy−12y2=0 and 15x2+14xy−8y2=0, then the equation of pair of lines joining the origin to the points of intersection of the curve 2x2−xy−y2+x−y=0 and the line L is
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
From a point A(0,3) on the circle (x+2)2+(y−3)2=4, a chord AB is drawn and it is extended to a point Q such that AQ=2AB. Then the locus of Q is
From a point A(0,3) on the circle (x+2)2+(y−3)2=4, a chord AB is drawn and it is extended to a point Q such that AQ=2AB. Then the locus of Q is
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If m1,m2 are the slopes of the tangents drawn from a point (1,−3) to the circle x2+y2−6x+4y+12=0 then 9(m12+m22)=
If m1,m2 are the slopes of the tangents drawn from a point (1,−3) to the circle x2+y2−6x+4y+12=0 then 9(m12+m22)=
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
If A,B are the points of contact of the tangents drawn from the point P(−2,−3) to the circle x2+y2−8x−10y+5=0 and the chord AB subtends an angle θ at P then tan‌θ=
If A,B are the points of contact of the tangents drawn from the point P(−2,−3) to the circle x2+y2−8x−10y+5=0 and the chord AB subtends an angle θ at P then tan‌θ=
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The equation of the transverse common tangent of the circles x2+y2−6x−8y+9=0 and x2+y2+2x−2y+1=0 is
The equation of the transverse common tangent of the circles x2+y2−6x−8y+9=0 and x2+y2+2x−2y+1=0 is
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If θ is the angle between the circles x2+y2−2x−4y−4=0 and x2+y2−8x−12y+43=0 then |7‌sec‌θ−18‌cos‌θ|=
If θ is the angle between the circles x2+y2−2x−4y−4=0 and x2+y2−8x−12y+43=0 then |7‌sec‌θ−18‌cos‌θ|=
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
If (0,3∕4) is the radical centre of the circles S≡x2+y2+αx+6y=0, S′≡x2+y2+2αx+αy+6=0 and S′′≡x2+y2+6αx−αy+3=0 then the distance between the radical centre and the centre of the circle S′=0 is
If (0,3∕4) is the radical centre of the circles S≡x2+y2+αx+6y=0, S′≡x2+y2+2αx+αy+6=0 and S′′≡x2+y2+6αx−αy+3=0 then the distance between the radical centre and the centre of the circle S′=0 is
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
The vertex and the focus of the parabola 2x2+5y−6x+1=0 respectively, are
The vertex and the focus of the parabola 2x2+5y−6x+1=0 respectively, are
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The axis of a parabola is along the line y=x and the distance of its vertex A from (0,0) is √2 and that of its focus S from (0,0) is 2√2. If A and S lie in first quadrant, then the equation of the parabola in parametric form is
The axis of a parabola is along the line y=x and the distance of its vertex A from (0,0) is √2 and that of its focus S from (0,0) is 2√2. If A and S lie in first quadrant, then the equation of the parabola in parametric form is
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
Let S≡‌
x2
a2
+‌
y2
b2
−1=0,S′≡‌
x2
α2
+‌
y2
β2
−1=0 be two intersecting ellipses. If p(a‌cos‌θ,b‌sin‌θ) and Q(a‌cos(‌
π
2
+θ),b‌sin(‌
π
2
+θ)) are their points of intersection then ‌
1
2
(a2β2+b2α2)=
Let S≡‌
x2
a2
+‌
y2
b2
−1=0,S′≡‌
x2
α2
+‌
y2
β2
−1=0 be two intersecting ellipses. If p(a‌cos‌θ,b‌sin‌θ) and Q(a‌cos(‌
π
2
+θ),b‌sin(‌
π
2
+θ)) are their points of intersection then ‌
1
2
(a2β2+b2α2)=
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
P(θ1) and Q(θ2) are two points on the ellipse ‌
x2
a2
+‌
y2
b2
=1 with eccentricity e. If PSQ is a focal chord and tan(‌
θ1
2
)‌tan(‌
θ2
2
)=−(2√2+3), then e and S are
P(θ1) and Q(θ2) are two points on the ellipse ‌
x2
a2
+‌
y2
b2
=1 with eccentricity e. If PSQ is a focal chord and tan(‌
θ1
2
)‌tan(‌
θ2
2
)=−(2√2+3), then e and S are
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
Let S be the focus of the hyperbola ‌
x2
16
−‌
y2
9
=1 lying on the positive X− axis and P(5,y1) be point on the hyperbola. Then SP=
Let S be the focus of the hyperbola ‌
x2
16
−‌
y2
9
=1 lying on the positive X− axis and P(5,y1) be point on the hyperbola. Then SP=
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
If P(θ)=(x1,‌
3√5
2
),0<θ<‌
π
2
 is a point on the hyperbola ‌
x2
25
−‌
y2
9
=1, where θ is the parameter in its parametric form, then 2x1+9sin2θ=
If P(θ)=(x1,‌
3√5
2
),0<θ<‌
π
2
 is a point on the hyperbola ‌
x2
25
−‌
y2
9
=1, where θ is the parameter in its parametric form, then 2x1+9sin2θ=
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
If the points A(1,3,5),B(2,4,6),C(4,5,k) form a right angled triangle then the number of possible values of k is
If the points A(1,3,5),B(2,4,6),C(4,5,k) form a right angled triangle then the number of possible values of k is
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Let A=(3,4,0),B=(4,4,4),C=(−6,2,3) and D=(1,1,2). If θ is the acute angle between the lines AB and CD then cos‌θ=
Let A=(3,4,0),B=(4,4,4),C=(−6,2,3) and D=(1,1,2). If θ is the acute angle between the lines AB and CD then cos‌θ=
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
A plane containing two lines whose direction ratios are (−1,2,1) and (1,3,2) passes through the point (2,1,k). If this plane also passes through the point (3,−1,4), then k=
A plane containing two lines whose direction ratios are (−1,2,1) and (1,3,2) passes through the point (2,1,k). If this plane also passes through the point (3,−1,4), then k=
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Let A=(aij) be an n×n matrix defined by aij={
ki‌∀i=j
0‌‌ otherwise ‌.
 If m= trace of A and
lim
k→1
‌
n−m
1−k
=171 then the value of n is
Let A=(aij) be an n×n matrix defined by aij={
ki‌∀i=j
0‌‌ otherwise ‌.
 If m= trace of A and
lim
k→1
‌
n−m
1−k
=171 then the value of n is
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
lim
x→∞
x3[√x2+√x4+1−√2x]=
lim
x→∞
x3[√x2+√x4+1−√2x]=
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Let f(x)={
3−x‌ if ‌x<−3
6‌ if ‌−3≤x≤3
3+x‌ if ‌x>3.
 Let α be the number of points of discontinuity of f and β be the number of points where f is not differentiable. Then α+β=
Let f(x)={
3−x‌ if ‌x<−3
6‌ if ‌−3≤x≤3
3+x‌ if ‌x>3.
 Let α be the number of points of discontinuity of f and β be the number of points where f is not differentiable. Then α+β=
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
If af(x)+bf(‌
1
x
)=x+1, and ‌
d
dx
(x2f(x))=2x2+2x+‌
1
3
, then a−b=
If af(x)+bf(‌
1
x
)=x+1, and ‌
d
dx
(x2f(x))=2x2+2x+‌
1
3
, then a−b=
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If f(x)=sin(cosh(‌
x2+1
x2+2
)) then f′(1)=
If f(x)=sin(cosh(‌
x2+1
x2+2
)) then f′(1)=
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
If an error of 0.02 sq.cm is found in the surface area of a sphere when its radius is measured as 10cm, then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is
If an error of 0.02 sq.cm is found in the surface area of a sphere when its radius is measured as 10cm, then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If θ is the angle between the curves y2=4x and x2+y2=5 then |tan‌θ|=
If θ is the angle between the curves y2=4x and x2+y2=5 then |tan‌θ|=
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
The local maximum value of the function f(x)=−(x−2)3(x+2)2 is
The local maximum value of the function f(x)=−(x−2)3(x+2)2 is
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
If ∫‌
1+cos‌8‌x
tan‌2‌x−cot‌2‌x
dx=f(x)⋅cos(g(x))+c, then f(‌
1
4
)+g(‌
1
4
)=
If ∫‌
1+cos‌8‌x
tan‌2‌x−cot‌2‌x
dx=f(x)⋅cos(g(x))+c, then f(‌
1
4
)+g(‌
1
4
)=
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
Let x≠‌
−3
5
,‌
2
5
, if f(‌
2x+1
5x+3
)=x+2, then ∫f(x)dx=
Let x≠‌
−3
5
,‌
2
5
, if f(‌
2x+1
5x+3
)=x+2, then ∫f(x)dx=
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
If ∫ex‌cos‌x‌d‌x=‌
ex
2
(cos‌x+sin‌x) and ∫‌
cos(log(
2x+3
3−2x
))
(3−2x)2
dx= ‌
f(x)
24
[cos(g(x))+sin(g(x))]+c then g(1)=
If ∫ex‌cos‌x‌d‌x=‌
ex
2
(cos‌x+sin‌x) and ∫‌
cos(log(
2x+3
3−2x
))
(3−2x)2
dx= ‌
f(x)
24
[cos(g(x))+sin(g(x))]+c then g(1)=
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
2
∫
1
x√4−x2dx=
2
∫
1
x√4−x2dx=
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
If [x] denotes the greatest integer function of x and
3∕2
∫
−3∕2
[2x−3]dx=k, then |k+‌
1
2
|=
If [x] denotes the greatest integer function of x and
3∕2
∫
−3∕2
[2x−3]dx=k, then |k+‌
1
2
|=
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The differential equation corresponding to the family of curves given by ax2+by2=1 where a and b are arbitrary constants is
The differential equation corresponding to the family of curves given by ax2+by2=1 where a and b are arbitrary constants is
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
For the differential equation √‌
d2y
dx2
=‌3√[y‌
dy
dx
+x‌sin(‌
dy
dx
)]2
For the differential equation √‌
d2y
dx2
=‌3√[y‌
dy
dx
+x‌sin(‌
dy
dx
)]2
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The general solution of the differential equation ‌
dy
dx
=‌
xy+x−2y−2
xy−2x+y−2
 is
The general solution of the differential equation ‌
dy
dx
=‌
xy+x−2y−2
xy−2x+y−2
 is
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Which of the following interaction is responsible for beta decay?
Which of the following interaction is responsible for beta decay?
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
In a RC circuit, where R is resistance and C is capacitance which of the following has the dimension of time.
In a RC circuit, where R is resistance and C is capacitance which of the following has the dimension of time.
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be

A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be

Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
Assertion(A): The zero velocity of a particle at any instant always implies zero acceleration at that instant
Reason(R) : A body is momentarily at rest when reverses its direction of motion.
The correct option among the following is
Assertion(A): The zero velocity of a particle at any instant always implies zero acceleration at that instant
Reason(R) : A body is momentarily at rest when reverses its direction of motion.
The correct option among the following is
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
A river has a steady speed of ' v '. A man swims upstream at a distance of ' d ' and swims back to the starting point in total time ' t '. The man can swim at a speed of ' 2v ' in still water. If the time taken by the man in still water is'to' to complete the same length of swim, then ‌
t
t0
 is
A river has a steady speed of ' v '. A man swims upstream at a distance of ' d ' and swims back to the starting point in total time ' t '. The man can swim at a speed of ' 2v ' in still water. If the time taken by the man in still water is'to' to complete the same length of swim, then ‌
t
t0
 is
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A projectile is given an initial velocity of (3i+4j)m∕s where,
^
i
 is along the ground and
^
j
 is along the vertical. Assuming g=10m∕s2, if the equation of its trajectory can be written as ‌
1
9
[βx+γx2], then the value of γ is
A projectile is given an initial velocity of (3i+4j)m∕s where,
^
i
 is along the ground and
^
j
 is along the vertical. Assuming g=10m∕s2, if the equation of its trajectory can be written as ‌
1
9
[βx+γx2], then the value of γ is
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A block is placed on a parabolic shape ramp given by equation y=‌
x2
20
. If the coefficient of static friction (µs) is 0.5, then what is the maximum height above the ground at which the block can be placed without slipping?
A block is placed on a parabolic shape ramp given by equation y=‌
x2
20
. If the coefficient of static friction (µs) is 0.5, then what is the maximum height above the ground at which the block can be placed without slipping?
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A small object slides down with initial velocity equal to zero from the top of a smooth hill of height H. The other end of the hill is horizontal and is at height ‌
H
2
 as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is

A small object slides down with initial velocity equal to zero from the top of a smooth hill of height H. The other end of the hill is horizontal and is at height ‌
H
2
 as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is

Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A moving particle collides with a stationary particle of mass ‌
1
n
 times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is
A moving particle collides with a stationary particle of mass ‌
1
n
 times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
A solid cylinder of mass m and radius R rolls down an inclined plane of height 30m without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [ use g=10m∕s2]
A solid cylinder of mass m and radius R rolls down an inclined plane of height 30m without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [ use g=10m∕s2]
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A simple pendulum consists of a small sphere of mass ' m ' suspended by a thread of length ' l '. The sphere carries a positive charge q. The pendulum is allowed to do small oscillations in a uniform electric field E with direction vertically upwards. The time period of oscillation is
A simple pendulum consists of a small sphere of mass ' m ' suspended by a thread of length ' l '. The sphere carries a positive charge q. The pendulum is allowed to do small oscillations in a uniform electric field E with direction vertically upwards. The time period of oscillation is
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
A rocket fired vertically with a speed of 4km∕s from the earth's surface. How far from the earth does the rocket go before returning to the earth?
(Take radius of earth =6.4×106m and g=10m∕s2 )
A rocket fired vertically with a speed of 4km∕s from the earth's surface. How far from the earth does the rocket go before returning to the earth?
(Take radius of earth =6.4×106m and g=10m∕s2 )
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
A swimming pool has a depth of 22m and area 700m2. Calculate fractional change ‌
∆v
v
 of water at the bottom of the swimming pool. Given that the bulk modulus of water is 2.2×109Nm−2,g=10m∕s2, and density of water 1000kg∕m3.
A swimming pool has a depth of 22m and area 700m2. Calculate fractional change ‌
∆v
v
 of water at the bottom of the swimming pool. Given that the bulk modulus of water is 2.2×109Nm−2,g=10m∕s2, and density of water 1000kg∕m3.
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
A hollow spherical body of outer and inner radii of 4cm and 2cm respectively floats half submerged in a liquid of density 2.0g∕cm3. The density of the material of the sphere is
A hollow spherical body of outer and inner radii of 4cm and 2cm respectively floats half submerged in a liquid of density 2.0g∕cm3. The density of the material of the sphere is
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
What is the terminal velocity of a rain drop of radius 0.02mm ?
[Note that the coefficient of viscosity of air is 1.8×10−5N∕m2, density of water is 1000Kg∕m3. Use g=10m∕s2 and density of air can be neglected in comparison with density of water]
What is the terminal velocity of a rain drop of radius 0.02mm ?
[Note that the coefficient of viscosity of air is 1.8×10−5N∕m2, density of water is 1000Kg∕m3. Use g=10m∕s2 and density of air can be neglected in comparison with density of water]
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
A hole of diameter 5cm is drilled in a metal sheet at 30‌∘C. The linear expansion of metal is 2×10−5K−1. The diameter of the hole when the temperature is raised to 230∘C, is equal to
A hole of diameter 5cm is drilled in a metal sheet at 30‌∘C. The linear expansion of metal is 2×10−5K−1. The diameter of the hole when the temperature is raised to 230∘C, is equal to
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A metal cube absorbs 2100.0J of heat when its temperature is raised by 2∘C. If the specific heat of the metal is 900Jkg−1K−1, then the mass of the cube is
A metal cube absorbs 2100.0J of heat when its temperature is raised by 2∘C. If the specific heat of the metal is 900Jkg−1K−1, then the mass of the cube is
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
The net work done by an ideal gas going through the cycle as shown in the P−V diagram below is
The net work done by an ideal gas going through the cycle as shown in the P−V diagram below is
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
A diatomic gas (CP=7∕2R) does 200J of work when it is expanded isobarically. The heat given to the gas in the process is
A diatomic gas (CP=7∕2R) does 200J of work when it is expanded isobarically. The heat given to the gas in the process is
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
Statement (I) : Gas thermometers are less sensitive than liquid thermometers.
Statement (II) : The ratio of universal gas constant and avagadro's number is called Boltzman's constant.
Statement (III) : The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.
The correct option among the following is
Statement (I) : Gas thermometers are less sensitive than liquid thermometers.
Statement (II) : The ratio of universal gas constant and avagadro's number is called Boltzman's constant.
Statement (III) : The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.
The correct option among the following is
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
The distance between two successive minima of a transverse wave is 2.7m. Five crests of the wave pass a given point along the direction of travel every 15.0s. The speed of the wave is
The distance between two successive minima of a transverse wave is 2.7m. Five crests of the wave pass a given point along the direction of travel every 15.0s. The speed of the wave is
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
A convex lens focusses an object 20cm from it on a screen placed 5cm away from it. A glass plate (refractive index =‌
7
5
 ) of thickness 1.4cm is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?
A convex lens focusses an object 20cm from it on a screen placed 5cm away from it. A glass plate (refractive index =‌
7
5
 ) of thickness 1.4cm is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
The angular width of a fringe in a double slit experiment is found to be 0.2∘ on a screen 1m away. The wavelength of light used is 600nm. The change in angular width of the fridge if the entire measurement system is immersed in water is
[Use refractive index of water as 4∕3 ]
The angular width of a fringe in a double slit experiment is found to be 0.2∘ on a screen 1m away. The wavelength of light used is 600nm. The change in angular width of the fridge if the entire measurement system is immersed in water is
[Use refractive index of water as 4∕3 ]
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
A large metal plate has a surface charge density of 8.85×10−6C∕m2. An electron having initial kinetic energy of 8×10−17J is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is
[ Take ε0=8.85×10−12C2∕Nm2]
A large metal plate has a surface charge density of 8.85×10−6C∕m2. An electron having initial kinetic energy of 8×10−17J is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is
[ Take ε0=8.85×10−12C2∕Nm2]
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
The equivalent capacitance between points A and B is
The equivalent capacitance between points A and B is
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by 6%. The percentage increase in its length is
A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by 6%. The percentage increase in its length is
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
Find the current in the three resistors as shown in the following figure?
Find the current in the three resistors as shown in the following figure?
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
A horizontal wire carries 160A current below which another wire of linear density 10g∕m carrying a current is kept at 4cm distance. If the wire is kept below hangs in air, what is the current in this wire when the direction of current in both the wires is same?
(g=10m∕s2‌ and ‌µ0=4π×10−7)
A horizontal wire carries 160A current below which another wire of linear density 10g∕m carrying a current is kept at 4cm distance. If the wire is kept below hangs in air, what is the current in this wire when the direction of current in both the wires is same?
(g=10m∕s2‌ and ‌µ0=4π×10−7)
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A long solenoid has 70turns∕cm and carries current I. An electron moves within the solenoid in a circle of radius 2.5cm perpendicular to the solenoid axis. If the speed of the electron is 4.4×106m∕s then the current I in the solenoid is
(Take µ0=4π×10−7SI unit, mass of electron =9×10−31kg, charge of electron = 1.6×10−19C)
A long solenoid has 70turns∕cm and carries current I. An electron moves within the solenoid in a circle of radius 2.5cm perpendicular to the solenoid axis. If the speed of the electron is 4.4×106m∕s then the current I in the solenoid is
(Take µ0=4π×10−7SI unit, mass of electron =9×10−31kg, charge of electron = 1.6×10−19C)
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
Assertion (A) : The magnetic field lines are continuous and form closed loops.
Reason (R) : Magnetic monopole does not exist.
The correct option among the following is
Assertion (A) : The magnetic field lines are continuous and form closed loops.
Reason (R) : Magnetic monopole does not exist.
The correct option among the following is
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A flat circular coil has 100 turns of wire of radius 10cm. A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of 0.1T∕sec. the induced emf in the coil is:
A flat circular coil has 100 turns of wire of radius 10cm. A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of 0.1T∕sec. the induced emf in the coil is:
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A 2µF capacitor is charged to 50V by a battery. The battery is removed after capacitor is fully charged. At time t=0, a 10mH coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is
A 2µF capacitor is charged to 50V by a battery. The battery is removed after capacitor is fully charged. At time t=0, a 10mH coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
An electromagnetic wave has its electric and magnetic fields given by
→
E
(t)=
→
E
m‌sin(kx−ωt)
→
B
(t)=
→
B
m‌sin(kx−ωt)
If the direction of
→
E
m&
→
B
m are in the direction of
^
i
+
^
j
 and
^
i
−
^
j
 respectively, the unit vector that gives the direction of propagation of the wave is
An electromagnetic wave has its electric and magnetic fields given by
→
E
(t)=
→
E
m‌sin(kx−ωt)
→
B
(t)=
→
B
m‌sin(kx−ωt)
If the direction of
→
E
m&
→
B
m are in the direction of
^
i
+
^
j
 and
^
i
−
^
j
 respectively, the unit vector that gives the direction of propagation of the wave is
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
The value of Plank's constant, if the slope of the graph of stopping potential vs frequency of incident light is 4×10−15Vs is (given charge of an electron =1.6×10−19C )
The value of Plank's constant, if the slope of the graph of stopping potential vs frequency of incident light is 4×10−15Vs is (given charge of an electron =1.6×10−19C )
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10W of power, the force exerted by it on the surface is
A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10W of power, the force exerted by it on the surface is
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
If the series limit frequency of Balmer series is vB, then the series limit frequency of the Brackett series is
If the series limit frequency of Balmer series is vB, then the series limit frequency of the Brackett series is
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Consider a nucleus ‌3060×. It's approximate density is
(Take 1amu=1.6×10−27kg,Ro=1.2×10−15m.)
Consider a nucleus ‌3060×. It's approximate density is
(Take 1amu=1.6×10−27kg,Ro=1.2×10−15m.)
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
The resistivity of a material is found to be 108Ω−m. Then the material would be
The resistivity of a material is found to be 108Ω−m. Then the material would be
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
The behaviour of the circuit is like gate

The behaviour of the circuit is like gate

Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A message signal of frequency 15kHz is used to modulate a carrier of frequency vc. If the side bands produced are 1515kHz and 1485kHz, then vc is
A message signal of frequency 15kHz is used to modulate a carrier of frequency vc. If the side bands produced are 1515kHz and 1485kHz, then vc is
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The total number of spectral lines observed when electron returns from the 6‌th ‌ shell until the 2‌nd ‌ shell in hydrogen atom is
The total number of spectral lines observed when electron returns from the 6‌th ‌ shell until the 2‌nd ‌ shell in hydrogen atom is
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The orbital angular momentum of an electron in d orbital is equal to
The orbital angular momentum of an electron in d orbital is equal to
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
The correct order of decreasing acidic nature of oxides
The correct order of decreasing acidic nature of oxides
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
The change in enthalpy [∆H] in kJmol−1 for the reaction is Mg+2F→MgF2
Given: EA of F=328kJmol‌−1,IE1 of Mg=737kJmol−1,IE2 of Mg=1451kJmol−1
The change in enthalpy [∆H] in kJmol−1 for the reaction is Mg+2F→MgF2
Given: EA of F=328kJmol‌−1,IE1 of Mg=737kJmol−1,IE2 of Mg=1451kJmol−1
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
Dipole - induced dipole interactions are present between which of the following pairs?
Dipole - induced dipole interactions are present between which of the following pairs?
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
According to the Lewis formula of O3, the correct option is
According to the Lewis formula of O3, the correct option is
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
A gaseous mixture of 2 moles of A,3 moles of B,5 moles of C and 10 moles of D contained in a vessel. Assuming that gases are ideal and partial pressure of C is 1.5atm, the total pressure is
A gaseous mixture of 2 moles of A,3 moles of B,5 moles of C and 10 moles of D contained in a vessel. Assuming that gases are ideal and partial pressure of C is 1.5atm, the total pressure is
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The rate constant of a reaction is increased 4 times after addition of catalyst to the reaction mixture at the same temperature of 27∘C. The change in the activation energy of this reaction is
( Take ln(‌
1
4
)=−1.386,R=8.314)
The rate constant of a reaction is increased 4 times after addition of catalyst to the reaction mixture at the same temperature of 27∘C. The change in the activation energy of this reaction is
( Take ln(‌
1
4
)=−1.386,R=8.314)
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
A cube of edge length 1cm is divided into smaller cubes of uniform size of length 1nm. Assuming that no voids are present, the ratio of total surface area of all the cubes of 1nm edge length to the surface area of the initial cube is
A cube of edge length 1cm is divided into smaller cubes of uniform size of length 1nm. Assuming that no voids are present, the ratio of total surface area of all the cubes of 1nm edge length to the surface area of the initial cube is
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
Calculate the number of moles of NaOH required to completely neutralise 100g of 118% oleum
Calculate the number of moles of NaOH required to completely neutralise 100g of 118% oleum
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
A certain mass of a gas was brought from state A to B by following three different paths, namely 1, 2 and 3, respectively. Which of the following relations is correct for the work done?
A certain mass of a gas was brought from state A to B by following three different paths, namely 1, 2 and 3, respectively. Which of the following relations is correct for the work done?
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
For the formation of ammonia gas from its constituent elements, the KP∕KC is
For the formation of ammonia gas from its constituent elements, the KP∕KC is
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt

The correct match is:

The correct match is:
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
The most effective water softening method is
The most effective water softening method is
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
Potassium superoxide on hydrolysis gives
Potassium superoxide on hydrolysis gives
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
When aluminium chloride is dissolved in water, it gives
When aluminium chloride is dissolved in water, it gives
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Among the following given substances, the one with zero ∆fH∘ is
Among the following given substances, the one with zero ∆fH∘ is
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
Identify the chiral molecule among the following.
Identify the chiral molecule among the following.
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
The most suitable solvent for Wurtz reaction is
The most suitable solvent for Wurtz reaction is
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
Propyne was subjected to a reaction with HgSO4∕ dil. H2SO4, which resulted in a product P. The product P was heated with Ba(OH)2 to give the product Q. The molecular formula of the product Q is
Propyne was subjected to a reaction with HgSO4∕ dil. H2SO4, which resulted in a product P. The product P was heated with Ba(OH)2 to give the product Q. The molecular formula of the product Q is
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The correct option for axial distances and axial angles for hexagonal crystal system is
The correct option for axial distances and axial angles for hexagonal crystal system is
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
Which of the following is/are "not correct" for CH3OH+CH3COOH mixture solution?
a) ‌‌∆H‌mix ‌<0
b) Does not obey Raoult's law
c) ‌‌∆H‌mix ‌>0
d) An example of ideal solution
Which of the following is/are "not correct" for CH3OH+CH3COOH mixture solution?
a) ‌‌∆H‌mix ‌<0
b) Does not obey Raoult's law
c) ‌‌∆H‌mix ‌>0
d) An example of ideal solution
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
Henry's law is valid for
A) Ammonia gas dissolution in water
B) O2 gas dissolution in unsaturated blood
C) O2 dissolution in water
D) CO2 dissolution in water
Henry's law is valid for
A) Ammonia gas dissolution in water
B) O2 gas dissolution in unsaturated blood
C) O2 dissolution in water
D) CO2 dissolution in water
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
On passing a current of 1.2 A through a solution of salt of copper for 40min,0.96g of copper was deposited. The equivalent weight of copper in g is
On passing a current of 1.2 A through a solution of salt of copper for 40min,0.96g of copper was deposited. The equivalent weight of copper in g is
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
Half life periods for a reaction at initial concentrations of 0.1M and 0.01M are 5 and 50 minutes, respectively. The order of reaction is
Half life periods for a reaction at initial concentrations of 0.1M and 0.01M are 5 and 50 minutes, respectively. The order of reaction is
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
Catalysts in the following reactions are
I) CH3COOCH3(l)+H2O(l)→CH3COOH(aq)+CH3OH(l)
II) 2SO2(g)→2SO3(g)
III) 2SO2(g)+O2(g)→2SO3(g)
IV) ‌‌N2(g)+3H2(g)→2NH3(g)
Catalysts in the following reactions are
I) CH3COOCH3(l)+H2O(l)→CH3COOH(aq)+CH3OH(l)
II) 2SO2(g)→2SO3(g)
III) 2SO2(g)+O2(g)→2SO3(g)
IV) ‌‌N2(g)+3H2(g)→2NH3(g)
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
The total number of paramagnetic gaseous products formed in all the following reactions [A+B+C]
(A) NH4NO3
∆
⟶
 Products
(B) 3NaNO2+3H2SO4⟶ Products
(C) Pb(NO3)2
673K
⟶
 Products
The total number of paramagnetic gaseous products formed in all the following reactions [A+B+C]
(A) NH4NO3
∆
⟶
 Products
(B) 3NaNO2+3H2SO4⟶ Products
(C) Pb(NO3)2
673K
⟶
 Products
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
The main products P and Q of the following unbalanced disproportionation reaction are
SeCl2→P+Q
The main products P and Q of the following unbalanced disproportionation reaction are
SeCl2→P+Q
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
The correct order of acidity of HClO,HBrO and HIO is
The correct order of acidity of HClO,HBrO and HIO is
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
The linear molecule among the following is
The linear molecule among the following is
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Assertion (A) : In general, transition metals have high melting points.
Reason (R) : More number of electrons from '(n-1)d' and 'ns' are involved in interatomic metallic bonding.
The correct option among the following is
Assertion (A) : In general, transition metals have high melting points.
Reason (R) : More number of electrons from '(n-1)d' and 'ns' are involved in interatomic metallic bonding.
The correct option among the following is
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
Among the given complexes that possess "CO" ligand bridges are
[Co2(CO)8]
I
‌‌‌‌
[Fe3(CO)12]
II
‌‌‌‌
[Mn2(CO)10]
III
‌‌‌‌
[Fe2(CO)9]
IV
Among the given complexes that possess "CO" ligand bridges are
[Co2(CO)8]
I
‌‌‌‌
[Fe3(CO)12]
II
‌‌‌‌
[Mn2(CO)10]
III
‌‌‌‌
[Fe2(CO)9]
IV
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
The amount of sucrose needed to produce 1 mole of glucose using acid hydrolysis is
The amount of sucrose needed to produce 1 mole of glucose using acid hydrolysis is
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
The order of reactivity of the following compounds towards dilute aqueous KOH in SN1 reaction is
CH3CH2CH2CH2Br
I
‌‌‌‌‌
H3CCH2CHBrCH3
II
‌‌‌‌‌
(CH3)CHCH2Br
III
‌‌‌‌‌
(CH3)3CBr
IV
The order of reactivity of the following compounds towards dilute aqueous KOH in SN1 reaction is
CH3CH2CH2CH2Br
I
‌‌‌‌‌
H3CCH2CHBrCH3
II
‌‌‌‌‌
(CH3)CHCH2Br
III
‌‌‌‌‌
(CH3)3CBr
IV
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
A,B,C,D in the following reactions are

A,B,C,D in the following reactions are

Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Which of the following statements are correct for phenol?
(A) In general, phenol is more acidic than alcohol.
(B) Phenol is used in the production of melamine plastic.
(C) Phenol gives violet colour with neutral ferric chloride solution.
(D) Phenol when heated with acetyl chloride gives phenetole.
Which of the following statements are correct for phenol?
(A) In general, phenol is more acidic than alcohol.
(B) Phenol is used in the production of melamine plastic.
(C) Phenol gives violet colour with neutral ferric chloride solution.
(D) Phenol when heated with acetyl chloride gives phenetole.
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
The major product in the following reactions is

The major product in the following reactions is

Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
The major product of the following reaction is

The major product of the following reaction is

Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
n− Propanol on treatment with concentrated HBr gives P. The product P on reaction with KCN gave the product Q. The product Q on heating with aqueous acidic solution, furnished the product R. The product ' R ' is
n− Propanol on treatment with concentrated HBr gives P. The product P on reaction with KCN gave the product Q. The product Q on heating with aqueous acidic solution, furnished the product R. The product ' R ' is
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
The major product of the following synthetic sequence is

The major product of the following synthetic sequence is

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