Chemistry
1. If $$\Delta x$$ is the uncertainty in position and $$\Delta v$$ is the uncertainty in velocity of a particle are equal, 2. The number of radial nodes and angular nodes of a $$4 f$$-orbital are respectively 3. Lithium shows diagonal relationship with element '$$X$$' and aluminium with $$Y . X$$ and $$Y$$ respectively are 4. The correct order of the metallic character of the elements $$\mathrm{Be}, \mathrm{Al}, \mathrm{Na}, \mathrm{K}$$ is 5. Choose the correct option from the following. 6. The bond lengths of $$\mathrm{C}_2, \mathrm{~N}_2$$ and $$\mathrm{B}_2$$ molecules are $$X_1, X_2$$ and $$X_3 \mathrm{~p 7. Among the gases a, b, c , d, e and f, the gases that show only positive deviation from ideal behaviour at all pressures 8. The statement related to law of definite proportions is 9. What are the oxidation states of three Br atoms in $$\mathrm{Br}_3 \mathrm{O}_8$$ molecule? 10. Identify the reaction/process in which the entropy increases. 11. State $$1 \rightleftharpoons$$ State $$2 \rightleftharpoons$$ State 3
$$\left(\begin{array}{l}T=300 \mathrm{~K} \\ p=15 12. The formation of ammonia from its constituent elements is an exothermic reaction. The effect of increased temperature on 13. Equal volumes of 0.5 N acetic acid and 0.5 N sodium acetate are mixed. What is the pH of resultant solution? ($$\mathrm{ 14. What are $$X$$ and $$Y$$ respectively in the following reactions?
$$\begin{aligned}
& \underline{X}+D_2 \mathrm{O} \long 15. Assertion (A) MgSO$$_4$$ is readily soluble in water.
Reason (R) The greater hydration enthalpy of Mg$$^{2+}$$ ions over 16. Identify A and B from the following reaction,
$$\mathrm{NaNO}_3 \xrightarrow{\Delta} x A+y B$$ 17. Identify the correct statements about boron.
I. It has high melting point.
II. It has high density.
III. It has high ele 18. Which of the following tetrahalides does not exist? 19. The correct order of acidity of the following compounds is
20. The compound or ion which is not aromatic in the following is 21. The number of network solids and ionic solids in the list given below is respectively. $$\mathrm{H}_2 \mathrm{O}$$ (ice) 22. If molten NaCl contains $$\mathrm{SrCl}_2$$ as impurity, crystallisation can generate 23. At $$T(\mathrm{~K}) \times \mathrm{g}$$ of a non-volatile solid (molar mass $$78 \mathrm{~g} \mathrm{~mol}^{-1}$$) when 24. Assertion (A) Blood cells collapse when suspended in saline water.
Reason (R) Cell membrane dissolves in saline water. 25. The reduction potential of hydrogen electrode at $$25^{\circ} \mathrm{C}$$ in a neutral solution is ($$p_{\mathrm{H}_2}= 26. . The rate constant for a zero order reaction $$A \longrightarrow$$ products is $$0.0030 \mathrm{~mol} \mathrm{~L}^{-1} 27. The diameters range of colloidal particles is approximately. 28. Photographic plates are prepared by coating emulsion of which of the following in gelatin? 29. What are $$x$$ and $$y$$ in the following reaction?
$$x \mathrm{~Pb}_3 \mathrm{O}_4 \longrightarrow y \mathrm{PbO}+\math 30. Assertion (A) HCl gas is dried by passing through concentrated H$$_2$$SO$$_4$$.
Reason (R) HCl gas reacts with NH$$_3$$ 31. The catalyst used in the manufacture of polyethylene is a mixture of 32. Which of the following is correct related to the colours of $$\mathrm{TiCl}_3(X)$$ and $$\left[\mathrm{Ti}\left(\mathrm{ 33. Which hormone tends to increase the blood glucose level in human? 34. Which of the following molecules is eliminated during peptide bond formation? 35. Identify the major product formed from the following.
36. When 1-chlorobutane is treated with aqueous KOH it gives P. However, when it is treated with alcoholic KOH it gives Q. I 37. Identify the major product formed in the following reaction sequence
38. Arrange the following in increasing order of their reactivity for nucleophilic addition reaction.
(A)
(B)
(C)
(D) 39. In the presence of peroxide, styrene reacts with HBr to give $$X$$. When $$X$$ is reacted with magnesium in dry ether fo 40. Arrange the following in decreasing order of their pKb values
A. ,$$\mathrm{CH}_3 \mathrm{NH}_2$$
B. $$(\mathrm{CH}_3)_3
Mathematics
1. The range of the real valued function $$f(x)=\sqrt{\frac{x^2+2 x+8}{x^2+2 x+4}}$$ is 2. If $$f(x)=\sqrt{2-x^2}$$ and $$g(x)=\log (1-x)$$ are two real valued functions, then the domain of the function $$(f+g)( 3. For $$i=1,2,3$$ and $$j=1,23$$
If $$a_i^2+b_i^2+c_i^2=1, a_i a_j+b_i b_j+c_i c_j=0, \forall i \neq j$$
and $$A=\left[\be 4. If $$A=\frac{1}{7}\left[\begin{array}{ccc}3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3\end{array}\right]$$, then 5. If $$A=\left[\begin{array}{cc}\alpha^2 & 5 \\ 5 & -\alpha\end{array}\right]$$ and $$\operatorname{det}\left(A^{10}\right 6. Let $$A=\left[\begin{array}{ccc}5 & \sin ^2 \theta & \cos ^2 \theta \\ -\sin ^2 \theta & -5 & 1 \\ \cos ^2 \theta & 1 & 7. $$i z^3+z^2-z+i=0 \Rightarrow|z|=$$ 8. If $$\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$$, then the true statement among the following is 9. If the identity $$\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c$$ holds for some $$a, b, c \in Q$$ then $$(a, b, c)=$ 10. The number of integer solutions of the equation $$|1-i|^x=2^x$$ is 11. If $$f(x)=a x^2+b x+c$$ for some $$a, b, c \in R$$ with $$a+b+c=3$$ and $$f(x+y)=f(x)+f(y)+x y, \forall x, y \in R$$. Th 12. The number of positive real roots of the equation $$3^{x+1}+3^{-x+1}=10$$ is 13. The number of real roots of the equation $$\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}$$ is 14. If $$4^x-3^{x-1 / 2}=3^{x+1 / 2}-2^{2 x-1}$$, then the value of $$x$$ is 15. The total number of permutations of $$n$$ different things taken not more than $$r$$ at a time, when each thing may be r 16. How many chords can be drawn through 21 points on a circle? 17. If a polygon of $$n$$ sides has 560 diagonals, then $$n=$$ 18. A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be plac 19. If $$\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}=\frac{A x+B}{x^2+1}$$ $$+\frac{C x+D}{\left(x^2+1\right)^2}+\frac{E x+F} 20. The value of $$\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$$ is 21. If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$ 22. $$\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=$$ 23. In a $$\triangle A B C$$, if $$a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=$$ 24. If $$\operatorname{cosech} x=\frac{4}{5}$$, then $$\sinh x=$$ 25. The value of $$\frac{1+\tan \mathrm{h} x}{1-\tan \mathrm{h} x}$$ is 26. If in a $$\triangle A B C, a=2, b=3$$ and $$c=4$$, then $$\tan (A / 2)=$$ 27. If the angles of a $$\triangle A B C$$ are in the ratio $$1: 2: 3$$, then the corresponding sides are in the ratio 28. In a $$\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=$$ 29. The point of intersection of the lines $$\mathbf{r}=2 \mathbf{b}+t(6 \mathbf{c}-\mathbf{a})$$ and $$\mathbf{r}=\mathbf{a 30. In quadrilateral $$A B C D, \mathbf{A B}=\mathbf{a}, \mathbf{B C}=\mathbf{b}$$. $$\mathbf{D A}=\mathbf{a}-\mathbf{b}, M$ 31. The vectors $$3 \mathbf{a}-5 \mathbf{b}$$ and $$2 \mathbf{a}+\mathbf{b}$$ are mutually perpendicular and the vectors $$a 32. Let $$\mathbf{a}=x \hat{i}+y \hat{j}+z \hat{k}$$ and $$x=2 y$$. If $$|\mathbf{a}|=5 \sqrt{2}$$ and a makes an angle of $ 33. Let $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ be the position vectors of the vertices of a $$\triangle A B C$$. Through the 34. The mean deviation about the mean for the following data.
$$5,6,7,8,6,9,13,12,15 \text { is }$$ 35. A box contains 100 balls, numbered from 1 to 100 . If 3 balls are selected one after the other at random with replacemen 36. In a lottery, containing 35 tickets, exactly 10 tickets bear a prize. If a ticket is drawn at random, then the probabili 37. A bag contains 7 green and 5 black balls. 3 balls are drawn at random one after the other. If the balls are not replaced 38. If $$x$$ is chosen at random from the set $$\{1,2,3, 4\}$$ and $$y$$ is chosen at random from the set $$\{5,6,7\}$$, the 39. The discrete random variables $$X$$ and $$Y$$ are independent from one another and are defined as $$X \sim B(16,0.25)$$ 40. If 6 is the mean of a Poisson distribution, then $$P(X \geq 3)=$$ 41. A stick of length $$r$$ units slides with its ends on coordinate axes. Then, the locus of the mid-point of the stick is 42. The least distance from origin to a point on the line $$y=x+3$$ which lies at a distance of 2 units from $$(0,3)$$ is 43. Starting from the point $$A(-3,4)$$, a moving object touches $$2 x+y-7=0$$ at $$B$$ and reaches the point $$C(0,1)$$. If 44. Suppose a triangle is formed by $$x+y=10$$ and the coordinate axes. Then, the number of points $$(x, y)$$ where $$x$$ an 45. If the lines represented by $$a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$$ intersect on the $$X$$-axis, which of the following 46. For $$\alpha \in\left[0, \frac{\pi}{2}\right]$$, the angle between the lines represented by $$[x \cos \theta-y] [(\cos \ 47. The locus of centers of the circles, possessing the same area and having $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as their co 48. For any two non-zero real numbers $$a$$ and $$b$$ if this line $$\frac{x}{a}+\frac{y}{b}=1$$ is a tangent to the circle 49. The length of the intercept on the line $$4 x-3 y-10=0$$ by the circle $$x^2+y^2-2 x+4 y-20=0$$ is 50. The pole of the line $$\frac{x}{a}+\frac{y}{b}=1$$ with respect to the circle $$x^2+y^2=c^2$$ is 51. If the tangent at the point $$P$$ on the circle $$x^2+y^2+6 x+6 y=2$$ meets the straight line $$5 x-2 y+6=0$$ at a point 52. Suppose a parabola with focus at $$(0,0)$$ has $$x-y+1=0$$ as its tangent at the vertex. Then, the equation of its direc 53. The eccentric angle of a point on the ellipse $$x^2+3 y^2=6$$ lying at a distance of 2 units from its centre is 54. Let origin be the centre, $$( \pm 3,0)$$ be the foci and $$\frac{3}{2}$$ be the eccentricity of a hyperbola.
Then, the l 55. The locus of a variable point whose chord of contact w.r.t. the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ subtends 56. If the point $$(a, 8,-2)$$ divides the line segment joining the points $$(1,4,6)$$ and $$(5,2,10)$$ in the ratio $$m: n$ 57. If $$(a, b, c)$$ are the direction ratios of a line joining the points $$(4,3,-5)$$ and $$(-2,1,-8)$$, then the point $$ 58. The $$x$$-intercept of a plane $$\pi$$ passing through the point $$(1,1,1)$$ is $$\frac{5}{2}$$ and the perpendicular di 59. Let $$f: R^{+} \longrightarrow R^{+}$$ be a function satisfying $$f(x)-x=\lambda$$ (constant), $$\forall x \in R^{+}$$ a 60. $$\begin{aligned}
& \text { If } \lim _{x \rightarrow 0} \frac{|x|}{\sqrt{x^4+4 x^2+5}}=k \\
& \lim _{x \rightarrow 0} x 61. If $$\lim _\limits{n \rightarrow \infty} x^n \log _e x=0$$, then $$\log _x 12=$$ 62. If $$f(x)=\cot ^{-1}\left(\frac{x^x+x^{-x}}{2}\right)$$, then $$f^{\prime}(1)=$$ 63. If $$f(x)=\operatorname{Max}\{3-x, 3+x, 6\}$$ is not differentiable at $$x=a$$, and $$x=b$$, then $$|a|+|b|=$$ 64. If $$x^3-2 x^2 y^2+5 x+y-5=0$$, then at $$(\mathrm{l}, \mathrm{l}), y^{\prime \prime}(\mathrm{l})=$$ 65. If the curves $$y=x^3-3 x^2-8 x-4$$ and $$y=3 x^2+7 x+4$$ touch each other at a point $$P$$, then the equation of common 66. If $$a x+b y=1$$ is a normal to the parabola $$y^2=4 p x$$, then the condition is 67. The maximum value of $$f(x)=\frac{x}{1+4 x+x^2}$$ is 68. The minimum value of $$f(x)=x+\frac{4}{x+2}$$ is 69. The condition that $$f(x)=a x^3+b x^2+c x+d$$ has no extreme value is 70. Assertion (A) If $$I_n=\int \cot ^n x d x$$, then
$$I_6+I_4=\frac{-\cot ^5 x}{5}$$
Reason (R) $$\int \cot ^n x d x=\frac 71. If $$I_n=\int \tan ^n x d x$$, and $$I_0+I_1+2 I_2+2 I_3+2 I_4 +I_5+I_6=\sum_\limits{k=1}^n \frac{\tan ^k x}{k}$$, then 72. $$\int \frac{e^{\cot x}}{\sin ^2 x}(2 \log \operatorname{cosec} x+\sin 2 x) d x=$$ 73. The parametric form of a curve is $$x=\frac{t^3}{t^2-1} y=\frac{t}{t^2-1}$$, then $$\int \frac{d x}{x-3 y}=$$
74. $$\int_0^1 a^k x^k d x=$$ 75. Let $$\alpha$$ and $$\beta(\alpha 76. $$\int_0^\pi x\left(\sin ^2(\sin x)+\cos ^2(\cos x)\right) d x=$$ 77. $$\lim _\limits{n \rightarrow \infty}\left(\frac{1}{1^5+n^5}+\frac{2^4}{2^5+n^5}+\frac{3^4}{3^5+n^5}+\ldots+\frac{n^4}{n 78. If the solution of $$\frac{d y}{d x}-y \log _e 0.5=0, y(0)=1$$, and $$y(x) \rightarrow k$$, as $$x \rightarrow \infty$$, 79. At any point $$(x, y)$$ on a curve if the length of the subnormal is $$(x-1)$$ and the curve passes through $$(1,2)$$, t 80. $$y=A e^x+B e^{-2 x}$$ satisfies which of the following differential equations?
Physics
1. If $$N_A, N_B$$ and $$N_C$$ are the number of significant figures in $$A=0.001204 \mathrm{~m}, B=43120000 \mathrm{~m}$$ 2. A car covers a distance at speed of $$60 \mathrm{~km} \mathrm{~h}^{-1}$$. It returns and comes back to the original poin 3. A car travels with a speed of $$40 \mathrm{~km} \mathrm{~h}^{-1}$$. Rain drops are falling at a constant speed verticall 4. A projectile with speed $$50 \mathrm{~ms}^{-1}$$ is thrown at an angle of $$60^{\circ}$$ with the horizontal. The maximu 5. Two rectangular blocks of masses 40 kg and 60 kg are connected by a string and kept on a frictionless horizontal table. 6. A ball of mass 0.5 kg moving horizontally at $$10 \mathrm{~ms}^{-1}$$ strikes a vertical wall and rebounds with speed $$ 7. A mass of 1 kg falls from a height of 1 m and lands on a massless platform supported by a spring having spring constant 8. A bead of mass 400 g is moving along a straight line under a force that delivers a constant power 1.2 W to the bead. If 9. Masses $$m\left(\frac{1}{3}\right)^N \frac{1}{N}$$ are placed at $$x=N$$, when $$N=2,3,4 \ldots \infty$$. If the total m 10. Consider a disc of radius $$R$$ and mass $$M$$. A hole of radius $$\frac{R}{3}$$ is created in the disc, such that the c 11. A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density $$\rho$$. If the m 12. An object undergoing simple harmonic motion takes 0.5 s to travel from one point of zero velocity to the next such point 13. A projectile is thrown straight upward from the earth's surface with an initial speed $$v=\alpha v_e$$ where $$\alpha$$ 14. Same tension is applied to the following four wires made of same material. The elongation is longest in 15. A cone with half the density of water is floating in water as shown in figure. It is depressed down by a small distance 16. Statement (A) When the temperature increases the viscosity of gases increases and the viscosity of liquids decreases.
St 17. A sphere of surface area $$4 \mathrm{~m}^2$$ at temperature 400 K and having emissivity 0.5 is located in an environment 18. A Carnot engine operates between a source and a sink. The efficiency of the engine is $$40 \%$$ and the temperature of t 19. A car engine has a power of 20 kW. The car makes a roundtrip of 1 h. If the thermal efficiency of the engine is $$40 \%$ 20. The number of vibrational degree of freedom of a diatomic molecule is 21. A body is suspended from a string of length 1 m and mass 2 g. The mass of the body to produce a fundamental mode of 100 22. Electrostatic force between two identical charges placed in vacuum at distance of $$r$$ is F. A slab of width $$\frac{r} 23. A ray is incident from a medium of refractive index 2 into a medium of refractive index 1. The critical angle is 24. An electric dipole with dipole moment $$5 \times 10^{-7} \mathrm{C}-\mathrm{m}$$ is in the electric field of $$2 \times 25. A capacitor of capacitance $$C_1=1 \mu \mathrm{F}$$ is charged using a 9 V battery. $$C_1$$ is, then removed from the ba 26. Two positive point charges of $$10 \mu \mathrm{C}$$ and $$12 \mu \mathrm{C}$$ are placed 10 cm apart in air. The work do 27. Current density in a cylindrical wire of radius $$R$$ varies with radial distance as $$\beta\left(r+r_0\right)^2$$. The 28. A cell can supply currents of 1 A and 0.5 A via resistances of $$2.5 \Omega$$ and $$10 \Omega$$, respectively. The inter 29. Two infinitely long wires each carrying the same current and pointing in $$+y$$ direction are placed in the $$x y$$-plan 30. Two electrons, $$e_1$$ and $$e_2$$ of mass $$m$$ and charge $$q$$ are injected into the perpendicular direction of the m 31. A compass needle oscillates 20 times per minute at a place where the dip is $$45^{\circ}$$ and the magnetic field is $$B 32. A plane electromagnetic wave travels in free space along $$Z$$-axis. At a particular point in space, the electric field 33. A coil of inductance 0.1 H and resistance $$110 \Omega$$ is connected to a source of 110 V and 350 Hz . The phase differ 34. If the average power per unit area delivered by an electromagnetic wave is $$9240 \mathrm{~Wm}^{-2}$$. then the amplitud 35. A beam of light with intensity $$10^{-3} \mathrm{~Nm}^{-2}$$ and cross-sectional area $$20 \mathrm{~cm}^2$$ is incident 36. The metal which has the highest work function in the following is 37. Energy of a stationary electron in the hydrogen atom is $$E=\frac{13.6}{n^2} \mathrm{~eV}$$, then the energies required 38. The graph of $$\ln \left(\frac{R}{R_0}\right)$$ versus $\ln A$ is where $$R$$ is radius of a nucleus, $$A$$ is its mass 39. Output of following logic circuit is
40. The maximum number of TV signals, that can be transmitted along a co-axial cable is
1
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0
Assertion (A) If $$I_n=\int \cot ^n x d x$$, then $$I_6+I_4=\frac{-\cot ^5 x}{5}$$
Reason (R) $$\int \cot ^n x d x=\frac{-\cot ^{n-1} x}{n} -\int \cot ^{n-2} x d x$$
A
A is false, R is false
B
A is true, R is true
C
A is true, R is false
D
A is false, R is true
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $$I_n=\int \tan ^n x d x$$, and $$I_0+I_1+2 I_2+2 I_3+2 I_4 +I_5+I_6=\sum_\limits{k=1}^n \frac{\tan ^k x}{k}$$, then $$n=$$
A
6
B
5
C
4
D
3
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$\int \frac{e^{\cot x}}{\sin ^2 x}(2 \log \operatorname{cosec} x+\sin 2 x) d x=$$
A
$$-2 e^{\cot x} \log \left(\operatorname{cosec}^2 x\right)+C$$
B
$$-2 e^{\cot x} \log (\operatorname{cosec} x)+C$$
C
$$-2 e^{\cot x} \log (\operatorname{cosec} x+\sin x)+C$$
D
$$-2 e^{\cot x} \log (\operatorname{cosec} x-\cot x)+C$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0
The parametric form of a curve is $$x=\frac{t^3}{t^2-1} y=\frac{t}{t^2-1}$$, then $$\int \frac{d x}{x-3 y}=$$
A
$$\frac{1}{2} \log \left(t^2-1\right)+C$$
B
$$2 \log \left(t\left(t^2-1\right)\right)+C$$
C
$$\frac{1}{4} \log \left(\frac{t}{t^2-3}\right)+C$$
D
$$\frac{5}{2} \log \left(t+\frac{1}{t^2}\right)+C$$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
AP EAPCET
Papers
2022