Chemistry
1. The reaction quotient ' $Q$ ' is useful inpredicting the direction of the reaction. Which of the following is incorrect? 2. Square planar complex of the type $M_{\text {AXBL }}$ (where $A, B, X$ and $L$ ) are unidenate ligands shows following s 3. By passing electric current, $\mathrm{NaClO}_3$ is converted in to $\mathrm{NaClO}_4$ according to the following equatio 4. The pressure of real gases is less than that of ideal gas because of
5. Which of the following reagent cannot be used to oxidise primary alcohols to aldehydes?
6. The product formed during the following reaction are
7. Bactericidal antibiotics among the following is
8. Which of the following is not a biodegradable polymer?
9. Reduction of ketones cannot be carried out with which of the following reagents?
10. Which of the following structure of a molecule is expected to have three bond pairs and one lone pair of electrons?
11. The standard reduction potential at 298 K for the following half cell reaction
$$ \begin{aligned} & 2 \mathrm{n}^{2+}(a 12. Plaster of Paris is represented as
13. Toluene reacts with halogen in presence of iron (III) chloride giving ortho and para halo compounds. The reaction is
14. In a face centred cubic arrangement of $A$ and $B$ atoms in which ' $A$ ' atoms are at the corners of the unit cell and 15. The correct order of increasing basic nature for the bases $\mathrm{NH}_3, \mathrm{CH}_3 \mathrm{NH}_2$ and $\left(\math 16. The electronegativities of $\mathrm{C}, \mathrm{N}, \mathrm{Si}$ and P are in the order of
17. For a reaction $\frac{1}{2} A \rightarrow 2 B$ rate of disappearance of $A$ is related to rate of appearance of $B$ by t 18. Which of the following statement is incorrect?
19. The coordination number and the oxidation state of the. element ' $M$ ' in the complex $\left[\mathrm{M}(e n)_2\left(\ma 20. Select wrong chemical reaction among the following.
21. If $3.01 \times 10^{20}$ molecules are removed from 98 mg of $\mathrm{H}_2 \mathrm{SO}_4$, then number of moles of $\mat 22. Which of the following elements forms $p_\pi-p_\pi$ bond with itself?
23. Which of the following statement is in accordance with the Arrhenius equations?
24. The glycosidic linkage present in sucrose is between
25. A reaction has both $\Delta H$ and $\Delta S$ -ve. The rate of reaction
26. Addition of mineral acid to an aqueous solution of borax, the following compound is formed
27. The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition 28. The process which is responsible for the formation of delta at a place where rivers meets the sea is
29. Extraction of chlorine from brine solution is based on
30. Lower members of aliphatic carboxylic acid are soluble in water. This is due to
31. Which one of the following is not a common component of photo-chemical smog?
32. Which of the following is not a favourable condition for physical adsorption?
33. The correct statement regarding defect in solids is
34. According to crystal field theory, the $M-L$ bond in a complex is
35. Which of the following crystal has unit cell such that $a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^{\ci 36. Which of the following statement is wrong regarding lanthanoids?
37. Hormones are secreted by ductless glands of human body. Iodine containing hormone is
38. The, vant Hoff's factor ' $\boldsymbol{i}$ ' accounts for
39. In which of the following, homolytic bond fission takes place?
40. The correct set of quantum number for the unpaired electrons of chlorine atom is
41. Which of the following metallic oxide exhibit amphoteric nature?
42. Which one of the following noble gas has an unusual property of diffusing through the materials such as rubber, glass or 43. When the pure solvent diffuses out of the solution through the semi-permeable membrane then the process is called
44. Cannizzaro's reaction is an example of auto oxidation
45. The equilibrium constant for the reaction $\mathrm{N}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})$ 46. Which of the following is correct electron dot structure of $\mathrm{N}_2 \mathrm{O}$ molecule? 47. Pick the correct statement among the following statement.
48. Pick the wrong statements from the following.
49. Which of the following order is true regarding the acidic nature of phenol?
50. Identify the correct statement in the following.
51. Galbriel phthalimide synthesis is used in the preparation of primary amine from phthalimide, which of the following reag 52. $3 \mathrm{ClO}^{-}(a q) \longrightarrow \mathrm{ClO}^{-}+2 \mathrm{Cl}^{-}$is an example of
53. Hydrogenation of vegetable oils in presence of finely divided nickel as catalyst.The reaction is
54. In the manufacture of hydrogen from water gas $\left(\mathrm{CO}+\mathrm{H}_2\right)$, which of the following is correct 55. In the following sequence of reactions
$$ \mathrm{CH}_3 \mathrm{Br} \xrightarrow{\mathrm{KCN}} A \xrightarrow{\mathrm{H} 56. The monomer used in novolac, a polymer used in paints
57. For the preparation of alkanes, aqueous solution of sodium of potassium salt of carboxylic acid is subjected to
58. Which of the following aqueous solution has highest freezing point?
59. In the electrolysis of aqueous sodium chloride solution, which of the half cell reaction will occur at anode?
60. The metal extracted by leaching with a cyanide is
Mathematics
1. If an LPP admits optimal solution at two consecutive vertices of a feasible region, then
2. $$
\text { } \begin{aligned}
Let\,\,\,\Delta & =\left|\begin{array}{lll}
A x & x^2 & 1 \\
B y & y^2 & 1 \\
C z & z^2 & 3. The total number of terms in the expansion of $(x+a)^{47}-(x-a)^{47}$ after simplification is
4. The function $f(x)=x^2+2 x-5$ is strictly increasing in the interval
5. The shaded region in the figure is the solution set of the inequations
6. The point on the curve $y^2=x$ where the tangent makes an angle of $\pi / 4$ with $X$-axis is
7. $$ \int\limits_{-\pi / 2}^{\pi / 2} \frac{d x}{e^{\sin x}+1} $$ 8. If $a$ and $\mathbf{b}$ are unit vectors, then angle between $\mathbf{a}$ and $\mathbf{b}$ for $\sqrt{3} \mathbf{a}-\mat 9. The contrapositive statement of the statement "If $x$ is prime number, then $x$ is odd" is
10. $\int\limits_{-5}^5|x+2| d x$ is equal to
11. If $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$, t 12. If $2\left|\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right|+\left|\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right|=\l 13. $$ \int\limits_0^{\pi / 2} \frac{1}{a^2 \cdot \sin ^2 x+b^2 \cdot \cos ^2 x} d x $$ 14. $$ \int \sqrt{x^2+2 x+5} d x \text { is equal to } $$ 15. A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with repla 16. The range of $\sec ^{-1} x$ is
17. $\int \frac{(x+3) e^x}{(x+4)^2} d x$ is equal to
18. $$ \text { If } y=\left|\begin{array}{ccc} f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c \end{array}\right| \text {, then 19. General solution of differential equations
$\frac{d y}{d x}+y=1(y \neq 1)$ is 20. If $A$ is a square matrix of order $3 \times 3$, then $|K A|$ is equal to
21. If $A=\frac{1}{\pi}\left|\begin{array}{ll}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\f 22. If ${ }^n C_{12}={ }^n C_8$, then $n$ is equal to
23. The probability distribution of $X$ is
$$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \bo 24. The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}$ is
25. $3+5+7+\ldots$ to $n$ terms is
26. $\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x$ is equal to
27. If $A$ and $B$ are finites sets and $A \subset B$, then
28. $$The\,\,value\,\,of\,\,\mathop {\lim }\limits_{\theta \to 0} {{1 - \cos 4\theta } \over {1 - \cos 6\theta }}\,\,is$$ 29. If $\mathbf{a}=2 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\ma 30. If $f(x)=\left\{\begin{array}{cll}k x^2 & \text { if } & x \leq 2 \\ 3 & \text { if } & x>2\end{array}\right.$ is contin 31. The area of triangle with vertices $(K, 0),(4,0)$, $(0,2)$ is 4 sq units, then value of $K$ is
32. If $\left(\frac{1+i}{1-i}\right)^m=1$, then the least positive integral value of $m$ is
33. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors such that $a+b+c=0$, then the value of $\mathbf{a} \cdot \mathb 34. The value of $\cos ^2 45^{\circ}-\sin ^2 15^{\circ}$ is
35. Let $f: R \rightarrow R$ be defined by $f(x)=x^4$, then
36. If $\sin x=\frac{2 t}{1+t^2}, \tan y+\frac{2 t}{1-t^2}$, then $\frac{d y}{d x}$ is equal to
37. The plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1}(\alpha)$ with $X$-axis, the value of $\alpha$ is equal to
38. If $f(x)=8 x^3, g(x)=x^{1 / 3}$, then $f \circ g(x)$ is
39. If $y=\log (\log x)$, then $\frac{d^2 y}{d x^2}$ is equal to
40. $\int\limits_{0.2}^{3.5}[x] d x$ is equal to :
41. If $|x-2| \leq 1$, then
42. The perpendicular distance of the point $P(6,7,8)$ from $X Y$-plane is
43. Binary operation * on $R-\{-1\}$ defined by $a^* b=\frac{a}{b+1}$ is
44. If $y=\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right)$, then $\frac{d y}{d x}$ is equal to
45. The eccentricity of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is
46. The integrating factor of the differential equation
$x \cdot \frac{d y}{d x}+2 y=x^2$ is $(x \neq 0)$ 47. The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is
48. The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is
49. $\int\limits_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x$ is equal to
50. The range of the function $f(x)=\sqrt{9-x^2}$ is
51. Reflexion of the point $(\alpha, \beta, \gamma)$ in $X Y$-plane is
52. The area of the region bounded by the curve $y=x^2$ and the line $y=16$
53. If coefficient of variation is 60 and standard deviation is 24 , then Arithmetic mean is
54. Two events $A$ and $B$ will be independent if
55. Area of the region bounded by the curve $y=\cos x, x=0$ and $x=\pi$ is
56. The value of $c$ in mean value theorem for the function $f(x)=x^2$ in $[2,4]$ is
57. Equation of line passing through the point $(1,2)$ and perpendicular to the line $y=3 x-1$
58. If $\tan ^{-1} x+\tan ^{-1} y=\frac{4 \pi}{5}$, then $\cot ^{-1} x+\cot ^{-1} y$ is equal to
59. If a matrix $A$ is both symmetric and skew symmetric, then
60. The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is
Physics
1. A coil of inductive reactance $1 / \sqrt{3} \Omega$ and resistance $1 \Omega$ is connected to a $200 \mathrm{~V}, 50 \ma 2. A car moving with a velocity of $20 \mathrm{~ms}^{-1}$ stopped at a distance of 40 m . If the same car is travelling at 3. The particle emitted in the decay of ${ }_{92}^{238} \mathrm{U}$ to ${ }_{92}^{234} \mathrm{U}$
4. Of the following graphs, the one that correctly represents the $I-V$ characteristics of a 'Ohmic device' is 5. The susceptibility of a ferromagnetic substance is
6. The working of magnetic braking of trains is based on
7. A substance of mass 49.53 g occupies $1.5 \mathrm{~cm}^3$ of volume. The density of the substance (in $\mathrm{g} \mathr 8. From the following graph of photo current against collector plate potential, for two different intensities of light $I_1 9. Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air
10. If $\mathbf{E}$ and $\mathbf{B}$ represent electric and magnetic field vectors of an electromagentic wave, the direction 11. A body of the mass 50 kg is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, t 12. Two point charges $A=+3 \mathrm{nC}$ and $B=+1 \mathrm{nC}$ are placed 5 cm apart in air. The work done to move charge $ 13. A proton, a deuteron and an $\alpha$-particle are projected perpendicular to the direction of a uniform magnetic field w 14. The S.I. unit of specific heat capacity is
15. In the three parts of a transistor, 'Emitter' is of
16. A bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a n 17. For which combination of working temperatures, the efficiency of Carnot's engine is the least?
18. A basic communication system consists of
(i) Transmitter
(ii) Information sources
(iii) User of information
(iv) Channel 19. According to Huygens' principle, during refraction of light from air to a denser medium
20. A galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \cdot \mathrm{~V}$ along with a${ }^{\text { }} 21. In the A.C. circuit shown, keeping ' $K$ ' pressed, if an iron rod inserted into the coil, the bulb in the circuit,
22. A magnetic dipole of magnetic moment $6 \times 10^{-2}$ A-m ${ }^2$ and moment of inertia $12 \times 10^{-6} \mathrm{~kg 23. $4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of t 24. The mass defect of ${ }_2^4 \mathrm{He}$ is 0.03 u . The binding energy per nucleon of helium (in MeV) is
25. A cylindrical conductor of diameter 0.1 mm carries a current of 90 mA . The current density ( in $\mathrm{Am}^{-2}$ ) is 26. Which of the following properties is 'False' for a bar magnet?
27. According to cartesian sign convention, in ray optics
28. A linear object of height 10 cm is kept in front of a concave mirror of radius of curvature 15 cm , at a distance of 10 29. The energy gap in case of which of the following is less than 3 eV ?
30. The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances $1 \mathrm{pF} 31. Two spheres of electric charges +2 nC and -8 nC are placed at a distance $d$ apart. If they are allowed to touch each ot 32. The value of acceleration due to gravity at a depth of 1600 km is equal to
33. Two simple pendulums $A$ and $B$ are made to oscillate simultaneously and it is found that $A$ completes 10 oscillations 34. A motor pump lifts 6 tonnes of water from a well of depth 25 m to the first floor of height 35 m from the ground floor i 35. The waves set up in a closed pipe are
36. In the figure shown, if the diode forward voltage drop is 0.2 V , the voltage difference between $A$ and $B$ is
37. If $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}$ is perpendicular to $\mathbf{B}=4 \hat{\mathbf{ 38. The angle between velocity and acceleration of a particle describing uniform circular motion is
39. A straight wire of length 50 cm carrying a current of 2.5 A is suspended in mid-air by a uniform magnetic field of 0.5 T 40. 'Young's modulus' is defined as the ratio of
41. Which of the following semi-conducting device is used as voltage regulator?
42. Which of the following logic gate is universal gate 43. A particle is dropped from a height $H$. The de-Broglie wavelength of the particle depends on height as
44. Three point charges of $+2 q,+2 q$ and $-4 q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $A B C 45. In a system of two crossed polarisers, it is found that the intensity of light from the second polariser is half from th 46. A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are ... 47. During scattering of light, the amount of scattering in inversely proportional to................ of wavelength of light 48. A jet plane of wing span 20 m is travelling towards west at a speed of $400 \mathrm{~ms}^{-1}$. If the earth's total mag 49. The energy (in eV ) required to excite an electron from $n=2$ to $n=4$ state in hydrogen atom is
50. 'Hydraulic lift' works on the basis of
51. In a nuclear reactor, the function of the moderator is to decreases
52. The scientist who is credited with the discovery of 'nucleus' in an atom is
53. A system of two capacitors of capacitance $2 \mu \mathrm{~F}$ and $4 \mu \mathrm{~F}$ is connected in series across a po 54. In meter bridge experiment, with a standard resistance in the right gap and a resistance coil dipped in water (in a beak 55. The power dissipated in $3 \Omega$ resistance in the following circuit is
56. The mean energy of a molecule of an ideal gas is
57. The magnetic field at the centre of a current carrying loop of radius 0.1 m is $5 \sqrt{5}$ times that at a point along 58. $$ \text { The value of } I \text { in the figure shown below is } $$
59. In Young's double-slit experiment, if yellow light is replaced by blue light, the interference fringes becomes
60. The output of a step down transformers is measured to be 48 V when connected to a 12 W bulb. The value of peak current i
1
KCET 2017
MCQ (Single Correct Answer)
+1
-0
The integrating factor of the differential equation
$x \cdot \frac{d y}{d x}+2 y=x^2$ is $(x \neq 0)$
A
$x$
B
$\log |x|$
C
$x^2$
D
$e^{\log x}$
2
KCET 2017
MCQ (Single Correct Answer)
+1
-0
The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is
A
$1-x^2$
B
$\frac{2}{x}$
C
$\frac{-1}{2 \sqrt{1-x^2}}$
D
2
3
KCET 2017
MCQ (Single Correct Answer)
+1
-0
The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is
A
$4 \mathrm{~cm}^3 / \mathrm{cm}^2$
B
$6 \mathrm{~cm}^3 / \mathrm{cm}^2$
C
$2 \mathrm{~cm}^3 / \mathrm{cm}^2$
D
$8 \mathrm{~cm}^3 / \mathrm{cm}^2$
4
KCET 2017
MCQ (Single Correct Answer)
+1
-0
$\int\limits_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x$ is equal to
A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{6}$
D
$\frac{\pi}{3}$