Chemistry
1. Which of the following set of polymers are used as fibre?
(i) Teflon
(ii) Starch
(iii) Terylene
(iv) Orlon 2. The biodegradable polymer obtained by polymerisation of glycine and aminocaproic acid is 3. The compound is 4. Which one of the following is a cationic detergent? 5. The type of linkage present between nucleotides is 6. $\alpha-D-(+)$-glucose and $\beta-D-(+)$-glucose are 7. Propanone and propanal are 8. Sodium ethanoate on heating with soda lime gives ' $X^{\prime}$. Electrolysis of aqueous solution of sodium ethanoate gi 9. But-1-yne on reaction with dil. $\mathrm{H}_2 \mathrm{SO}_4$ in presence of $\mathrm{Hg}^{2+}$ ions at 333 K gives 10. Biologically active adrenaline and ephedrine used to increase blood pressure contain 11. In the reaction,
Aniline $\xrightarrow[\text { Dil. } \mathrm{HCl}]{\mathrm{NaNO}_2} P \xrightarrow[\text { NaOH }]{\tex 12. The female sex hormone which is responsible for the development of secondary female characteristics and participates in 13. In the following scheme of reaction.
X, y and Z respectively are 14. 8.8 g of monohydric alcohol added to ethyl magnesium iodide in ether liberates $2240 \mathrm{~cm}^3$ of ethane at STP. T 15. When a tertiary alcohol ' $A^{\prime}\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ reacts with $20 \% \mathrm{H} 16. PCC is 17. On treating 100 mL of 0.1 M aqueous solution of the complex $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$ with exces 18. The complex compounds $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ and $\left[\mathr 19. Which of the following statements are true about $\left[\mathrm{CoF}_6\right]^{3-}$ ion ?
I. The complex has octahedral 20. A haloalkane undergoes $\mathrm{S}_{\mathrm{N}} 2$ or $\mathrm{S}_{\mathrm{N}} 1$ reaction depending on 21. 2-methyl propane can be prepared by Wurtz reaction. The haloalkanes taken along with metallic sodium and dry ether are : 22. In the analysis of III group basic radicals of salts, the purpose of adding $\mathrm{NH}_4 \mathrm{Cl}(s)$ to $\mathrm{N 23. Solubility product of $\mathrm{CaC}_2 \mathrm{O}_4$ at a given temperature in pure water is $4 \times 10^{-9}\left(\math 24. In the reaction between moist $\mathrm{SO}_2$ and acidified permanganate solution. 25. Which one of the following properties is generally not applicable to ionic hydrides?
26. Which one of the following nitrate will decompose to give $\mathrm{NO}_2$ on heating ? 27. Which of the following halides cannot be hydrolysed? 28. 0.48 g of an organic compound on complete combustion produced 0.22 g of $\mathrm{CO}_2$. The percentage of C in the give 29. In the given sequence of reactions, identify ' $P^{\prime}, Q^{\prime}, R^{\prime}$ and ' $S$ respectively.
30. The first chlorinated organic insecticide prepared is 31. Which of the following crystals has the unit cell such that $a=b \neq c$ and $\alpha=\beta=90^{\circ}$, $\gamma=120^{\ci 32. MnO exhibits 33. The number of atoms in 4.5 g of a face-centred cubic crystal with edge length 300 pm is
(Given : Density $=10 \mathrm{~g 34. Vapour pressure of a solution containing 18 g of glucose and 178.2 g of water at $100^{\circ} \mathrm{C}$ is
(Vapour pre 35. A mixture of phenol and aniline shows negative deviation from Raoult's law. This is due to the formation of 36. Which one of the following pairs will show positive deviation from Raoult's law? 37. How many coulombs are required to oxidise 0.1 mole of $\mathrm{H}_2 \mathrm{O}$ to oxygen? 38. A current of 3 A is passed through a molten calcium salt for 1 hr 47 min 13 s . The mass of calcium deposited is
(Molar 39. The value of ' $A$ ' in the equation $\lambda_{\mathrm{m}}=\lambda_{\mathrm{m}}^{\circ}-A \sqrt{C}$ is same for the pair 40. For the reaction, $A \rightleftharpoons B, E_a=50 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta H=-20 \mathrm{~kJ} \mathr 41. For the reaction, $\mathrm{PCl}_5 \longrightarrow \mathrm{PCl}_3+\mathrm{Cl}_2$, rate and rate constant are $1.02 \times 42. Which one of the following does not represent Arrhenius equation? 43. Identify the incorrect statement 44. For the coagulations of positively charged hydrated ferric - oxide sol, the flocculating power of the ions is in the ord 45. Gold sol is not a 46. The incorrect statement about Hall -Heroult process is 47. Select the correct statement : 48. $\mathrm{NO}_2$ gas is 49. Identify the incorrect statement from the following. 50. The correct decreasing order of boiling point of hydrogen halides is 51. The synthetically produced radioactive noble gas by the collision of ${ }_{98}^{249} \mathrm{Cf}$ with ${ }_{20}^{48} \m 52. The transition element $(\approx 5 \%)$ present with lanthanoid metal in misch metal is 53. Match the following.
I. $\mathrm{Zn}^{2+}\quad$ (i) $d^8$ configuration
II. $\mathrm{Cu}^{2+}\quad$ (ii) Colourless
III. 54. Which of the following statements related to lanthanoids is incorrect? 55. A metalloid is 56. A pair of isoelectronic species having bond order of one is 57. Identify the wrong relation for real gases : 58. From the diagram $(Z)=\frac{V_{\text {real }}}{V_{\text {ideal }}}$
$\Delta_r H$ for the reaction, $C \rightarrow A$ is 59. For which one of the following mixtures is composition uniform throughout? 60. The energy associated with first orbit of $\mathrm{He}^{+}$ is
Mathematics
1. Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is 56 more than the 2. If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then 3. If in two circles, arcs of the same length subtend angles $30^{\circ}$ and $78^{\circ}$ at the centre, then the ratio of 4. If $\triangle A B C$ is right angled at $C$, then the value of $\tan A+\tan B$ is 5. The real value of ' $\alpha$ ' for which $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely real is 6. The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then 7. The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is 8. In the expansion of $(1+x)^n$ $\frac{C_1}{C_0}+2 \frac{C_2}{C_1}+3 \frac{C_3}{2}+\ldots+n \frac{C_n}{C_{n-1}}$ is equal 9. If $S_n$ stands for sum to $n$-terms of a GP with $a$ as the first term and $r$ as the common ratio, then $S_n: S_{2 n}$ 10. If $A M$ and GM of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation is 11. The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is 12. The equation of parabola whose focus is $(6,0)$ and directrix is $x=-6$ is 13. $\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{2} \cos x-1}{\cot x-1}$ is equal to 14. The negation of the statement "For every real number $x ; x^2+5$ is positive" is 15. Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the obs 16. Let $f: R \rightarrow R$ be given $f(x)=\tan x$. Then, $f^{-1}(1)$ is 17. Let $f: R \rightarrow R$ be defined by $f(x)=x^2+1$. Then, the pre images of 17 and $-$3 , respectively are 18. Let $(g \circ f)(x)=\sin x$ and $f \circ g(x)=(\sin \sqrt{x})^2$. Then, 19. Let $A=\{2,3,4,5, \ldots, 16,17,18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defi 20. If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then $x(y+z)+y(z+x)+z(x+y)$ equals to 21. If $2 \sin ^{-1} x-3 \cos ^{-1} x=4, x \in[-1,1]$, then $2 \sin ^{-1} x+3 \cos ^{-1} x$ is equal to
22. If $A$ is a square matrix, such that $A^2=A$, then $(I+A)^3$ is equal to 23. If $A=\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$, then $A^{10}$ is equal to 24. If $f(x)=\left|\begin{array}{ccc}x-3 & 2 x^2-18 & 2 x^3-81 \\ x-5 & 2 x^2-50 & 4 x^3-500 \\ 1 & 2 & 3\end{array}\right|$ 25. If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 26. If $A=\left|\begin{array}{cc}x & 1 \\ 1 & x\end{array}\right|$ and $B=\left|\begin{array}{ccc}x & 1 & 1 \\ 1 & x & 1 \\ 27. Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x & 2 x \\ \sin x & x & x\end{array}\right|$. Then, $\lim 28. Which one of the following observations is correct for the features of logarithm function to any base $b>1$ ? 29. The function $f(x)=|\cos x|$ is 30. If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is 31. Let the function satisfy the equation $f(x+y)=f(x) f(y)$ for all $x, y \in R$, where $f(0) \neq 0$. If $f(5)=3$ and $f^{ 32. The value of $C$ in $(0,2)$ satisfying the mean value theorem for the function $f(x)=x(x-1)^2, x \in[0,2]$ is equal to 33. $\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is 34. For the function $f(x)=x^3-6 x^2+12 x-3$; $x=2$ is 35. The function $x^x ; x>0$ is strictly increasing at 36. The maximum volume of the right circular cone with slant height 6 units is 37. If $f(x)=x e^{x(1-x)}$, then $f(x)$ is 38. $$\int \frac{\sin x}{3+4 \cos ^2 x} d x$$ 39. $\int_{-\pi}^\pi\left(1-x^2\right) \sin x \cdot \cos ^2 x d x$ is 40. $$\int \frac{1}{x\left[6(\log x)^2+7 \log x+2\right]} d x \text { is }$$ 41. $\int \frac{\sin \frac{3 x}{2}}{\sin \frac{x}{2}} d x$ is 42. $\int\limits_1^5(|x-3|+|1-x|) d x=$ 43. $$\lim _\limits{n \rightarrow \infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\ldots+\frac{1}{5 n}\ri 44. The area of the region bounded by the line $y=3 x$ and the curve $y=x^2$ sq units is 45. The area of the region bounded by the line $y=x$ and the curve $y=x^3$ is 46. The solution of $e^{d y / d x}=x+1, y(0)=3$ is 47. The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coor 48. The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}} 49. The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{ 50. Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{ 51. If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $\ 52. If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are mutually 53. The distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is 54. The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}$ are the plane $2 x-2 y+z=5$ 55. The equation $x y=0$ in three-dimensional space represents 56. The plane containing the point $(3,2,0)$ and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is 57. Corner points of the feasible region for an LPP are $(0,2),(3,0),(6,0),(6,8)$ and $(0,5)$. Let $Z=4 x+6 y$ be the object 58. A die is thrown 10 times. The probability that an odd number will come up at least once is 59. A random variable $X$ has the following probability distribution:
.tg {border-collapse:collapse;border-spacing:0;}
.tg 60. If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is e
Physics
1. The ratio of molar specific heats of oxygen is
2. For a particle executing simple harmonic motion (SHM), at its mean position 3. A motor-cyclist moving towards a huge cliff with a speed of $18 \mathrm{kmh}^{-1}$, blows a horn of source frequency 325 4. A body has a charge of $-3.2 \mu \mathrm{C}$. The number of excess electrons will be 5. A point charge $A$ of $+10 \mu \mathrm{C}$ and another point charge $B$ of $+20 \mu \mathrm{C}$ are kept 1 m apart in fr 6. A uniform electric field $E=3 \times 10^5 \mathrm{NC}^{-1}$ is acting along the positive $Y$-axis. The electric flux thr 7. The total electric flux through a closed spherical surface of radius $r$ enclosing an electric dipole of dipole moment $ 8. Under electrostatic conditien of a charged conductor, which among the following statements is true? 9. A cube of side 1 cm contains 100 molecules each having an induced dipole moment of $0.2 \times 10^{-6} \mathrm{C}-\mathr 10. A capacitor of capacitance $5 \mu \mathrm{~F}$ is charged by a battery of emf 10 V . At an instant of time, the potentia 11. E is the electric field inside a conductor whose material has conductivity $\sigma$ and resistivity $\rho$. The current 12. In the circuit shown, the end $A$ is at potential $V_0$ and end $B$ is grounded. The electric current $I$ indicated in t 13. The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free 14. The $I-V$ graph for a conductor at two different temperatures $100^{\circ} \mathrm{C}$ and $400^{\circ} \mathrm{C}$ is a 15. An electric blub of $60 \mathrm{~W}, 120 \mathrm{~V}$ is to be connected to 220 V source. What resistance should be conn 16. In an experiment to determine the temperature coefficient of resistance of a conductor, a coil of wire $X$ is immersed i 17. A moving electron produces 18. A coil having 9 turns carrying a current produces magnetic field $B_1$ at the centre. Now the coil is rewounded into 3 t 19. 19. A particle of specific charge $q / m=\pi \mathrm{C} \mathrm{kg}^{-1}$ is projected the origin towards positive $X$-a 20. The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is 64 times the magnetic field at 21. Magnetic hysterisis is exhibited by ............ magnetic materials 22. Magnetic susceptibility of Mg at 300 K is $1.2 \times 10^{-5}$. What is its susceptibility at $200 \mathrm{~K} ?$ 23. A uniform magnetic field of strength $B=2 \mathrm{mT}$ exists vertically downwards. These magnetic field lines pass thro 24.
In the figure, a conducting ring of certain resistance is falling towards a current carrying straight long conductor. T 25. An induced current of 2 A flows through a coil. The resistance of the coil is $10 \Omega$. What is the change in magneti 26. A square loop of side length $a$ is moving away from an infinitely long current carrying conductor at a constant speed $ 27. Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication? 28. In an $L-C-R$ series circuit, the value of only capacitance $C$ is varied. The resulting variation of resonance frequenc 29.
The figure shows variation of $R, X_L$ and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. Then, for what frequen 30. Electromagnetic waves are incident normally on a perfectly reflecting surface having surface area $A$. If $I$ is the int 31. The final image formed by an astronomical telescope is 32. If the angle of minimum deviation is equal to angle of a prism for an equilateral prism, then the speed of light inside 33. A luminous point object $O$ is placed at a distance $2 R$ from the spherical boundary separating two transparent media o 34. An equiconvex lens of radius of curvature 14 cm is made up of two different materials. Left half and right half of verti 35. A galaxy is moving away from the Earth so that a spectral line at 600 nm is observed at 601 nm . Then, the speed of the 36.
Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids 2 and 3 make $30^{\ 37. In Young's double slit experiment, an electron beam is used to produce interference fringes of width $\beta_1$. Now the 38. Light of energy $E$ falls normally on a metal of work function $\frac{E}{3}$. The kinetic energies $K$ of the photo elec 39. The photoelectric work function for photo metal is 2.4 eV . Among the four wavelengths, the wavelength of light for whic 40. In alpha particle scattering experiment, if $v$ is the initial velocity of the particle, then the distance of closest ap 41. The ratio of area of first excited state to ground state of orbit of hydrogen atom is 42. The ratio of volume of $\mathrm{Al}^{27}$ nucleus to its surface area is (Given, $R_0=1.2 \times 10^{-15} \mathrm{~m}$) 43. Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ } 44. The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$, there are $N_ 45. Depletion region in an unbiased semiconductor diode is a region consisting of
only free electrons
only holes 46. The upper level of valence band and lower level of conduction band overlap in the case of
47. In the diagram shown, the Zener diode has a reverse breakdown voltage of $V_Z$. The current through the load resistance 48. A $p-n$ junction diode is connected to a battery of emf 5.7 V in series with a resistant $5 \mathrm{k} \Omega$ such that 49. An athlete runs along a circular track of diameter 80 m . The distance travelled and the magnitude of displacement of th 50. Among the given pair of vectors, the resultant of two vectors can never be 3 units. The vectors are 51. A block of certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is 30$^\circ 52. A particle of mass 500 g is at rest. It is free to move along a straight line. The power delivered to the particle varie 53. Dimensional formula for activity of a radioactive substance is 54. A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along .......... .
55. A body of mass 1 kg is suspended by a weightless string which passes over a frictionless pulley of mass 2 kg as shown in 56. What is the value of acceleration due to gravity at a height equal to half the radius of the Earth, from its surface ? 57. A thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due 58. Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$. The 59. A solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\th 60. One mole of an ideal monoatomic gas is taken round the cyclic process MNOM. The work done by the gas is
1
KCET 2024
MCQ (Single Correct Answer)
+1
-0
If $f(x)=x e^{x(1-x)}$, then $f(x)$ is
A
increasing in $R$
B
decreasing in $R$
C
decreasing in $\left[-\frac{1}{2}, 1\right]$
D
increasing in $\left[-\frac{1}{2}, 1\right]$
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0
$$\int \frac{\sin x}{3+4 \cos ^2 x} d x$$
A
$-\frac{1}{2 \sqrt{3}} \tan ^{-1}\left(\frac{2 \cos x}{\sqrt{3}}\right)+C$
B
$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{\cos x}{3}\right)+C$
C
$\frac{1}{2 \sqrt{3}} \tan ^{-1}\left(\frac{\cos x}{3}\right)+C$
D
$-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \cos x}{3}\right)+C$
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0
$\int_{-\pi}^\pi\left(1-x^2\right) \sin x \cdot \cos ^2 x d x$ is
A
$\pi-\frac{\pi^2}{3}$
B
$2 \pi-\pi^3$
C
$\pi-\frac{\pi^3}{2}$
D
$0$
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0
$$\int \frac{1}{x\left[6(\log x)^2+7 \log x+2\right]} d x \text { is }$$
A
$\frac{1}{2} \log \left|\frac{2 \log x+1}{3 \log x+2}\right|+C$
B
$\log \left|\frac{2 \log x+1}{3 \log x+2}\right|+c$
C
$\log \left|\frac{3 \log x+2}{2 \log x+1}\right|+C$
D
$\frac{1}{2} \log \left|\frac{3 \log x+2}{2 \log x+1}\right|+C$