AP EAPCET 2024 - 19th May Evening Shift
Paper was held on
Sun, May 19, 2024 9:30 AM
Chemistry
1
In the ground state of hydrogen atom, electron absorbs 1.5 times energy than the minimum energy $\left(2.18 \times 10^{-18} \mathrm{~J}\right)$ to escape from the atom. The wavelength of the emitted electron (in $m$ ) is ( $m_e=9 \times 10^{-31} \mathrm{~kg}$ )
2
A golf ball of mass $m \mathrm{~g}$ has a speed of $50 \mathrm{~ms}^{-1}$. If the speed can be measured within accuracy of $2 \%$ the uncertainty in the position is (in m)
3
If the first ionisation enthalpy of $\mathrm{Li}, \mathrm{Be}$ and C respectively are $520,899,1086 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The first ionisation enthalpy (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of B will be
4
In which of the following sets of molecules, the centil atoms of molecules have same hybridisation?
5
The correct increasing order of number of lone pair of electrons on the central atom of $\mathrm{SnCl}_2, \mathrm{XeF}_2, \mathrm{CIF}_3$ and $\mathrm{SO}_3$ is
6
Identify the correct statements from the following
I. For an ideal gas, the compressibility factor is 1.0
II. The kinetic energy of $\mathrm{NO}(g)$ (molar mass $=30 \mathrm{~g} \mathrm{~mol}^{-1}$ ) at $T(\mathrm{~K})$ is $x \mathrm{~J} \mathrm{~mol}^{-1}$. The kinetic energy of $\mathrm{N}_2 \mathrm{O}_4(g)\left(\right.$ molar mass $\left.=92 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ at $T(\mathrm{~K})$ is $2 x \mathrm{~J} \mathrm{~mol}^{-1}$
III. The rate of diffusion of a gas is inversely proportional to square root of its density.
7
The following graph is obtained for a gas at different temperatures $\left(T_1, T_2, T_3\right)$. What is the correct order of temperature? $(x$-axis $=$ velocity, $y$-axis $=$ number of molecules)
8
Observe the following stoichiometric equation
$$ \mathrm{P}_4+3 \mathrm{OH}^{-}+3 \mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{PH}_3+3 x^{-} $$
What is the conjugate acid of $x^{-}$?
9
Given below are two statements :
Statement I For isothermal irreversible change of an ideal gas, $q=-w=p_{\text {ext }}\left(V_{\text {final }}-V_{\text {initial }}\right)$
Statement II For adiabatic change, $\Delta U=w_{\text {adiabatic }}$
The correct answer is :
10
A thermodynamic process $(B \rightarrow E)$ was completed as shown below. The work done is equal to area under the limits 
11
$K_{\mathrm{c}}$ for the following reaction is 99.0
$$ A_2(g) \stackrel{T(K)}{\rightleftharpoons} B_2(g) $$
In a one litre flask, 2 moles of $A_2$ was heated to $T(\mathrm{~K})$ and the above equilibrium is reached. The concentration at equilibrium of $A_2$ and $B_2$ are $C_1\left(A_2\right)$ and $C_2\left(B_2\right)$ respectively. Now, one mole of $A_2$ was added to flask and heated to $T(\mathrm{~K})$ to established the equilibrium again. The concentration of $A_2$ and $B_2$ are $C_3\left(A_2\right)$ and $C_4\left(B_2\right)$ respectively. what is the value of $C_3\left(A_2\right)$ in $\mathrm{mol} \mathrm{L}^{-1}$ ?
12
What is the conjugate base of chloric acid?
13
The correct statements among the following are
(i) saline hydrides produce $\mathrm{H}_2$ gas when reacted with water
(ii) presently $\sim 77 \%$ of the industrial dihydrogen is produced from coal
(iii) commercially marketed $\mathrm{H}_2 \mathrm{O}_2$ contains $3 \% \mathrm{H}_2 \mathrm{O}_2$
14
The correct order of decomposition temperature of $\mathrm{MgCO}_3(X), \mathrm{BaCO}_3(Y), \mathrm{CaCO}_3(Z)$ is
15
Identify the correct statements
i. Oxidation of $\mathrm{NaBH}_4$ with $\mathrm{I}_2$ gives $\mathrm{B}_2 \mathrm{H}_6$
ii. $\mathrm{B}_2 \mathrm{H}_6$ burns in oxygen and releases an enormous amount of energy
iii. $\mathrm{B}_2 \mathrm{H}_6$ on hydrolysis gives a tribasic acid
16
Which one of the following is used as piezoelectric material?
17
Two statements are given below :
I. In dry cleaning, the solvent $\mathrm{Cl}_2 \mathrm{C}=\mathrm{CCl}_2$ was earlier used and now it is replaced by liquefied $\mathrm{CO}_2$
II. In bleaching of paper, $\mathrm{H}_2 \mathrm{O}_2$ was used earlier and now it is replaced by chlorine gas. Correct anwer is
18
Tropolone is an example for which of the following class of compounds?
19
What are $X$ and $Y$ respectively in the following reaction sequence?
$$ \text { Isopentane } \xrightarrow{\mathrm{KMnO}_4} X \xrightarrow{\text { Dehydration }} Y \text { Major } $$
20
Some substances are given below
$$ \begin{aligned} & \mathrm{Ag}, \mathrm{CO}_2(s), \mathrm{SiO}_2, \mathrm{ZnS} \\ & \mathrm{SO}_2(s), \mathrm{AlN}, \mathrm{HCl}(\mathrm{~s}), \mathrm{H}_2 \mathrm{O}(\mathrm{~s}) \end{aligned} $$
The number of molecular solids and network solids in the above list is respectively.
21
The $\Delta T_b$ value for 0.01 m KCl solution is 0.01 K . What is the van't Hoff factor?
$$
\left(K_b \text { for water }=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)
$$
22
200 g of $20 \% \frac{\mathrm{w}}{\mathrm{w}}$ urea solution is mixed with 400 g of $40 \% \frac{w}{w}$ urea solution. What is the weight percentage $\left(\frac{w}{w} \%\right)$ of resultant solution?
23
2.644 g of metal $(M)$ was deposited when 8040 coulombs of electricity was passed through molten $M \mathrm{~F}_2$ salt. What is the atomic mass of M?
$$
\left(\mathrm{F}=96500 \mathrm{C} \mathrm{~mol}^{-1}\right)
$$
24
The first order reaction, $A(g) \rightarrow B(g)+2 C(g)$ occurs at $25^{\circ} \mathrm{C}$. After 24 minutes the ratio of the concentration of products to the concentration of the reactant is $1: 3$ What is the half life is of the reaction (in min )? $\log 1.11=0.046$
25
Which of the following has maximum coagulating power in the coagulation of positively charged sol?
26
Identify the autocatalytic reaction from the following
27
The anode and cathode used in electrolytic refining of copper respectively are
28
The disproportionation products of ortho phosphorus acid are
29
In neutral medium potassium permanganate oxidises $I^{-}$to $X$.. Identify the $X$.
30
The spin only magnetic moments of the complexes $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ are respectively.
31
PHBV is a biodegradable polymer of two monomers $X$ and $Y . X$ and $Y$ respectively are.
32
The carbohydrate which does not react with ammonical $\mathrm{AgNO}_3$ solution is
33
Identify the amino acid which has
34
The structure given below represents
35
The major product $(X)$ formed in the given reaction is an example of
36
Identify the Swarts reaction from the following
37
An alcohol $X\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ reacts with conc. HCl at room temperature to give $Y\left(\mathrm{C}_4 \mathrm{H}_9 \mathrm{Cl}\right)$. Reaction of $X$ with copper at 573 K gave $Z$. What is $Z$ ?
38
$$
\text { What is } Y \text { in the following reaction sequence? }
$$
39
A carbonyl compound $X\left(\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}\right)$ on oxidation gave a carboxylic acid $Y\left(\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}_2\right)$. Oxime of $X$ is
40
The correct sequence of reactions involved in the following conversion is
Mathematics
1
If a real valued function $f:[a, \infty) \rightarrow[b, \infty)$ defined by $f(x)=2 x^2-3 x+5$ is a bijection. Then, $3 a+2 b=$
2
The domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{0.5}(2 x-3)}}+\sqrt{4-9 x^2}$ is
3
$$
2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots \text { to } 10 \text { terms }=
$$
4
$$
\left|\begin{array}{ccc}
1 & 1 & 1 \\
a^2 & b^2 & c^2 \\
a^3 & b^3 & c^3
\end{array}\right|=
$$
5
If $A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]$ and $\alpha A^2+\beta A=2 I$ for some $\alpha, \beta \in R$, then $\alpha+\beta=$
6
The system of equations
$$
x+2 y+3 z=6, x+3 y+5 z=9 \text {, }
$$
$2 x+5 y+a z=12$ has no solution when $a=$
7
If $m, n$ are respectively the least positive and greatest negative integer value of $k$ such that $\left(\frac{1-i}{1+i}\right)^k=-i$, then $m-n=$
8
If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is $\frac{z-2 i}{z-2}$
9
Real part of $\frac{(\cos a+i \sin a)^6}{(\sin b+i \cos b)^8}$ is
10
$$
4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}}=
$$
11
If $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$ have a common root, then that common root is
12
If $\alpha, \beta, \gamma$ are roots of equations $x^3+a x^2+b x+x=0$, then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}=$
13
If the roots of equation $x^3-13 x^2+K x-27=0$ are in geometric progression, then $K=$
14
If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is
15
If Set $A$ contains 8 elements, then number of subsets of $A$ which contain at least 6 elements is
16
The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word 'REPETITION' is
17
Numerically greatest term in the expansion of $(5+3 x)^6$ When, $x=1$, is
18
$$
1-\frac{2}{3}+\frac{2 \cdot 4}{3 \cdot 6}-\frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9}+\ldots \infty=
$$
19
If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$, then $B D-A C=$
20
The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+50^{\circ}\right) \tan (\theta) \tan \left(\theta-50^{\circ}\right)$ is valid, is
21
The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between
22
Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$
Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$
Which one of the following is correct?
23
The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$
24
The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is
25
$$
\cosh \left(\sinh ^{-1}(\sqrt{8})+\cosh ^{-1} 5\right)=
$$
26
In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$
27
In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$
28
In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$
29
If $L M N$ are the mid-points of the sides $P Q, Q R$ and $R P d$ $\triangle P Q R$ respectively, then
$$
\begin{aligned}
& \mathbf{Q M}+\mathbf{L N}+\mathbf{M L}+\mathbf{R N}-\mathbf{M N}-\mathbf{Q L}=
\end{aligned}
$$
30
Let $\mathbf{a} \times \mathbf{b}=7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{a}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. If the length of projection of $\mathbf{b}$ on $\mathbf{a}$ is
$$
\frac{8}{\sqrt{14}}, \text { then }|b|=
$$
31
Let $A B C$ be an equilateral triangle of side a. $M$ and $N$ are two points on the sides $A B$ and $A C$, respectively such that $\mathbf{A N}={ }^{\prime} K \mathbf{A C}$ and $\mathbf{A B}=3 \mathbf{A M}$. If the vectors $\mathbf{B N}$ and $\mathbf{C M}$ are perpendicular, then $K=$
32
Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ and $\mathbf{v}=\mathbf{a} \times \mathbf{b}$, then $|\mathbf{v}|=$
33
The shortest distance between the skew lines $\mathbf{r}=(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$ and $\mathbf{r}=(7 \hat{\mathbf{i}}+4 \hat{\mathbf{k}})+s(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})$ is
34
If $m$ and $M$ denote the mean deviations about mean and about median respectively of the data $20,5,15,2$, $7,3,11$, then the mean deviation about the mean of $m$ and $M$ is
35
If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls is
36
Out of first 5 consecutive natural numbers, if two different numbers $x$ and $y$ are chosen at random, then the probability that $x^4-y^4$ is divisible by 5 is
37
A bag contains 2 white, 3 green and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red is
38
There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is
39
If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number of kings is
40
In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is
41
If a variable straight line passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y-1=0$ intersects the $X, Y$-axes at $A$ and $B$ respectively, then the equation of the locus of a point which divides the segment $A B$ in the ratio $-2: 3$ is
42
Point $(-1,2)$ is changed to $(a, b)$, when the origin is shifted to the point $(2,-1)$ by translation of axes, Point $(a, b)$ is changed to $(c, d)$, when the axes are rotated through an angle of $45^{\circ}$ about the new origin, $(c, d)$ is changed to $(e, f)$, when $(c, d)$ is reflected through $y=x$. Then, $(e, f)=$
43
The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3,1)$ to the line $x+3 y+4=0$. If $(p, q)$ is the image of $(a, b)$ with respect to the line $3 x-4 y+11=0$, then $\frac{p}{a}+\frac{q}{b}=$
44
A ray of light passing through the point $(2,3)$ reflects on $Y$-axis at a point $P$. If the reflected ray passes through the point $(3,2)$ and $P=(a, b)$, then $5 b=$
45
The area (in sq units) of the triangle formed by the lines $6 x^2+13 x y+6 y^2=0$ and $x+2 y+3=0$ is
46
The angle subtended by the chord $x+y-1=0$ of the circle $x^2+y^2-2 x+4 y+4=0$ at the origin is
47
Let $P$ be any point on the circle $x^2+y^2=25$. Let $L$ be the chord of contact of $P$ with respect to the circle $x^2+y^2=9$. The locus of the poles of the lines $L$ with respect to the circle $x^2+y^2=36$ is
48
If the circles $S \equiv x^2+y^2-14 x+6 y+33=0$ and $S^1 \equiv x^2+y^2-a^2=0(a \in N)$ have 4 common tangents, then possible number of values of $a$ is
49
If the area of the circum-circle of triangle formed by the line $2 x+5 y+\alpha=0$ and the positive coordinate axes is $\frac{29 \pi}{4} S q$, units, then $|\alpha|=$
50
The circle $S \equiv x^2+y^2-2 x-4 y+1=0$ cuts the $Y$-axis at $A, B(O A>O B)$. If the radical axis of $S \equiv 0$ and $S' \equiv x^2+y^2-4 x-2 y+4=0$ cuts the $Y$-axis at $C$, then the ratio in which $C$ divides $A B$ is
51
If the circle $S=0$ cuts the circles $x^2+y^2-2 x+6 y=0$, $x^2+y^2-4 x-2 y+6=0$ and $x^2+y^2-12 x+2 y+3=0$ orthogonally, then equation of the tangent at $(0,3)$ on $S=0$ is
52
The normal drawn at a point $(2,-4)$ on the parabola $y^2 \pm 8 x$ cuts again the same parabola at $(\alpha, \beta)$, then $\alpha+\beta=$
53
If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ touches the circle $x^2+y^2=4$, then maximum value of $a b$ is
54
The locus of the mid-points of the chords of the hyperbola $x^2-y^2=a^2$ which touch the parabola $y^2=4 a x$ is
55
If the product of eccentricities of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$ is 1 , then $b^2=$
56
If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\angle B A C$ is
57
The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is
58
A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2)$, $(-2,-3,6),(0,2,-1)$. If $\theta$ is the angle between the line $L$ and plane $\pi$, then $27 \cos ^2 \theta=$
59
$$
\lim \limits_{x \rightarrow 3} \frac{x^3-27}{x^2-9}=
$$
60
If $f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x>1 \\ a x+b+1, & x<1\end{array}\right.$ and
$\lim \limits_{x \rightarrow 1} f(x)$ exists, then the relation between $a$ and $b$ is
61
The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x<3 \\ 5-x, & x \geq 3\end{array}\right.$ is
62
If $y=f(x)$ is a thrice differentiable function and a bijection, then $\frac{d^2 x}{d y^2}\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}=$
63
If $f(x)=\left\{\begin{array}{cl}x^\alpha \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$
which of the following is true?
64
Let $f(x)=\min \left\{x, x^2\right\}$ for every real number of $x$, then
65
If $y=\left(1+\alpha+\alpha^2+\ldots\right) e^{\eta x}$, where $\alpha$ and $n$ are constants, then the relative error in $y$ is
66
If the equation of tangent at $(2,3)$ on $y^2=a x^3+b$ is $y=4 x-5$, then the value of $a^2+b^2=$
67
If Rolle's theorem is applicable for the function $f(x)=x(x+3) e^{-x / 2}$ on $[3,0]$, then the value of $c$ is
68
For all $x \in[0,2024]$ assume that $f(x)$ is differentiable, $f(0)=-2$ and $f^{\prime}(x) \geq 5$. Then, the least possible value of $f(2024)$ is
69
$$
\int \frac{2 x^2 \cos x^2-\sin x^2}{x^2} d x=
$$
70
If $\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}$
$(h(x))+c$, then $h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=$
71
Let $f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{4} \log \left(\frac{5}{6}\right)$, then $f(0)=$
72
$$
\int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x=
$$
73
$$
\int\left(\frac{x}{x \cos x-\sin x}\right)^2 d x=
$$
74
If $\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=a e^b$, then
$$
a+b=
$$
75
$$
\int_0^\pi x \sin ^4 x \cos ^6 x d x=
$$
76
If $I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$, then $I_{13}+I_{11}=$
77
The area (in sq units) of the smaller region lying above the $X$-axis and bounded between the circle $x^2+y^2=2 a x$ and the parabola $y^2=a x$ is
78
The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\left(\frac{d^3 y}{d x^3}\right)^2-\left(\frac{d^2 y}{d x^2}\right)^{-\frac{5}{2}}\left(\frac{d^4 y}{d x^4}\right)=0$ is
79
If $x d y+\left(y+y^2 x\right) d x=0$ and $y=1$ at $x=1$, then
80
The solution of $x d y-y d x=\sqrt{x^2+y^2} d x$ when $y(\sqrt{3})=1$ is
Physics
1
The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$, respectively. The percentage error in the measurement of kinetic energy is
2
A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is
3
A 2 kg ball thrown vertically upward and another 3 kg ball projected with certain angle $\left(\theta \neq 90^{\circ}\right)$ both will have same time of flight, then this ratio of their maximum heights is
4
In a sport event, a disc is thrown such that it reaches its maximum range of 80 m , the distance travelled in first 3 s is $\left(g=10 \mathrm{~ms}^{-2}\right)$
5
A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is $0.5 \mathrm{kgm}^{-1}$ and initially the block is at rest, the time in which the block moves a distance of 9 m is
6
A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of $10 \mathrm{~ms}^{-1}$. If the block comes to rest after travelling a distance of 12.5 m , the coefficient of kinetic friction between the surface and the block is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
7
A force of $\left(6 x^2-4 x+3\right) \mathrm{N}$ acts on a body of mass 0.75 kg and displaces it from $x=2 \mathrm{~m}$ to $x=5 \mathrm{~m}$. The work done by the force is
8
A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \mathrm{~ms}^{-1}$ and the coefficient of restitution is 0.75 , the total distance travelled by the ball before it comes to rest is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
9
A solid cylinder rolls down an inclined plane without slipping. If the translation kinetic energy of the cylinder is 140 J . The total kinetic energy of the cylinder is
10
Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
11
The displacement of a particle executing simple harmonic motion is $y=A \sin (2 t+\phi) \mathrm{m}$, where $t$ is time in second and $\phi$ is phase angle. At time $t=0$, the displacement and velocity of the particle are 2 m and $4 \mathrm{~ms}^{-1}$. The phase angle, $\phi=$
12
The displacement of a damped oscillator is $x(t)=\exp (-0.2 t) \cos (3.2 t+\phi)$, where $t$ is time in second The time requirement for the amplitude of the oscillator to become $\frac{1}{e^{1.2}}$ times its initial amplitude is
13
Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ( $R=$ Radius of the earth)
14
If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material but with double radius of cross-section and half the length by 1 mm is
15
If $S_1, S_2$ and $S_3$ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively and $\theta$ is the angle of contact at the solid-liquid interface, then
16
If ambient temperature is 300 K , the rate of cooling at 600 K is $H$. In the same surroundings, the rate of cooling at 900 K is
17
An ideal heat engine operates in Carnot cycle between $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. It absorbs $5 \times 10^4 \mathrm{Cal}$ of heat at height temperature. Amount of heat converted to work is
18
One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$. The value of $\gamma$ for the mixture is ( $\gamma$ is the ratio of the specific heats of the gas)
19
A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is
20
The rms velocity of a gas molecules oí mass $m$ at a given temperature is proportional to
21
The speed of a wave on a string is $150 \mathrm{~ms}^{-1}$ when the tension is 120 N . The percentage increase in the tension in order to raise the wave speed by $20 \%$ is
22
The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^{\circ}$. The light ray is also, found to be refracted at an angle of $30^{\circ}$. Then, the refractive index of the liquid is
23
In Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity, $\frac{I}{I_0}$ is equal to
24
Two particles of equal mass $m$ and equal charge $q$ are separated by a distance of 16 cm . They do not experience any force. The value of $\frac{q}{m}$ is (if $G$ is the universal gravitational constant and $g$ is the acceleration due to gravity)
25
In the following diagram, the work done in moving a point charge from point $P$ to points $A, B$ and $C$ are $W_A, W_B$ and $W_C$ respectively. Then ( $A, B, C$ are points on semi-circle and point charge $q$ is at the centre of semi-circle) 
26
Four condensers each of capacitance $8 \mu \mathrm{~F}$ are joined as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be 
27
A steady current is flowing in a metallic conductor of non-uniform cross-section. The physical quantity which remains constant is
28
The resistance between points $A$ and $C$ in the given network is 
29
A wire shaped in a regular hexagon of side 2 cm carries a current of 4 A . The magnetic field at the centre of hexagon is 
30
A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A . Magnetic field at the centre of the coil is
31
The domain in ferromagnetic material is in the form of a cube of side $2 \mu \mathrm{~m}$. Number of atoms in that domain is $9 \times 10^{10}$ and each atom has a dipole movement of $9 \times 10^{-24} \mathrm{Am}^2$. The magnetisation of the domain is (approximately).
32
Magnetic field at a distance of $r$ from $Z$-axis is $B=B_0$ $r t \hat{\mathbf{k}}$ present in the region. $B_0$ is constant and $t$ is time. The magnitude of induced electric field at a distance of $r$ from $Z$-axis is
33
A series $L-C-R$ circuit is shown in the figure. Where the inductance of 10 H , capacitance $40 \mu \mathrm{~F}$ and resistance $60 \Omega$ are connected to a variable frequency 240 V source. The current at resonating frequency is 
34
An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is 1 . Then, the relative permittivity is
35
The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is
36
A hydrogen atom falls from $n$th higher energy orbit to first energy orbit $(n=1)$. The energy released is equal to 12.75 eV . The $n$th orbit is
37
The decrease in each day in the uranium mass of the material in a uranium reactor operating at a power of 12 MW is (Energy released in one ${ }_{92} \mathrm{U}^{235}$ fission is about 200 MeV )
38
When a signal is applied to the input of a transistor, it was found that output signal is phase-shifted by $180^{\circ}$. The transistor configuration is
39
The voltage $V_0$ in the network shown is 
40
A message signal of 3 kHz is used to modulate a carric signal frequency 1 MHz , using amplitude modulation. The upper side band frequency and band width respectively are