KCET 2018
Paper was held on
Mon, Apr 30, 2018 4:30 AM
Chemistry
1
1.0 g of Mg is burnt with 0.28 g of $\mathrm{O}_2$ in a closed vessel. Which reactant is left in excess and how much?
2
The orbital nearest to the nucleus is
3
Which of the following is the correct order of radius?
4
The intramolecular hydrogen bond is present in
5
The state of hybrid orbitals of carbon in $\mathrm{CO}_2$, $\mathrm{CH}_4$ and $\mathrm{CO}_3^{2-}$ respectively is
6
For an ideal gas, compressibility factor is
7
The relationship between $K_p$ and $K_c$ is $K_p=K_c(R T)^{\Delta n}$. What would be the value of $\Delta n$ for the reaction
$$
\mathrm{NH}_4 \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_3(g)+\mathrm{HCl}(g) ?
$$
8
For the redox reaction
$$ \begin{aligned} x \mathrm{MnO}_4^{-}+y \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4+ & z \mathrm{H}^{+} \longrightarrow \\ & m \mathrm{Mn}^{2+}+n \mathrm{CO}_2+p \mathrm{H}_2 \mathrm{O} . \end{aligned} $$
The values of $x, y, m$ and $n$ are
9
$\mathrm{H}_2 \mathrm{O}_2$ is
10
Dead burnt plaster is
11
Identify the following compound which exhibits geometrical isomerism
12
During the fusion of organic compound with sodium metal, nitrogen present in the organic compound is converted into
13
The reagent $X$ used for the following reaction is
14
Which of the following ions will cause hardness in water?
15
Which of the following oxides shows electrical properties like metals?
16
Which of the following aqueous solutions should have the highest boiling point?
17
The charge required for the reduction of $1 \mathrm{~mol}$ of $ \mathrm{MnO}_4^{-}$to $\mathrm{MnO}_2$ is
18
For the reaction, $2 \mathrm{SO}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{SO}_3$, the rate of disappearance of $\mathrm{O}_2$ is $2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The rate of appearance of $\mathrm{SO}_3$ is
19
Which of the following electrolytes will have maximum coagulating value for $\mathrm{AgI} / \mathrm{Ag}^{+}$ sol?
20
Electrolytic refining is used to purify which of the following metals?
21
Dry ice is
22
Which of the following is an amphoteric oxide?
23
The IUPAC name of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}$ is
24
Which of the following statements is true is case of alkyl halides?
25
Phenol can be distinguished from ethanol by the reagent
26
Which of the following compounds undergoes haloform reaction?
27
Which of the following will be the most stable diazonium salt $\left(R \mathrm{~N}_2^{+} \mathrm{X}^{-}\right)$?
28
Which of the following bases is not present in DNA?
29
Which one of the following is a polyamide polymer?
30
In FCC, the unit cell is shared equally by how many unit cells?
31
At a particular temperatur , the ratio of molar conductance of specific conductance of 0.01 M NaCl solution is
32
Isotonic solutions are solutions having the same
33
The temperature coefficient of a reaction is
2. When the temperature is increased from $30^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$, the rate of saction is increased by
34
Gold sol is not a
35
The common impurity present in bauxite is
36
Very pure $\mathrm{N}_2$ can be obtained by
37
Which of the following oxidation states is common for all lanthanides?
38
The electronic configuration of transition element " $X$ ", $[\mathrm{Ar}] 3 d^5$ is oxidation state is +3 . What is its atomic number?
39
$n$-propyl chloride reacts with sodium metal in dry ether to give
40
When the vapours of tertiary butyl alcohol are passed through heated copper at 573 K , the product formed is
41
What is the increasing order of acidic strength among the following?
(i) p-methoxy phenol
(ii) $p$-methyl phenol
(iii) $p$-nitro phenol
42
Which of the following is more basic than aniline?
43
The two forms of D-glucopyranose are called
44
Among the following, the branched chain polymer is
45
Edge length of a cube is 300 pm . Its body diagonal would be
46
Which of the following is not a conductor of electricity?
47
For a cell involving two electron changes, $E_{\text {cell }}^{\circ}=03 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$. The equilibrium constant of the reaction is
48
The value of rate constant of a pseudo first order reaction
49
$\left(\mathrm{CH}_3\right)_3 \mathrm{SiCl}$ is used during polymerisation of organosilicons because
50
When $\mathrm{PbO}_2$ reacts with concentrated $\mathrm{HNO}_3$, the gas evolved is
51
$\mathrm{KMnO}_4$ acts as an oxidising agent in alkaline medium. When alkaline $\mathrm{KMnO}_4$ is treated with KI , iodide ion is oxidised to
52
$\left[\mathrm{Fe}\left(\mathrm{NO}_2\right)_3 \mathrm{Cl}_3\right]$ and $\left[\mathrm{Fe}(\mathrm{O}-\mathrm{NO})_3 \mathrm{Cl}_3\right]$ shows
53
Tertiary alkyl halide is practically inert to substitution by $\mathrm{S}_{\mathrm{N}} 2$ mechanism because of
54
The products $X$ and $Z$ in the following raction sequence are
55
The appropriate reagent for the following ransformation is
56
In the following reaction,
57
The reaction of benzenediazonium chloride with aniline yields yellow dye. The name of the yellow dye is
58
The glycosidic linkage involved in linking the glucose units in amylase part of starch is
59
Ziegler-Natta catalyst is used to prepare
60
Acidity of $\mathrm{BF}_3$ can be explained on which of the following concepts?
Mathematics
1
$\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to
2
$ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to
3
The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is
4
The area bounded by the line $y=x, X$-axis and ordinates $x=-1$ and $x=2$ is
5
The degree and the order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^2}$ respectively are
6
The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of
7
The integrating factor of $\frac{d y}{d x}+y=\frac{1+y}{x}$ is
8
If $|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144$ and $|\vec{a}|=4$, then the value of $|\vec{b}|$ is
9
If $\vec{a}$ and $\vec{b}$ are mutually perpendicular unit vectors, then $(3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})$ is equal to
10
If the vector $a \hat{i}+\hat{j}+\hat{k} ; \hat{i}+b \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c \hat{k}$ are coplanar $(a \neq b \neq c \neq 1)$, then the value of $a b c-(a+b+c)$ is equal to
11
If $\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}$ are orthogonal and $|\vec{a}|=|\vec{b}|$, then $(\lambda, \mu)$ is equal to
12
The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is
13
The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is
14
The value of $k$ such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies on the plane $2 x-4 y+z=7$ is
15
The locus represented by $x y+y z=0$ is
16
The feasible region of an LPP is shown in the figure. If $z=3 x+9 y$, then the minimum value of $z$ occurs at
17
For the LPP, maximize $z=x+4 y$ subject to the constraints $x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0$
18
For the probability distribution given by
$$ \begin{array}{|c|c|c|c|} \hline X=x_i & 0 & 1 & 2 \\ \hline P_i & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\ \hline \end{array} $$
the standard deviation $(\sigma)$ is
$$ \begin{array}{|c|c|c|c|} \hline X=x_i & 0 & 1 & 2 \\ \hline P_i & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\ \hline \end{array} $$
the standard deviation $(\sigma)$ is
19
A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is
20
A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is
21
If $|x+5| \geq 10$, then
22
Everybody in a room shakes hands with everybody else. The total number of handshakes is 45 . The total number of persons in the room is
23
The constant term in the expansion of $\left(x^2-\frac{1}{x^2}\right)^{16}$ is
24
$P (n): 2^{2 n}-1$ is divisible by $k$ for all $n \in N^{\prime \prime}$ is true, then the value of ' $k$ ' is
25
The equation of the line parallel to the line $3 x-4 y+2=0$ and passing through $(-2,3)$ is
26
If $\left(\frac{1-i}{1+i}\right)^{96}=a+i b$, then $(a, b)$ is
27
The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is
28
The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is
29
If $a, b, c$ are three consecutive terms of an AP and $x, y, z$ are three consecutive terms of a GP, then the value of $x^{b-c} \cdot y^{c-a} \cdot z^{a-b}$ is
30
The value of $\lim \limits_{x \rightarrow 0} \frac{[x]}{x}$ is :
31
Let $f(x)=x-\frac{1}{x}$, then $f(-1)$ is
32
The negation of the statement " 72 is divisible by 2 and $3^{\prime \prime}$ is
33
The probability of happening of an event $A$ is 0.5 and that of $B$ is 0.3 . If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ is
34
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is
35
If $A$ and $B$ are mutually exclusive events, given that $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$, then $P(A$ or $B)$ is
36
Let $f, g: R \rightarrow R$ be two functions defined as $f(x)=|x|+x$ and $g(x)=|x|-x \forall x \in R$. Then $(f \circ g)(x)$ for $x<0$ is
37
A is a set having 6 distinct elements. The number of distinct functions from $A$ to $A$ which are not bijections is
38
If $\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}$, then $\cos ^{-1} x+\sin ^{-1} y$ is
39
The value of the expression $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is
40
If $A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]$, then $A^n=2^k A$, where $k$ is equal to
41
If $\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right]$, then the values of $x$ and $y$ respectively are
42
If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A A^{\prime}$ is equal to
43
If $x, y, z \in R$, then the value of determinant $\left|\begin{array}{lll}\left(5^x+5^{-x}\right)^2 & \left(5^x-5^{-x}\right)^2 & 1 \\ \left(6^x+6^{-x}\right)^2 & \left(6^x-6^{-x}\right)^2 & 1 \\ \left(7^x+7^{-x}\right)^2 & \left(7^x-7^{-x}\right)^2 & 1\end{array}\right|$ is
44
The value of determinant $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is
45
If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is ' $k$ ' square units, then $\left|\begin{array}{lll}x_1 & y_1 & 4 \\ x_2 & y_2 & 4 \\ x_3 & y_3 & 4\end{array}\right|^2$ is
46
Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to
47
If $f(x)=\left\{\begin{array}{clc}\frac{\sqrt{1+k x}-\sqrt{1-k x}}{x} & \text { if }-1 \leq x<0 \\ \frac{2 x+1}{x-1} & \text { if } 0 \leq x \leq 1\end{array}\right.$
is continuous at $x=0$, then the value of $k$ is
48
If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to
49
If $f(x)=|\cos x-\sin x|$, then $f^{\prime}\left(\frac{\pi}{6}\right)$ is equal to
50
$$
\text { If } y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \infty}}} \text {, then } \frac{d y}{d x} \text { is equal }
$$ to
51
If $f(x)=\left\{\begin{array}{cl}\frac{\log _e x}{x-1} & ; x \neq 1 \\ k & ; x=1\end{array}\right.$
is continuous at $x=1$, then the value of $k$ is
52
Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $3 \%$ is
53
The maximum value of $\left(\frac{1}{x}\right)^x$ is
54
$f(x)=x^x$ has stationary point at
55
The maximum area of a rectangle inscribed in the circle $(x+1)^2+(y-3)^2=64$ is
56
$\int \frac{1}{1+e^x} d x$ is equal to
57
$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to
58
$\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to
59
$\int_{-2}^2|x \cos \pi x| d x$ is equal to
60
Let $f: R \rightarrow R$ be defined by
$f(x)=\left\{\begin{array}{lc}2 x ; & x > 3 \\ x^2 ; & 1 < x \leq 3 . \text { Then } \\ 3 x ; & x \leq 1\end{array}\right.$
$$ f(-1)+f(2)+f(4) \text { is }$$
Physics
1
The energy equivalent to a substance of mass 1 g is
2
The half-life of tritium is 12.5 years. What mass of tritium of initial mass 64 mg will remain undecayed after 50 years?
3
In a CE amplifier, the input AC signal to be amplified is applied across
4
If $A=1$ and $B=0$, then in terms of Boolean algebra, $A+\bar{B}=$
5
The density of electron-hole pair in a pure germanium is $3 \times 10^{16} \mathrm{~m}^{-3}$ at room temperature. On doping with aluminium, the hole density increases to $4.5 \times 10^{22} \mathrm{~m}^{-3}$. Now, the electron density (in $\mathrm{m}^{-3}$ ) in doped germanium will be
6
The DC common emitter current gain of an $n-p-n$ transistor is 50 . The potential difference applied across the collector and emitter of a transistor used in CE configuration is, $V_{C E}=2 \mathrm{~V}$. If the collector resistance $R_C=4 \mathrm{k} \Omega$, the base current $\left(I_B\right)$ and the collector current $\left(I_C\right)$ are
7
The radius of the Earth is 6400 km . If the height of an antenna is 500 m , then its range is
8
A space station is at a height equal to the radius of the Earth. If ' $v_E$ ' is the escape velocity on the surface of the Earth, the same on the space station is $\qquad$ times $v_E$.
9
A particle shows distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point.
10
Which of the following graphs correctly represents the variation of $g$ on the Earth?
11
A cup of tea cools from $65.5^{\circ} \mathrm{C}$ to $62.5^{\circ} \mathrm{C}$ in 1 min in a room at $22.5^{\circ} \mathrm{C}$. How long will it take to cool from $46.5^{\circ} \mathrm{C}$ to $40.5^{\circ} \mathrm{C}$ in the same room?
12
The dimensions of the ratio of magnetic flux
$(\phi)$ and permeability $(\mu)$ are
13
A mass $m$ on the surface of the Earth is shifted to a target equal to the radius of the Earth. If $R$ is the radius and $M$ is the mass of the Earth, then work done in this process is
14
First overtone frequency of a closed pipe of length $l_1$ is equal to the second harmonic frequency of an open pipe of length $l_2$. The ratio $\frac{l_1}{l_2}$ is equal to
15
The resistance $R=\frac{V}{I}$, where $V=(100 \pm 5) \mathrm{V}$ and $I=(10 \pm 0.2) \mathrm{A}$. The percentage error in $R$ is
16
A block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal, The coefficient of static friction between the block and the plane is 0.8 . If the frictional force on the block is 10 N , the mass of the block is (Take $g=10 \mathrm{~ms}^{-2}$ )
17
Two particles of masses $m_1$ and $m_2$ have equal kinetic energies. The ratio of their momentum is
18
The pressure at the bottom of a liquid tank is not proportional to the
19
A Carnot engine takes 300 calories of heat from a source at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is
20
Pressure of an ideal gas is increased by keeping temperature constant. The kinetic energy of molecules
21
A man weighing 60 kg is in a lift moving down with an acceleration of $1.8 \mathrm{~ms}^{-2}$. The force exerted by the floor on him is
22
Moment of inertia of a body about two perpendicular axes $X$ and $Y$ in the plane of lamina are $20 \mathrm{~kg}-\mathrm{m}^2$ and $25 \mathrm{~kg}-\mathrm{m}^2$, respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of $X$ and $Y$-axes is
23
Two wires $A$ and $B$ are stretched by the same load. If the area of cross-section of wire $A$ is double that of $B$, then the stress on $B$ is
24
The magnitude of point charge due to which the electric field 30 cm away has the magnitude $2 \mathrm{NC}^{-1}$ will be
25
A mass of 1 kg carrying a charge of 2 C is accelerated through a potential of 1 V . The velocity acquired by it is
26
The force of repulsion between two identical positive charges when kept with a separation $r$ in air is $F$. Half the gap between the two charges is filled by a dielectric slab of dielectric constant $=4$. Then, the new force of repulsion between those two charges becomes
27
For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points $A$ and $B$ is (capacitance of each capacitor is $4 \mu \mathrm{~F}$ )
28
The work done to move a charge on an equipotential surface is
29
Two capacitors of $3 \mu \mathrm{~F}$ and $6 \mu \mathrm{~F}$ are connected in series and a potential difference of 900 V is applied across the combination. They are then disconnected and reconnected in parallel. The potential difference across the combination is
30
Ohm's law is applicable to
31
If the last band on the carbon resistor is absent, then the tolerance is
32
The effective resistance between $P$ and $Q$ for the following network is
33
Five identical resistors each of resistance $R=1500 \Omega$ are connected to a 300 V battery as shown in the circuit. The reading of the ideal ammeter $A$ is
34
Two cells of internal resistances $r_1$ and $r_2$ and of same emf are connected in series, across a resistor of resistance $R$. If the terminal potential difference across the cells of internal resistance $r_1$ is zero, then the value of $R$ is
35
The $I-V$ graphs for two different electrical appliances $P$ and $Q$ are shown in the diagram: If $R_P$ and $R_Q$ be the resistances of the devices, then
36
The correct Biot-Savart law in vector form is
37
An electron is moving in a circle of radius $r$ in a uniform magnetic field $B$. Suddenly, the field is reduced to $\frac{B}{2}$. The radius of the circular path now becomes
38
A charge $q$ is accelerated through a potential difference $V$. It is then passed normally through a uniform magnetic field, where it moves in a circle of radius $r$. The potential difference required to move it in a circle of radius $2 r$ is
39
A cyclotron's oscillator frequency is 10 MHz and the operating magnetic field is 0.66 T . If the radius of its dees is 60 cm , then the kinetic energy of the proton beam produced by the accelerator is
40
Needles $N_1, N_2$ and $N_3$ are made of a ferromagnetic, a paramagnetic and adiamagnetic substance, respectively. A magnet when brought close to them will
41
The strength of the Earth's magnetic field is
42
A jet plane having a wing-span of 25 m is travelling horizontally towards East with a speed of $3600 \mathrm{~km} / \mathrm{hr}$. If the Earth's magnetic field at the location is $4 \times 10^{-4} \mathrm{~T}$ and the angle of dip is $30^{\circ}$, then the potential difference between the ends of the wing is
43
Which of the following, represents the variation of inductive reactance $\left(X_L\right)$ with the frequency of voltage sources $(v)$ ?
44
The magnetic flux linked with a coil varies as $\phi=3 t^2+4 t+9$. The magnitude of the emf induced at $t=2 \mathrm{~s}$ is
45
A 100 W bulb is connected to an AC source of $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Then, the current flowing through the bulb is
46
In the series $L-C-R$ circuit, the power dissipation is through
47
In Karnataka, the normal domestic power supply AC is $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Here, 220 V and 50 Hz refer to
48
A step-up transformer operates on a 230 V "ne and a load current of 2 A . The ratio of primary and secondary windings is $1: 25$. Then, the current in the primary is
49
The number of photons falling per second on a completely darkened plate to produce a force of $6.62 \times 10^{-5} \mathrm{~N}$ is $n$. If the wavelength of the light falling is $5 \times 10^{-7} \mathrm{~m}$, then $n=$ $\ldots \ldots \ldots \times 10^{22}$. (Take, $h=6.62 \times 10^{-34} \mathrm{~J}-\mathrm{s}$ )
50
An object is placed at the principal focus of a convex mirror. The image will be at
51
An object is placed at a distance of 20 cm from the pole of a concave mirror of focal length 10 cm . The distance of the image formed is
52
A candle placed 25 cm from a lens forms an image on a screen placed 75 cm on the other side of the lens. The focal length and type of the lens should be
53
A plane wavefront of wavelength $\lambda$ is incident on a single slit of width $a$. The angular width of principal maximum is
54
In a Fraunhofer diffraction at a single slit, if yellow light illuminating that slit is replaced by blue light, then diffraction bands
55
In Young's double slit experiment, two wavelengths $\lambda_1=780 \mathrm{~nm}$ and $\lambda_2=520 \mathrm{~nm}$ are used to obtain interference fringes. If the $n^{\mathrm{th}}$ bright band due to $\lambda_1$ coincides with $(n+1)^{\text {th }}$ bright band due to $\lambda_2$, then the value of $n$ is
56
In Young's double slit experiment, slits are separated by 2 mm and the screen is placed at a distance of 1.2 m from the slits. Light consisting of two wavelengths $$6500\mathop A\limits^o $$ and $$5200\mathop A\limits^o $$ are used to obtain interference fringes. Then, the separation between the fourth bright fringes of two different patterns produced by the two wavelengths is
57
The maximum kinetic energy of emitted photoelectrons depends on
58
A proton and an $\alpha$-particle are accelerated through the same potential difference $V$. The ratio of their de-Broglie wavelength is
59
The total energy of an electron revolving in the second orbit of hydrogen atom is
60
The period of revolution of an electron in the ground state of hydrogen atom is $T$. The period of revolution of the electron in the first excited state is