AP EAPCET 2024 - 21th May Morning Shift
Paper was held on
Tue, May 21, 2024 3:30 AM
Chemistry
1
The energy of third orbit of $\mathrm{Li}^{2+}$ ion (in J ) is
2
The number of $d$ electrons in Fe is equal to which of the following?
(i) Total number of ' $s$ ' electrons of Mg .
(ii) Total number of ' $p$ ' electrons of Cl .
(iii) Total number of ' $p$ ' electrons of Ne .
The correct option is
3
The correct order of atomic radii of given element is
4
Which of the following orders are correct regarding their covalent character?
(i) $\mathrm{KF}<\mathrm{KI}$
(ii) $\mathrm{LiF}<\mathrm{KF}$
(iii) $\mathrm{SnCl}_2<\mathrm{SnCl}_4$
(iv) $\mathrm{NaCl}<\mathrm{CuCl}$
The correct option is
5
$$ \text { Observe the following sets. } $$
$$ \begin{array}{lll} \hline \text { Order } & \text { Property } \\ \hline \text { (i) } \mathrm{NH}_3>\mathrm{H}_2 \mathrm{O}>\mathrm{SO}_2 & \text { Bond angle } \\ \hline \text { (ii) } \mathrm{H}_2 \mathrm{O}>\mathrm{NH}_3>\mathrm{H}_2 \mathrm{~S} & \text { Dipole moment } \\ \text { (iii) } \mathrm{N}_2>\mathrm{O}_2>\mathrm{H}_2 & \text { Bond enthalpy } \\ \hline \text { (iv) } \mathrm{NO}^{+}>\mathrm{O}_2>\mathrm{O}_2^{2-} & \text { Bond order } \\ \hline \end{array} $$
6
The RMS velocity ( $u_{\mathrm{rms}}$ ) of one mole of an ideal gas was measured at different temperatures and the following graph is obtained. What is the slope $(m)$ of straight line ?
$$ \begin{aligned} & \left(X \text {-axis }=T(\mathrm{~K}): Y \text {-axis }=\left(u_{\mathrm{rms}}\right)^2: M=\right.\text { molar mass : } \\ & R=\text { gas constant } \end{aligned} $$
7
Two statements are given below.
Statement I : Viscosity of liquid decreases with increase in temperature.
Statement II : The units of viscosity coefficient are pascal.
The correct answer is
8
0.1 mole of potassium permanganate was heated at $300^{\circ} \mathrm{C}$. What is weight (ing) of the residue?
$$
(\mathrm{Mn}=55 \mathrm{u}, \mathrm{~K}=39 \mathrm{u}, \mathrm{O}=16 \mathrm{u})
$$
9
Identify the correct statements from the following.
I. $\Delta_r G$ is zero for $A \rightleftharpoons B$ reaction.
II. The entropy of pure crystalline solids approaches. zero as the temperature approaches absolute zero.
III. $\Delta U$ of a reaction can be determined using bomb calorimeter.
10
Observe the following reactions.
$$ \begin{array}{ll} A B(g)+25 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow\left(25 \mathrm{H}_2 \mathrm{O}\right) A B ; & \Delta H=x \mathrm{~kJ} \mathrm{~mol}^{-1} \\ A B(g)+50 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow\left(50 \mathrm{H}_2 \mathrm{O}\right) A B ; & \Delta H=y \mathrm{~kJ} \mathrm{~mol}^{-1} \end{array} $$
11
$K_C$ for the reaction,
$A_2(g) \stackrel{T(\mathrm{~K})}{\rightleftharpoons} B_2(\mathrm{~g})$
is 39.0. In a closed one litre flask, one mole of $A_2(g)$ was heated to $T(\mathrm{~K})$. What are the concentrations of $A_2(g)$ and $B_2(g)$ (in mol L ${ }^{-1}$ ) respectively at equilibrium?
$A_2(g) \stackrel{T(\mathrm{~K})}{\rightleftharpoons} B_2(\mathrm{~g})$
is 39.0. In a closed one litre flask, one mole of $A_2(g)$ was heated to $T(\mathrm{~K})$. What are the concentrations of $A_2(g)$ and $B_2(g)$ (in mol L ${ }^{-1}$ ) respectively at equilibrium?
12
At $T(\mathrm{~K})$, the solubility product of $A X$ is $10^{-10}$. What is the molar solubility of $A X$ in 0.1 MHX ?
13
The equation that represents 'coal gasification' is
14
As per standard reduction potential values, which is the strongest reducing agent among the given elements?
15
A Lewis acid ' $X$ ' reacts with $\mathrm{LiAlH}_4$ in ether medium to give a highly toxic gas. ${ }^{\prime} Y^{\prime}$, ' $Y$ ' when heated with $\mathrm{NH}_3$ gives a compound known as inorganic benzene. ' $Y^{\prime}$ burns in oxygen and gives $\mathrm{H}_2 \mathrm{O}$ and ' $Z$ ', ' $Z$ ' is
16
The method for preparation of water gas is
17
The BOD values for pure water and highly polluted water are respectively.
18
A mixture of ethyl iodide and $n$-propyl iodide is subjected to Wurtz reaction. The hydrocarbon which will not be formed is
19
Which of the following alkenes does not undergo anti Markownikoff addition of HBr ?
20
What are the variables in the graph of powder diffraction pattern of a crystalline solid?
21
100 mL of $\frac{M}{10} \mathrm{Ca}\left(\mathrm{NO}_3\right)_2$ and 200 mL of $\frac{M}{10} \mathrm{KNO}_3$ solutions are mixed. What is the normality of resulted solution with respect to $\mathrm{NO}_3^{-}$?
22
A solution was prepared by dissolving 0.1 mole of a non- volatile solute in 0.9 moles of water. What is the relative lowering of vapour pressure of solution?
23
The standard free energy change $\left(\Delta G^{\circ}\right)$ for the following reaction (in kJ ) at $25^{\circ} \mathrm{C}$ is
$$
3 \mathrm{Ca}(s)+2 \mathrm{Au}^{3+}(a q, 1 M) \longrightarrow 3 \mathrm{Ca}^{2+}(a q, 1 M)+2 \mathrm{Au}(s)
$$
24
The rate constant of a first order reaction is $3.46 \times 10^{-2} \mathrm{~s}^{-1}$ at 298 K . What is the rate constant of the reaction at 350 K if its activation energy is $50.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$, $\left(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)(\log 2=0.3010)$
25
The correct statement regarding chemisorption is
26
Which of the following is incorrectly matched?
27
Improve silver ore $+\mathrm{CN}^{-}+\mathrm{H}_2 \mathrm{O} \xrightarrow{\mathrm{O}_2}[\mathrm{X}]^{-}+\mathrm{OH}^{-}$
$$ [X]^{-}+\mathrm{Zn} \longrightarrow[Y]^{2-}+\mathrm{Ag} \text { (pure) } $$
The co-ordination numbers of the metals in $[X]$. [ $Y$ ] are respectively
28
In the reaction of sulphur with concentrated sulphuric acid, the oxidised product is $X$ and reduced product is $Y, X$ and $Y$ are respectively.
29
Which of the following lanthanoids have [Xe] $4 f^x 5 d^1 6 s^2$ configuration in their ground state.
$$
(X=1-14)
$$
30
How many of the following ligands are stronger than
$$ \begin{aligned} & \mathrm{H}_2 \mathrm{O} \text { ? } \\ & \mathrm{S}^{2-}, \mathrm{Br}^{-}, \mathrm{C}_2 \mathrm{O}_4^{2-}, \mathrm{CN}^{-} \text {, en, } \mathrm{NH}_3, \mathrm{CO}, \mathrm{OH}^{-} \\ & \begin{array}{ll} \text { } & \text { } \end{array} \end{aligned} $$
31
$$ \text { The common monomer for both terylene and glyptal is } $$
32
Which of the following structure of proteins represellis its constitution?
33
Carrot and curd are sources for the vitamins repectively.
34
$$ \text { Match the following. } $$
| List I (Drug) | List I (Use) | ||
|---|---|---|---|
| A | Veronal | i | Antihistamine |
| B | Morphine | ii | Hypnotic |
| C | Seldane | iii | Analgesic |
| iv | $$ \text { Antidepressant } $$ |
||
35
The major products $X$ and $Y$ respectively from the following reactions are
36
An isomer of $\mathrm{C}_5 \mathrm{H}_{12}$ on reaction with $\mathrm{Br}_2$ /light gave only one isomer $\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}(X)$. Reaction of $X$ with $\mathrm{AgNO}_2$ gave $Y$ as major product. What is $Y$ ?
37
What are the major products $X$ and $Y$ respectively in the following reactions?
$$ \begin{aligned} & \left(\mathrm{CH}_3\right)_3 \mathrm{CONa}+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br} \longrightarrow X \\ & \left(\mathrm{CH}_3\right)_3 \mathrm{CBr}+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{ONa} \longrightarrow Y \end{aligned} $$
38
Match the following reagents with the products obtained when they reacted with a ketone.
| List I | List II | ||
|---|---|---|---|
| A. | $$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{NHNH}_2 $$ |
i. | Schiff base |
| B. | $$ \mathrm{NH}_2 \mathrm{OH} $$ |
ii. | Hydrazone |
| C. | $$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2 $$ |
iii. | Oxime |
| iv. | Phenyl hydrazone | ||
$$ \text { Correct answer is } $$
39
What are $X$ and $Y$ respectively in the following reactions?
40
Arrange the following in decreasing order of their basicity.
Mathematics
1
The domain of the real valued function $f(x)$ $=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)$ is
2
The range of the real valued function $f(x)=\left(\frac{x^2+2 x-15}{2 x^2+13 x+15}\right)$ is
3
$\frac{1}{1 \cdot 5}+\frac{1}{5 \cdot 9}+\frac{1}{9 \cdot 13}+\ldots$. upto $n$ terms $=$
4
If $A=\left|\begin{array}{lll}2 & 3 & 4 \\ 1 & k & 2 \\ 4 & 1 & 5\end{array}\right|$ is singular matrix, then the quadratic equation having the roots $k$ an $\frac{1}{k}$ is
5
Let $A$ be a $4 \times 4$ matrix and $P$ be is adjoint matrix, If $|P|=\left|\frac{A}{2}\right|$ then $\left|A^{-1}\right|$
6
The system $x+2 y+3 z=4,4 x+5 y+3 z=5,3 x+4 y+3 z=\lambda$ is consistent and $3 \lambda=n+100$, then $n=$
7
The complex conjugate of $(4-3 i)(2+3 i)(1+4 i)$ is.
8
If the amplitude of $(z-2)$ is $\frac{\pi}{2}$, then the locus of $z$ is
9
If $\omega$ is the cube root of unity,
$$
\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+b \omega^2}=
$$
10
Roots of the equation $a(b-c) x^2+b(c-a) x+c(a-b)=0$ are
11
If $(3+i)$ is a root of $x^2+a x+b=0$, then $a=$
12
The algebraic equation of degree 4 whose roots are translate of the roots of the equation. $x^4+5 x^3+6 x^2+7 x+9=0$ by -1 is
13
If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are in arithmetic progression, then $m=$
14
The number of 5 -digit odd numbers greater than 40000 that can be formed by using 3,4,5,6,7,0 so that at least one of its digit must be repeated is
15
The number of ways in which 3 men and 3 women can be arranged in a row of 6 seats, such that the first and last seats must be filled by men is
16
If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is
17
If the eleventh term in the binomial expansion of $(x+a)^{15}$ is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is
18
The sum of the rational terms in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is
19
If $\frac{1}{(3 x+1)(x-2)}=\frac{A}{3 x+1}+\frac{B}{x-2}$ and $\frac{x+1}{(3 x+1)(x-2)}=\frac{C}{3 x+1}+\frac{D}{x-2}$, then
20
If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$
21
If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$
22
If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$
23
For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval
24
If the general solution .set of $\sin x+3 \sin 3 x+\sin 5 x=1$ is $S$, then $\{\sin \alpha / \alpha \in S\}=$
25
If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$
26
In a $\Delta$ if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is
27
In a $\triangle A B C$, if $B C=5, C A=6$ and $A B=7$, then the length of the median drawn from $B$ onto $A C$ is
28
In $\triangle A B C$, if $A B: B C: C A=6: 4: 5$, then $R: r$ is equal to
29
$\mathbf{a}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \mathbf{b}=\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ ar linearly dependent vectors and magnitude of $ \alpha $$ \sqrt{14} $${\text {}}{ }^{}$ If $\alpha, \beta$ are integers, then $\alpha+\beta=$
30
$\mathbf{c}$ is a vector along the bisector of the internal angle between the vectors $\mathbf{a}=4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{b}=12 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. If the magnitude of $\mathbf{c}$ is $3 \sqrt{13}$, then c=
31
$\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are two vectors and $\mathbf{c}$ is a unit vectors lying in the plane of $\mathbf{a}$ and $\mathbf{b}$. If $\mathbf{c}$ is perpendicular to $\mathbf{b}$, then $\mathbf{c}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})=$
32
$A(1,2,1), B(2,3,2), C(3,1,3)$ and $D(2,1,3)$ are the vertices of a tetrahedron. If $\theta$ is the angle between the faces $A B C$ and $A B D$, then $\cos \theta=$
33
If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$. $\mathbf{d}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are four vector, then $(\mathbf{a} \times \mathbf{c}) \times(\mathbf{b} \times \mathbf{d})=$
34
Mean deviation about the mean for the following data is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text { Frequency } & 1 & \,2 & \,3 & \,2 & \,1 \\ \hline \end{array} $$
35
If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is
36
If a number is drawn at random from the set $\{1,3,5,7, \ldots . .59\}$, then the probability that it lies in the interval in which the function $f(x)=x^3-16 x^2+20 x-5$ is stricly decreasing is
37
In a class consisting of 40 boys and 30 girls. $30 \%$ of the boy and $40 \%$ of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is
38
A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting atmost one rotten apple is
39
7 coins are tossed simultaneously and the number of heads turned up is denoted by random variable $X$. If $\mu$ is the mean and $\sigma^2$ is the variance of $X$, then $\frac{\mu \sigma^2}{P(X=3)}=$
40
A manufacturing company noticed that $1 \%$ of its products are defective. If a dealer order for 300 items from this company, then the probability that the number of defective items is atmost one is
41
$P$ is a variable point such that the distance of $P$ from $A$ $(4,0)$ is twice the distance of $P$ from $B(-4,0)$. If the line $3 y-3 x-20=0$ intersects the locus of $P$ at the points $C$ and $D$, then the distance between $C$ and $D$ is
42
When the origin is shifted to $(h, k)$ by translation of axes, the transformed equation of $x^2+2 x+2 y-7=0$ does not contain $x$ term and constant term. Then, $(2 h+k)=$
43
Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$, then $h^2+k^2=$
44
If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2),(5,1),(4,4)$, then $\alpha+\beta=$
45
The area of the triangle formed by the lines represented by $3 x+y+15=0$ and $3 x^2+12 x y-13 y^2=0$ is
46
If all chords of the curve $2 x^2-y^2+3 x+2 y=0$, which subtend a right angle at the origin always passing through the point $(\alpha, \beta)$, then $(\alpha, \beta)=$
47
$2 x-3 y+1=0$ and $4 x-5 y-1=0$ are the equations of two diameters of the circle $S \equiv x^2+y^2+2 g x+2 f y-11=0 . Q$ and $R$ are the points of contact of the tangents drawn from the point $P(-2,-2)$ to this circle. If $C$ is the centre of the circle $S=0$, then the area (in square units ) of the quadrilateral $P Q C R$ is
48
If the inverse point of the point $(-1,1)$ with respect to the circle $x^2+y^2-2 x+2 y-1=0$ is $(p, q)$, then $p^2+q^2=$
49
If $(a, b)$ is the mid-point of the chord $2 x-y+3=0$ of the circle $x^2+y^2+6 x-4 y+4=0$, then $2 a+3 b=$
50
If a direct common tangent drawn to the circle $x^2+y^2-6 x+4 y+9=0$ and $x^2+y^2+2 x-2 y+1=0$ touches the circles at $A$ and $B$, then $A B=$
51
The radius of the circle which cuts the circles $x^2+y^2-4 x-4 y+7=0, x^2+y^2+4 x-4 y+6=0$ and $x^2+y^2+4 x+4 y+5=0$ orthogonally is
52
The equation of the normal drawn to the parabola $y^2=6 x$ at the point $(24,12)$ is
53
If $A_1, A_2, A_3$ are the areas of ellipse $x^2+4 y^2-4=0$ its director circle and auxiliary circle respectively, then $A_2+A_3-A_1=$
54
The equation of the pair of asymptotes of the hyperbola $4 x^2-9 y^2-24 x-36 y-36=0$ is
55
The equation of one of the tangents drawn from the point $(0,1)$ to the hyperbola $45 x^2-4 y^2=5$ is
56
Consider the tetrahedron with the vertices $A(3,2,4)$, $B\left(x_1, y_1, 0\right), C\left(x_2, y_2, 0\right)$ and $D\left(x_3, y_3, 0\right)$.If the $\triangle B C D$ is formed by the lines $y=x, x+y=6$ and $y=1$, then the centroid of the tetrahedron is
57
If $P(2, \beta, \alpha)$ lies on the plane $x+2 y-z-2=0$ and $Q(\alpha,-1, \beta)$ lies on the plane $2 x-y+3 z+6=0$, then the direction cosines of the $P Q$ are
58
Let $\pi$ be the plane that passes through the point $(-2,1,-1)$ and parallel to the plane $2 x-y+2 z=0$. Then the foot of perpendicular drawn from the point $(1,2,1)$ to the plane $\pi$ is
59
If $f(x)=\frac{5 x \cdot \operatorname{cosec}(\sqrt{x})-1}{(x-2) \operatorname{cosec}(\sqrt{x})}$, then $\lim \limits_{x \rightarrow \infty} f\left(x^2\right)=$
60
$\lim \limits_{x \rightarrow 2} \frac{\sqrt{1+4 x}-\sqrt{3+3 x}}{x^3-8}=$
61
If
$$
\lim _{x \rightarrow \infty} \frac{(\sqrt{2 x+1}+\sqrt{2 x-1})^8+(\sqrt{2 x+1}-\sqrt{2 x-1})^8\left(P x^4-16\right)}{\left(x+\sqrt{x^2-2}\right)^8+\left(x-\sqrt{x^2-2}\right)^8}=1
$$
then $P=$
62
The rate of change of $x^{\sin x}$ with respect to $(\sin x)^x$ is
63
If $y=\frac{\alpha x+\beta}{\gamma \alpha+\delta}$, then $2 y_1 y_3=$
64
Which one of the following is false ?
65
The point which lies on the tangent drawn to the curve $x^4 e^y+2 \sqrt{y+1}=3$ at the point $(1,0)$ is
66
If $f(x)=x^x$, then the interval in which $f(x)$ decrease is
67
If the Rolle's theorem is applicable for the function $f(x)$ defined by $f(x)=x^3+P x-12$ on $[0,1]$ then the value of $C$ of the Rolle's theorem is
68
The number of all the value of $x$ for which the function $f(x)=\sin x+\frac{1-\tan ^2 x}{1+\tan ^2 x}$ attains it maximum value on [ $0.2 \pi$ ] is
69
If $x \in\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]$ and $n \in Z$, then $\int \sqrt{1-\sin 2 x} d x=$
70
$\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=$
71
If $\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c$, then one of the values of $\frac{\pi \alpha}{4}-\beta$ is
72
If $729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b$, then $(a-b)=$
73
If $n \geq 2$ is a natural number and $0<\theta<\frac{\pi}{2}$, then $\int \frac{\left(\cos ^n \theta-\cos \theta\right)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta=$
74
$\lim \limits_{n \rightarrow \infty} \frac{1^{17}+2^{77}+\ldots+n^{77}}{n^{78}}=$
75
$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{6 x^2+1}{4 x^3+2 x+3} & , 0 < x < 1 \\ x^2+1 & , 1 \leq x < 2 \end{array} \text {, then } \int_0^2 f(x) d x=\right. $$
76
If $\int_1^n[x] d x=120$, then $n=$
77
The area of the region under the curve $y=|\sin -\cos x|$, $0 \leq x \leq \frac{n}{2}$ and above $X$-axis, is (in sq units)
78
The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is
79
If $y=a^3 e^{y^2 x+c}$ is the general solution of a differential equation, where $a$ and $c$ are arbitrary constants and $b$ is fixed constant, then the order of differential equation is
80
The solution of differential equation $\left(x+2 y^3\right) \frac{d y}{d x}=y$ ls
Physics
1
Five equal resistances each $2 R$ connected as shown in figure. A battery of $V$ volts connected between $A$ and $B$. Then, current through $F C$ is
2
A lamp is rated at $240 \mathrm{~V}, 60 \mathrm{~W}$. When in use the resistance of the filament of the lamp is 20 times that of cold filament. The resistance of the lamp when not in use is
3
When an electron placed in a uniform magnetic field is accelerated from rest through a potential difference $V_1$. It experiences a force $F$. If the potential difference is changed to $V_2$, the force experienced by the electron in same magnetic field is $2 F$, then the ratio of potential differences $\frac{V_2}{V_1}$ is
4
A rectangular loop of sides 25 cm and 10 cm carrying a current of 10 A is placed with its longer side parallel to a long straight conductor 10 cm apart carrying current 25 A . The net force on the loop is
5
If the vertical component of the earth's magnetic field is 0.45 G at a location and angle of dip is $60^{\circ}$, then magnetic field of earth in that location is
6
$X$ and $Y$ are two circuits having coefficient of mutual inductance 3 mH and resistance $10 \Omega$ and $4 \Omega$ respectively. To have induced current $60 \times 10^{-4} \mathrm{~A}$ in circuit $Y$, the amount of current to be changed in circuit $X$ in 0.02 s is
7
Two figures are shown as Fig. $A$ and Fig. $B$. The time constant of Fig. $A$ is $\tau_A$ and time constant of Fig. $B$ is $\tau_B$. Then
8
Which of the following produces electromagnetic waves?
9
A blue lamp emits light of mean wavelength $4500$ Å. The lamp is rated at 150 W and $8 \%$ efficiency. Then, the number of photons are emitted by the lamp per second
10
The ground state energy of hydrogen atom is -13.6 eV . The potential energy of the electron in this state is
11
If the energy released per fission of a ${ }_{92}^{235} \mathrm{U}$ nucleus is 200 MeV . The energy released in the fission of 0.1 kg d ${ }_{92}^{235} \mathrm{U}$ in kilowatt - hour is
12
The semiconductor used for fabrication of visible LEDS must at least have a band gap of
13
In a common emitter amplifier, AC current gains 40 and input resistance is $2 \mathrm{k} \Omega$. The load resistance is given as $10 \mathrm{k} \Omega$. Then, the voltage gain is
14
An information signal of frequency 10 kHz is modulated with a carried wave of frequency $3.62 \mathrm{MHz}^{}$ The upper side and lower side frequencies are
15
The time period of revolution of a satellite $T$ around the carth depends on the radius of the circular orbit $R$. mass of the earth $M$ and universal gravitational constant $G$. The expression for $T$, using dimensional analysis is ( $K$ is constant of proportionality)
16
An object projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of 8 s and the object reaches foot after 16 s . The height of the tower is $\left(g=10 \mathrm{~ms}^{-2}\right)$
17
The centripetal acceleration of a particle in uniform circular motion is $18 \mathrm{~ms}^{-2}$. If the radius of the circular path is 50 cm , the change in velocity of the particle in a time of $\frac{\pi}{18} \mathrm{~s}$ is
18
The horizontal range of a projectile projected at an angle of $45^{\circ}$ with the horizontal is 50 m . The height of the projectile when its horizontal displacement is 20 m is
19
A body of mass 1.5 kg is moving towards south with a uniform velocity of $8 \mathrm{~ms}^{-1}$. A force of 6 N is applied to the body towards east. The displacement of the body 3 s after the application of the force is
20
The upper $\left(\frac{1}{n}\right)$ th of an inclined plane is smooth and the remaining lower part is rough with coefficient of friction $\mu_k$. If a body starting from rest at the top of the inclined plane will again come to rest at the bottom of the plane, then the angle of inclination of the inclined plane is
21
A spring of spring constant $200 \mathrm{~N}-\mathrm{m}^{-1}$ is initially stretched by 10 cm from the unstretched position. The work to be done to stretch the spring further by another 10 cm is
22
A ball falls freely from rest from a height of 6.25 m on a hard horizontal surface. If the ball reaches a heightd 81 cm after second bounce from the surface, the coefficient of restitution is
23
The masses of a solid cylinder and hollow cylinder ate 3.2 kg and 1.6 kg respectively. Both the solid and hollow cylinders start from rest from the top of an inclined plane and roll down without slipping. If both the cylinder have equal radius and the acceleration of solid cylinder is $4 \mathrm{~ms}^{-1}$, the acceleration of hollow cylinder is
24
A solid sphere of mass 50 kg and radius 20 cm is rotating about its diameter with an angular velocity d 420 rpm . The angular momentum of the sphere is
25
The mass of a particle is 1 kg and it is moving along $X$-axis. The period of its oscillation is $\frac{\pi}{2}$. Its potential energy at a displacement of 0.2 m is
26
The potential energy of a particle of mass 10 g as a function of displacement $x$ is $\left(50 x^2+100\right) \mathrm{J}$. The frequency of oscillation is
27
If the time period of revolution of a satellite is $T$, the its kinetic energy is proportional to
28
The elastic energy stored per unit volume in terms of longitudinal strain $\varepsilon$ and Young's modulus $Y$ is
29
A large tank filled water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time taken for the level to fall from $h$ to $\frac{h}{2}$ and that taken for the level to fall from $\frac{h}{2}$ to 0 is
30
A slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} \mathrm{C}$ and that of copper at $100^{\circ} \mathrm{C}$. If the thermal conductivities of brass and copper are in the ratio $1: 4$, then the temperature of interface is
31
A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is
32
In a Carnot engine, when the temperatures are $T_2=0^{\circ} \mathrm{C}$ and $T_1=200^{\circ} \mathrm{C}$, its efficiency is $\eta_1$ and when the temperature are $T_1=0^{\circ} \mathrm{C}$ and $T_2=-200^{\circ} \mathrm{C}$, its efficiency is $\eta_2$. Then, the value of $\frac{\eta_1}{\eta_2}$ is
33
Heat energy absorbed by a system going through the cyclic process shown in the figure is
34
A polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $N$ is Avogadro's number )
35
A car sounding a horn of frequency 1000 Hz passes a stationary observer. The ratio of frequen'ies of the horn noted by the observer before and after passing of the car is $11: 9$. The speed of car is (speed of sound $v=340 \mathrm{~ms}^{-1}$ )
36
A ray of light travels from an optically denser to rare medium. The critical angle for the media is $C$. The maximum possible deviation of the ray will be
37
The angle of polarisation for a medium with respect to air is $60^{\circ}$. The critical angle of this medium with respect to air is
38
A point charge $q \mathrm{C}$ is placed at the centre of a cube of a side length $L$. Then, the electric flux linked with each face of the cube is
39
Three equal electric charges of each charge $q$ are placed at the vertices of an equilateral triangle of side of length $L$. Then, potential energy of the system is
40
Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is $C$, then capacity of the big drop is