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KCET 2018
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180
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180 mins
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KCET - Previous Year Papers
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PYP
KCET 2018
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
PYP
KCET 2018
$$
\text { If } y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \infty}}} \text {, then } \frac{d y}{d x} \text { is equal }
$$ to
PYP
KCET 2018
Dry ice is
PYP
KCET 2018
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
PYP
KCET 2018
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 $g=10 \mathrm{~ms}^{-2}$ )
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
Two particles of masses $m_1$ and $m_2$ have equal kinetic energies. The ratio of their momentum is
PYP
KCET 2018
The dimensions of the ratio of magnetic flux
$(\phi)$ and permeability $(\mu)$ are
PYP
KCET 2018
A particle shows distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point.
PYP
KCET 2018
Which of the following graphs correctly represents the variation of $g$ on the Earth?
PYP
KCET 2018
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 $v_E$.
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
The pressure at the bottom of a liquid tank is not proportional to the
PYP
KCET 2018
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
PYP
KCET 2018
In a Fraunhofer diffraction at a single slit, if yellow light illuminating that slit is replaced by blue light, then diffraction bands
PYP
KCET 2018
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?
PYP
KCET 2018
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
PYP
KCET 2018
A plane wavefront of wavelength $\lambda$ is incident on a single slit of width $a$. The angular width of principal maximum is
PYP
KCET 2018
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
PYP
KCET 2018
Pressure of an ideal gas is increased by keeping temperature constant. The kinetic energy of molecules
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
An object is placed at the principal focus of a convex mirror. The image will be at
PYP
KCET 2018
The correct Biot-Savart law in vector form is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
The strength of the Earth's magnetic field is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
Ohm's law is applicable to
PYP
KCET 2018
The work done to move a charge on an equipotential surface is
PYP
KCET 2018
The magnitude of point charge due to which the electric field 30 cm away has the magnitude $2 \mathrm{NC}^{-1}$ will be
PYP
KCET 2018
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
PYP
KCET 2018
If the last band on the carbon resistor is absent, then the tolerance is
PYP
KCET 2018
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 $4 \mu \mathrm{~F}$ )
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
Which of the following, represents the variation of inductive reactance $\left(X_L\right)$ with the frequency of voltage sources $(v)$ ?
PYP
KCET 2018
The effective resistance between $P$ and $Q$ for the following network is
PYP
KCET 2018
The half-life of tritium is 12.5 years. What mass of tritium of initial mass 64 mg will remain undecayed after 50 years?
PYP
KCET 2018
In the series $L-C-R$ circuit, the power dissipation is through
PYP
KCET 2018
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
PYP
KCET 2018
The total energy of an electron revolving in the second orbit of hydrogen atom is
PYP
KCET 2018
In Karnataka, the normal domestic power supply AC is $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Here, 220 V and 50 Hz refer to
PYP
KCET 2018
The energy equivalent to a substance of mass 1 g is
PYP
KCET 2018
The maximum kinetic energy of emitted photoelectrons depends on
PYP
KCET 2018
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
PYP
KCET 2018
If $A=1$ and $B=0$, then in terms of Boolean algebra, $A+\bar{B}=$
PYP
KCET 2018
In a CE amplifier, the input AC signal to be amplified is applied across
PYP
KCET 2018
A proton and an $\alpha$-particle are accelerated through the same potential difference $V$. The ratio of their de-Broglie wavelength is
PYP
KCET 2018
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, $h=6.62 \times 10^{-34} \mathrm{~J}-\mathrm{s}$ )
PYP
KCET 2018
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?
PYP
KCET 2018
For an ideal gas, compressibility factor is
PYP
KCET 2018
The orbital nearest to the nucleus is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
The radius of the Earth is 6400 km . If the height of an antenna is 500 m , then its range is
PYP
KCET 2018
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
$$
\mathrm{NH}_4 \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_3(g)+\mathrm{HCl}(g) ?
$$
PYP
KCET 2018
Which of the following electrolytes will have maximum coagulating value for $\mathrm{AgI} / \mathrm{Ag}^{+}$ sol?
PYP
KCET 2018
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
PYP
KCET 2018
$\mathrm{KMnO}_4$ acts as an oxidising agent in alkaline medium. When alkaline $\mathrm{KMnO}_4$ is treated with KI , iodide ion is oxidised to
PYP
KCET 2018
Isotonic solutions are solutions having the same
PYP
KCET 2018
Which of the following aqueous solutions should have the highest boiling point?
PYP
KCET 2018
The charge required for the reduction of $1 \mathrm{~mol}$ of $ \mathrm{MnO}_4^{-}$to $\mathrm{MnO}_2$ is
PYP
KCET 2018
Edge length of a cube is 300 pm . Its body diagonal would be
PYP
KCET 2018
In FCC, the unit cell is shared equally by how many unit cells?
PYP
KCET 2018
At a particular temperatur , the ratio of molar conductance of specific conductance of 0.01 M NaCl solution is
PYP
KCET 2018
Which of the following is not a conductor of electricity?
PYP
KCET 2018
Gold sol is not a
PYP
KCET 2018
Which of the following is the correct order of radius?
PYP
KCET 2018
The value of rate constant of a pseudo first order reaction
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
Which of the following is an amphoteric oxide?
PYP
KCET 2018
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
PYP
KCET 2018
The state of hybrid orbitals of carbon in $\mathrm{CO}_2$, $\mathrm{CH}_4$ and $\mathrm{CO}_3^{2-}$ respectively is
PYP
KCET 2018
The common impurity present in bauxite is
PYP
KCET 2018
The electronic configuration of transition element " $X$ ", $[\mathrm{Ar}] 3 d^5$ is oxidation state is +3 . What is its atomic number?
PYP
KCET 2018
Electrolytic refining is used to purify which of the following metals?
PYP
KCET 2018
Acidity of $\mathrm{BF}_3$ can be explained on which of the following concepts?
PYP
KCET 2018
The intramolecular hydrogen bond is present in
PYP
KCET 2018
When $\mathrm{PbO}_2$ reacts with concentrated $\mathrm{HNO}_3$, the gas evolved is
PYP
KCET 2018
Which of the following oxides shows electrical properties like metals?
PYP
KCET 2018
$\mathrm{H}_2 \mathrm{O}_2$ is
PYP
KCET 2018
Dead burnt plaster is
PYP
KCET 2018
Which of the following ions will cause hardness in water?
PYP
KCET 2018
Very pure $\mathrm{N}_2$ can be obtained by
PYP
KCET 2018
$\left[\mathrm{Fe}\left(\mathrm{NO}_2\right)_3 \mathrm{Cl}_3\right]$ and $\left[\mathrm{Fe}(\mathrm{O}-\mathrm{NO})_3 \mathrm{Cl}_3\right]$ shows
PYP
KCET 2018
Which of the following is more basic than aniline?
PYP
KCET 2018
Identify the following compound which exhibits geometrical isomerism
PYP
KCET 2018
The two forms of D-glucopyranose are called
PYP
KCET 2018
The IUPAC name of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}$ is
PYP
KCET 2018
Which of the following oxidation states is common for all lanthanides?
PYP
KCET 2018
When the vapours of tertiary butyl alcohol are passed through heated copper at 573 K , the product formed is
PYP
KCET 2018
Which of the following statements is true is case of alkyl halides?
PYP
KCET 2018
The reagent $X$ used for the following reaction is
PYP
KCET 2018
$n$-propyl chloride reacts with sodium metal in dry ether to give
PYP
KCET 2018
Tertiary alkyl halide is practically inert to substitution by $\mathrm{S}_{\mathrm{N}} 2$ mechanism because of
PYP
KCET 2018
Phenol can be distinguished from ethanol by the reagent
PYP
KCET 2018
In the following reaction,
PYP
KCET 2018
During the fusion of organic compound with sodium metal, nitrogen present in the organic compound is converted into
PYP
KCET 2018
Which of the following compounds undergoes haloform reaction?
PYP
KCET 2018
The appropriate reagent for the following ransformation is
PYP
KCET 2018
What is the increasing order of acidic strength among the following?
(i) p-methoxy phenol
(ii) $p$-methyl phenol
(iii) $p$-nitro phenol
PYP
KCET 2018
The products $X$ and $Z$ in the following raction sequence are
PYP
KCET 2018
Which of the following will be the most stable diazonium salt $\left(R \mathrm{~N}_2^{+} \mathrm{X}^{-}\right)$?
PYP
KCET 2018
Which one of the following is a polyamide polymer?
PYP
KCET 2018
$\left(\mathrm{CH}_3\right)_3 \mathrm{SiCl}$ is used during polymerisation of organosilicons because
PYP
KCET 2018
Among the following, the branched chain polymer is
PYP
KCET 2018
Ziegler-Natta catalyst is used to prepare
PYP
KCET 2018
The reaction of benzenediazonium chloride with aniline yields yellow dye. The name of the yellow dye is
PYP
KCET 2018
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
PYP
KCET 2018
Which of the following bases is not present in DNA?
PYP
KCET 2018
The glycosidic linkage involved in linking the glucose units in amylase part of starch is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
The constant term in the expansion of $\left(x^2-\frac{1}{x^2}\right)^{16}$ is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is
PYP
KCET 2018
The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is
PYP
KCET 2018
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
PYP
KCET 2018
Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to
PYP
KCET 2018
If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A A^{\prime}$ is equal to
PYP
KCET 2018
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
PYP
KCET 2018
The locus represented by $x y+y z=0$ is
PYP
KCET 2018
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
PYP
KCET 2018
If $A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]$, then $A^n=2^k A$, where $k$ is equal to
PYP
KCET 2018
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
PYP
KCET 2018
The negation of the statement " 72 is divisible by 2 and $3^{\prime \prime}$ is
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
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
PYP
KCET 2018
$P (n): 2^{2 n}-1$ is divisible by $k$ for all $n \in N^{\prime \prime}$ is true, then the value of ' $k$ ' is
PYP
KCET 2018
For the LPP, maximize $z=x+4 y$ subject to the constraints $x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0$
PYP
KCET 2018
If $\left(\frac{1-i}{1+i}\right)^{96}=a+i b$, then $(a, b)$ is
PYP
KCET 2018
The area bounded by the line $y=x, X$-axis and ordinates $x=-1$ and $x=2$ is
PYP
KCET 2018
The value of the expression $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is
PYP
KCET 2018
If $\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}$, then $\cos ^{-1} x+\sin ^{-1} y$ is
PYP
KCET 2018
The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is
PYP
KCET 2018
Let $f: R \rightarrow R$ be defined by
$f(x)=\left\{\begin{array}{lc}2 x ; & x > 3 \\ x^2 ; & 1 < x \leq 3 . \text { Then } \\ 3 x ; & x \leq 1\end{array}\right.$
$$ f(-1)+f(2)+f(4) \text { is }$$
PYP
KCET 2018
A is a set having 6 distinct elements. The number of distinct functions from $A$ to $A$ which are not bijections is
PYP
KCET 2018
Let $f(x)=x-\frac{1}{x}$, then $f(-1)$ is
PYP
KCET 2018
The value of $\lim \limits_{x \rightarrow 0} \frac{[x]}{x}$ is :
PYP
KCET 2018
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
PYP
KCET 2018
If $|x+5| \geq 10$, then
PYP
KCET 2018
$\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to
PYP
KCET 2018
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
PYP
KCET 2018
$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to
PYP
KCET 2018
If $f(x)=|\cos x-\sin x|$, then $f^{\prime}\left(\frac{\pi}{6}\right)$ is equal to
PYP
KCET 2018
$\int \frac{1}{1+e^x} d x$ is equal to
PYP
KCET 2018
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
PYP
KCET 2018
The maximum value of $\left(\frac{1}{x}\right)^x$ is
PYP
KCET 2018
The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of
PYP
KCET 2018
If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to
PYP
KCET 2018
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
PYP
KCET 2018
The integrating factor of $\frac{d y}{d x}+y=\frac{1+y}{x}$ is
PYP
KCET 2018
Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $3 \%$ is
PYP
KCET 2018
$\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to
PYP
KCET 2018
$\int_{-2}^2|x \cos \pi x| d x$ is equal to
PYP
KCET 2018
$ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to
PYP
KCET 2018
$f(x)=x^x$ has stationary point at
PYP
KCET 2018
The equation of the line parallel to the line $3 x-4 y+2=0$ and passing through $(-2,3)$ is
PYP
KCET 2018
The maximum area of a rectangle inscribed in the circle $(x+1)^2+(y-3)^2=64$ is
PYP
KCET 2018
The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is
PYP
KCET 2018
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
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