# Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2015

### done JCECE Engineering Solved Paper-2015

• question_answer1) A vector of magnitude $|\psi |$ is turned through angle$\frac{\phi }{2}$. The magnitude of change in the vector is given by

A) $2|\psi ||\cos \phi /4|$

B) $|\psi ||\sin \phi /4|$

C) $|\psi {{|}^{2}}|\sin \phi /4{{|}^{2}}$

D) $2|\psi ||\sin \phi /4|$

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• question_answer2) A transmitting antenna of height $h$ and the receiving antenna of height $\frac{3}{4}h$ are separated by a distance of d for satisfactory communication in line-of-sight mode. Then, the value of $h$ is [Given, radius of the earth is$R$]

A) $\frac{{{d}^{2}}}{2R}{{(2\sqrt{2}-\sqrt{6})}^{2}}$

B) $\frac{{{d}^{2}}}{4R}{{(2\sqrt{2}-\sqrt{6})}^{2}}$

C) $\frac{{{d}^{2}}}{R}{{(2\sqrt{2}-\sqrt{6})}^{2}}$

D) $\frac{{{d}^{2}}}{8R}{{(2\sqrt{2}-\sqrt{6})}^{2}}$

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• question_answer3) The difference of sound levels between two points is$40\,\,dB$. What is the ratio of pressure amplitudes between the two points?

A) $10$

B) $200$

C) $100$

D) $400$

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• question_answer4) With a standard rectangular bar magnet of length$(L)$, breadth $(b;\,\,b<<l)$ and magnetic moment$M$, the time period of the magnet in a vibration magnetometer is$8\,\,s$. If the magnet is cut normal to its length into 8 equal pieces, then the time period (in second) with one of the pieces is

A) $8\,\,s$

B) $2\,\,s$

C) $1\,\,s$

D) $4\,\,s$

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• question_answer5) A disc of radius $a$ and mass $m$ is pivoted at the rim and is set in small oscillation. If a simple pendulum have the same period as that of the disc, then the length of the simple pendulum should be

A) $\frac{5}{2}a$

B) $\frac{3}{2}a$

C) $\frac{7}{2}a$

D) $\frac{1}{2}a$

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• question_answer6) The effective resistance across the points$P$ and $Q$ is

A) $\frac{r}{4}$

B) $\frac{r}{2}$

C) $\frac{r}{8}$

D) $\frac{r}{16}$

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• question_answer7) A physical quantity $X$ is represented by$X=[{{M}^{n}}{{L}^{-\theta }}{{T}^{-\phi }}]$. The maximum percentage errors in the measurement of $M,\,\,L$ and$T$, respectively are $\alpha %,\,\,\beta %$ and$\gamma %$. The maximum percentage error in the measurement of$X$will be

A) $(\eta \alpha -\theta \beta -\phi \gamma )%$

B) $(\theta \beta +\phi \gamma -\eta \alpha )%$

C) $\left( \frac{\alpha }{\eta }-\frac{\beta }{\theta }-\frac{\gamma }{\theta } \right)%$

D) $(\eta \alpha +\theta \beta +\phi \gamma )%$

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• question_answer8) A Galilean telescope has an objective of focal length $200\,\,cm$ and magnifying power$100$. What is the distance between the two lenses in normal?

A) $98\,\,cm$

B) $198\,\,cm$

C) $298\,\,cm$

D) $3\,\,m$

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• question_answer9) An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension 5. The force required to pull the ring away from the liquid surface is

A) $2\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S$

B) $\pi ({{a}_{1}}+{{b}_{1}}+{{a}_{2}}+{{b}_{2}})S$

C) $\pi \left( \frac{{{a}_{1}}+{{a}_{2}}}{2}+\frac{{{b}_{1}}+{{b}_{2}}}{2} \right)S$

D) $\sqrt{2}\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S$

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• question_answer10) A $50\Omega$ galvanometer is shunted by a resistance of$5\Omega$. The percentage of the total current, which passes through the galvanometer is

A) $8.1%$

B) $10.1%$

C) $11.1%$

D) $9.1%$

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• question_answer11) An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy$\frac{{{E}_{0}}}{4}$. Its potential energy is

A) $\frac{{{E}_{0}}}{4}$

B) $\frac{{{E}_{0}}}{2}$

C) $\frac{{{E}_{0}}}{8}$

D) ${{E}_{0}}$

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• question_answer12) A plano-convex glass lens $({{\mu }_{g}}=3/2)$ of radius of curvature $R=20\,\,cm$ is placed at a distance $'a'$ from a concave lens of focal length$40\,\,cm$. What should be the distance $'b'$ of a point object $O$ from plano-convex lens so that the position of final image is independent of$a$?

A) $20\,\,cm$

B) $60\,\,cm$

C) $40\,\,cm$

D) $30\,\,cm$

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• question_answer13) In the figure, the ball $P$ is released from rest, when the spring is at its natural length. For the block $Q$ of mass $2{{m}_{0}}$ to leave contact with ground at some stage, the minimum mass of P must be

A) ${{m}_{0}}$

B) $2{{m}_{0}}$

C) ${{m}_{0}}/2$

D) ${{m}_{0}}/4$

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• question_answer14) Consider the circuit, the current through the Zener diode is

A) $20\,\,mA$

B) $10\,\,mA$

C) $15\,\,mA$

D) $40\,\,mA$

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• question_answer15) The potential energy of a particle varies with height $h$ from a fixed point as $E=\left( \frac{\operatorname{P}\sqrt{h}}{h+Q} \right)$ where, $P$ and $Q$ are constants. The dimensions of $PQ$ are

A) $[M{{L}^{2}}{{T}^{-2}}]$

B) $[{{M}^{3/2}}{{L}^{3/2}}{{T}^{-2}}]$

C) $[M{{L}^{7/2}}{{T}^{-2}}]$

D) $[M{{L}^{3/2}}{{T}^{-2}}]$

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• question_answer16) Figure shows two convex lenses $P$ and$Q$, each made up of three different transparent materials. The number of images formed of an object kept on the principal axis of lenses $P$ and $Q$ respectively

A) 3 and 1

B) 3 and 3

C) 3 and 2

D) 1 and 3

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• question_answer17) What is the minimum acceleration $({{a}_{0}})$ of the cart in the given figure so that block $P$ will not fall? (Assume coefficient of friction as$\mu$).

A) $g/\sqrt{\mu }$

B) $g/\mu$

C) $2\mu g$

D) ${{\mu }^{2}}g$

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• question_answer18) The output resistance of a common emitter transistor amplifier, if the input resistance is$200\,\,\Omega$($\alpha =0.98$ and power gain is$5\times {{10}^{6}}$, is)

A) $516\,\,k\Omega$

B) $216\,\,k\Omega$

C) $300\,\,k\Omega$

D) $416\,\,k\Omega$

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• question_answer19) In the shown figure, length of the rod is$L$, area of cross-section$A$, Young's modulus of the material of the rod is$Y$. Then, $B$ and $A$ is subjected to a tensile force ${{F}_{A}}$ while force applied at end$B$, ${{F}_{B}}$ is lesser than${{F}_{A}}$. Total change in length of the rod will be

A) ${{F}_{A}}\times \frac{L}{2AY}$

B) ${{F}_{B}}\times \frac{L}{2AY}$

C) $\frac{({{F}_{A}}+{{F}_{B}})L}{2AY}$

D) $\frac{({{F}_{A}}-{{F}_{B}})L}{2AY}$

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• question_answer20) A long insulated copper wire is closely wound as a spiral of ${{N}_{0}}$ turn. The spiral lies in the $y-z$ plane and a steady current ${{I}_{0}}$ flows through the wire. The $X-$component of the magnetic field at the centre of the spiral is (assume inner radius as ${{R}_{1}}$ and outer radius as${{R}_{2}}$).

A) $\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{4({{R}_{2}}-{{R}_{1}})}\ln ({{R}_{2}}/{{R}_{1}})$

B) $\frac{2{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{{{R}_{2}}-{{R}_{1}}}\ln ({{R}_{2}}/{{R}_{1}})$

C) $\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{2({{R}_{2}}-{{R}_{1}})}\ln {{({{R}_{2}}/{{R}_{1}})}^{2}}$

D) $\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{2({{R}_{2}}-{{R}_{1}})}\ln ({{R}_{2}}/{{R}_{1}})$

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• question_answer21) A cable in the form of a spiral roll (shown in the figure) has a linear density$\rho$. It is uncoiled at a uniform speed$v$. If the total length of the cable is$L$. The work done in uncoiling the cable is

A) $\rho L{{v}^{2}}/4$

B) $\rho L{{v}^{2}}/2$

C) $\rho L{{v}^{2}}/3$

D) $\rho L{{v}^{2}}$

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• question_answer22) A person can see objects clearly only upto a maximum distance of 60 cm. His eye defect, nature of the corrective lens and its focal length are respectively

A) myopia, convex,$60\,\,cm$

B) myopia, concave,$60\,\,cm$

C) hypermetropia, concave,$60\,\,cm$

D) contract, convex,$60\,\,cm$

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• question_answer23) Consider two identical iron spheres $P$ and$Q$, one which lie on a thermally insulating plate, while the other hangs from an insulated thread. Equal amount of heat $(\Delta Q)$ is supplied to the two spheres. Then,

A) the temperature of Q will be greater than P

B) the temperature of P will be greater than Q

C) their temperature will be equal

D) can't be predicted

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• question_answer24) A plane electromagnetic wave of frequency $50\,\,MHz$ travels in free space along the $X-$direction. At a particular point in space$E=7.2\widehat{\mathbf{j}}\,\,V/m$. At this point, B is equal to

A) $8.4\times {{10}^{-8}}\widehat{\mathbf{k}}T$

B) $2.4\times {{10}^{-8}}\widehat{\mathbf{k}}T$

C) $7.4\times {{10}^{-6}}\widehat{\mathbf{i}}T$

D) $2.4\times {{10}^{-8}}\widehat{\mathbf{j}}T$

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• question_answer25) Two tuning forks $P$ and $Q$ sounded together and 6 beats per second are heard. $P$ is in unison with a $30\,\,cm$ air column open at both ends and $Q$ is in resonance when length of air column is increased by$2\,\,cm$. The frequencies of forks $P$ and $Q$ are

A) $90\,\,Hz$and$84\,\,Hz$

B) $100\,\,Hz$and$106\,\,Hz$

C) $96\,\,Hz$ and$90\,\,Hz$

D) $206\,\,Hz$ and$200\,\,Hz$

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• question_answer26) An electrical cable having a resistance of$0.4\,\,\Omega$delivers $20\,\,kW$ at $400\,\,V\,\,DC$ to a factory. What is the efficiency of transformer?

A) $89.5%$

B) $99.5%$

C) $79.5%$

D) $90.5%$

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• question_answer27) Consider a track having frictional coefficient$\mu$. A block of mass $m$ is released from point$P$ situated at height$h$. Which of the following is correct?

A) It can reach at$V$

B) It cannot reach at$V$

C) It can reach at$V$, if $\mu$ is reduced to$\mu /2$

D) It can reach at$V$, if $\mu$ is increased to$2\mu$

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• question_answer28) Suppose, we split a spherical surface into two parts by a circular loop. Now, a bar magnet is placed near the spherical system as shown in the figure. Through which of the two parts is the magnitude of the magnetic flux larger?

A) Part I

B) Part II

C) The magnitude of the flux is same for both

D) Cannot be predicted without more information about magnetic field

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• question_answer29) A partition divides a container having insulated walls into two compartments. The same gas fills the two compartments (see figure). The ratio of the number of molecules is compartments I and II is

A) $6:1$

B) $1:6$

C) $4:1$

D) $1:4$

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• question_answer30) In the circuit shown in the figure, the $AC$ source gives a voltage$V=10\sin (1000t)$. Neglecting source resistance, the voltmeter and ammeter reading will be

A) $20\sqrt{\frac{125}{538}}V$and$\frac{10}{\sqrt{538}}A$

B) $10\sqrt{\frac{250}{538}}V$and$\frac{10}{\sqrt{538}}A$

C) $\sqrt{\frac{250}{538}}V$and$\frac{1}{\sqrt{538}}A$

D) $\sqrt{\frac{125}{539}}V$and$\frac{1}{\sqrt{538}}A$

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• question_answer31) The amplitude of a wave disturbance propagating in the positive $X-$direction is given by $y=\frac{1}{2+{{x}^{2}}}$at$t=0$and$y=\frac{1}{[2+{{(x-1)}^{2}}]}$at $t=3s$, where x and y are in metre. If the shape of the wave disturbance does not change during the propagation, the velocity of the wave is

A) $\frac{1}{2}m{{s}^{-1}}$

B) $\frac{1}{3}m{{s}^{-1}}$

C) $\frac{1}{4}m{{s}^{-1}}$

D) $\frac{1}{5}m{{s}^{-1}}$

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• question_answer32) Assume an YDSE that has different slits width, as a result, amplitude of waves from two slits are $2A$ and $4A$ respectively. If $4{{I}_{0}}$ be the maximum intensity of the interference pattern, then intensity of the pattern of a point, where phase difference between waves is $2\phi$, is

A) $4{{I}_{0}}{{\cos }^{2}}\phi /2$

B) $\frac{4{{I}_{0}}}{3}{{\sin }^{2}}\phi$

C) $\frac{4{{I}_{0}}}{9}[5+4\cos 2\phi ]$

D) $\frac{4{{I}_{0}}}{9}[5+8\cos 2\phi ]$

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• question_answer33) A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of the same mass and of coefficient of restitution$(e)$. The ratio of velocities of the two spheres, after collision will be

A) $\frac{1-e}{1+e}$

B) $\frac{e}{e+1}$

C) $2/e$

D) $\frac{e+1}{2e}$

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• question_answer34) The circuit is equivalent to

A) NOR gate

B) AND gate

C) NAND gate

D) OR gate

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• question_answer35) A particle of mass m is located in a one-dimensional potential field, where the potential energy of the particle depends on the coordinates as$U(x)={{U}_{0}}(1-\sin bx)$; where ${{U}_{0}}$ and $b$ are constant. Find the period of small oscillations that the particle performs about the equilibrium position.

A) $\frac{2\pi }{{{b}^{2}}}\sqrt{\frac{m}{{{U}_{0}}}}$

B) $\frac{\pi }{b}\sqrt{\frac{m}{{{U}_{0}}}}$

C) $\frac{{{\pi }^{2}}}{2b}\sqrt{\frac{m}{{{U}_{0}}}}$

D) $\frac{2\pi }{b}\sqrt{\frac{m}{{{U}_{0}}}}$

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• question_answer36) A square loop of side length $a$ having $m$ turns is kept in a horizontal plane. A uniform magnetic field $B$ exists in vertical direction as shown in figure. Now, the loop is rotated with constant angular speed $\omega$ as shown below. Which of the following statement is correct?

A) Same emf is induced in both cases (i) and (ii)

B) Maximum emf is induced in case (i)

C) Emf induced in case (ii) is more than (i)

D) No emf induced in case (ii)

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• question_answer37) Two blocks are resting on ground with masses ${{m}_{1}}$ and ${{m}_{2}}$. A string connects them which goes over a mass less pulley$P$. There is no friction between pulley and string. A force $F$ is applied on pulley$P$. The acceleration of centre of mass of blocks is (Given that$T=2{{m}_{1}}g$and${{m}_{2}}=3{{m}_{1}}$)

A) $g/8$

B) $g/4$

C) $\frac{g}{2}$

D) $g$

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• question_answer38) The binding energy per nucleon of ${{C}^{12}}$ is ${{E}_{1}}$ and that of ${{C}^{13}}$ is${{E}_{2}}$. The energy required to remove one neutron from ${{C}^{13}}$ is

A) $12{{E}_{1}}+12{{E}_{2}}$

B) $13{{E}_{2}}-12{{E}_{1}}$

C) $12{{E}_{2}}-13{{E}_{1}}$

D) $13{{E}_{2}}+12{{E}_{1}}$

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• question_answer39) One mole of an ideal gas is taken from state $P$ to state $Q$ by three different processes (i)$PRQ$, (ii) $PSQ$ and (iii) $PTQ$ as shown in the $p-V$ diagram. The heat absorbed by the gas is

A) the least in process (ii)

B) greater in process (ii) than in process (i)

C) the same in the processes (i) and (iii)

D) less in process (iii) than in process (ii)

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• question_answer40) $_{87}^{221}Ra$ undergoes radioactive decay with a half-life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is

A) $\frac{1}{2}$

B) $\frac{3}{8}$

C) $\frac{1}{4}$

D) $\frac{3}{4}$

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• question_answer41) A uniform rod of mass m and length$L$is rotated about an axis passing through the point $P$ as shown in figure. The magnitude of angular momentum of the rod about the rotational axis$yy'$ passing through the point $P$is

A) $\frac{M{{L}^{2}}}{18}$

B) $\frac{M{{(x+y)}^{2}}}{9}$

C) $\frac{M({{L}^{2}}+{{x}^{2}})}{9}$

D) $\frac{M({{L}^{2}}+2{{y}^{2}})}{18}$

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• question_answer42) A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If $R$ is the Rydberg's constant and m is the mass of the atom, then the velocity acquired by the atom is (neglect energy absorbed by the photon)

A) $\frac{4m}{Rh}$

B) $\frac{Rh}{4m}$

C) $\frac{3Rh}{4m}$

D) $\frac{4m}{3Rh}$

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• question_answer43) Three metal rods of same length and area of cross-section are arranged to form an equilateral triangle as shown in figure.$S$ is the middle point of side$QR$. If $PS$ is independent of temperature, then $[{{\alpha }_{1}}$is coefficient of linear expansion for rod $QR$ and ${{\alpha }_{2}}$ is that for $PQ$ and$PR]$

A) ${{\alpha }_{1}}=2{{\alpha }_{2}}$

B) ${{\alpha }_{1}}={{\alpha }_{2}}/2$

C) ${{\alpha }_{1}}={{\alpha }_{2}}$

D) ${{\alpha }_{1}}=4{{\alpha }_{2}}$

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• question_answer44) A graph regarding photoelectric effect is shown between the maximum kinetic energy of electrons and the frequency of the incident light. On the basis of the data as shown in the graph, calculate the work function.

A) $4\,\,eV$

B) $2\,\,eV$

C) $4.2\,\,eV$

D) $2.5\,\,eV$

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• question_answer45) A tetrahedral is consisting of 6 identical wires as shown in the figure. Each wire is having a resistance of$4\Omega$. When an ideal cell of $emf\,5\,\,V$ is connected across $AB$ as shown, then current through $OR$ is

A) $4\,\,A$

B) $\frac{6}{19}A$

C) $zero$

D) $1\,\,A$

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• question_answer46) A stone is projected from the point on the ground in such a direction so as to hit a bird on the top of a telegraph post of height and then attain the maximum height $3h/2$ above the ground. If at the instant of projection, the bird were to fly away horizontally with uniform speed. Find the ratio between horizontal velocities of the bird and stone, if the stone still hits the bird while decreasing

A) $\sqrt{3}-1$

B) $1/\sqrt{3}-1$

C) $\sqrt{3}+1$

D) $1/\sqrt{3}+1$

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• question_answer47) Four equal capacitors are connected to a battery as shown in the adjoining figure. The potentials of $P$ and $Q$ are

A) $5V$and$5V$

B) $10V$and$5V$

C) $10V$and$-10V$

D) $5V$and$-5V$

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• question_answer48) Three charges${{q}_{1}}=2\times {{10}^{6}}C$,${{q}_{2}}=3\times {{10}^{-6}}C$ and ${{q}_{3}}=6\times {{10}^{-6}}C$have been placed as shown in figure. Then, the net electric flux will be minimum for the surface

A) ${{S}_{1}}$

B) ${{S}_{2}}$

C) ${{S}_{3}}$

D) same for all

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• question_answer49) Find the electric field vector at $P(b,\,\,b,\,\,b)$ due to three infinitely long lines of charges along $x,\,\,y$ and $z-$axes, respectively. The charge density, $i.e.$ charge per unit length of each wire is$\sigma$.

A) $\frac{\sigma }{\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})$

B) $\frac{\sigma }{2\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})$

C) $\frac{\sigma }{\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}})$

D) $\frac{\sigma }{2\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}})$

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• question_answer50) A 2 m wide truck is moving with a uniform speed ${{v}_{0}}=8\,\,m{{s}^{-1}}$ along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed$v$, when the truck is $4\,\,m$ away from him. The minimum value of $v$ so that he can cross the road safely is

A) $2.62\,\,m{{s}^{-1}}$

B) $4.6\,\,m{{s}^{-1}}$

C) $0.89\,\,m{{s}^{-1}}$

D) $1.414\,\,m{{s}^{-1}}$

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• question_answer51) In the following reaction, product formed is

A)

B)

C)

D)

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• question_answer52) Which of the following compounds has same oxidation state of the central metal atom in the cationic and anionic part?

A) $[Pt{{(N{{H}_{3}})}_{4}}][PtC{{l}_{6}}]$

B) $[Pt{{(py)}_{4}}][PtC{{l}_{4}}]$

C) $[Pt{{(N{{H}_{3}})}_{4}}C{{l}_{2}}][PtC{{l}_{4}}]$

D) ${{K}_{4}}[Ni{{(CN)}_{6}}]$

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• question_answer53) Which of the following calcium salt will : give cyclopentanone on heating?

A) Calcium succinate

B) Calcium adipate

C) Calcium glucarate

D) Calcium oxalate

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• question_answer54) In the reaction,$C{{H}_{3}}COOH\xrightarrow{LiAl{{H}_{4}}}A\xrightarrow{PC{{l}_{5}}}B\xrightarrow{Alc.\,\,KOH}C$the product is

A) acetaldehyde

B) acetylene

C) ethylene

D) acetylchloride

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• question_answer55) Complete hydrolysis of cellulose gives

A) D-fructose

B) D-ribose

C) D-glucose

D) L-glucose

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• question_answer56) Bakelite is obtained from phenol by reacting with

A) ${{(C{{H}_{2}}OH)}_{2}}$

B) $C{{H}_{3}}CHO$

C) $C{{H}_{3}}COC{{H}_{3}}$

D) $HCHO$

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• question_answer57) Phosgene can be obtained when

A) white phophorus reacts with alkali

B) calcium phosphide reacts with water

C) chloroform reacts with air

D) bone comes in contact with water

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• question_answer58) Select the coloured and paramagnetic ions

A) $C{{u}^{+}},\,\,Z{{n}^{2+}},\,\,C{{a}^{2+}}$

B) $S{{c}^{3+}},\,\,T{{i}^{4+}},\,\,{{V}^{5+}}$

C) $C{{u}^{2+}},\,\,C{{r}^{+}},\,\,M{{n}^{2+}}$

D) $N{{i}^{2+}},\,\,C{{u}^{+}},\,\,H{{g}^{2+}}$

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• question_answer59) Which of the following process is used in extractive metallurgy of magnesium?

A) Fused salt electrolysis

B) Self reduction

C) Aqueous solution electrolysis

D) Thermite reduction

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• question_answer60) Which of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?

A) $SrS{{O}_{4}}$

B) $CaS{{O}_{4}}$

C) $BeS{{O}_{4}}$

D) $BaS{{O}_{4}}$

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• question_answer61) Which of the following statements is true?

A) ${{H}_{3}}P{{O}_{4}}$ is stronger acid, than${{H}_{2}}S{{O}_{3}}$

B) In aqueous medium, $HF$ is a stronger acid than$HCl$

C) $HCl{{O}_{4}}$ is a weaker acid than$HCl{{O}_{3}}$

D) $HN{{O}_{3}}$ is a stronger acid than$HN{{O}_{2}}$

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• question_answer62) The orbital angular momentum of an electron is $2s$ orbital is

A) $+\frac{1}{2}.\frac{h}{2\pi }$

B) $zero$

C) $\frac{h}{2\pi }$

D) $\sqrt{2}\cdot \frac{h}{2\pi }$

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• question_answer63) The enthalpy change for a reaction does not depend upon the

A) physical state of reactants and products

B) use of different reactants for the same product

C) nature of intermediate reaction steps

D) difference in initial or final temperature of involved substances

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• question_answer64) The role of a catalyst is to change......

A) Gibbs energy of reaction

B) enthalpy of reaction

C) activation energy of reaction

D) equilibrium constant

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• question_answer65) When ortho boric acid $({{H}_{3}}B{{O}_{3}})$ is heated, the residue is

A) boron

B) metaboric acid

C) boric anhydride

D) borax

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• question_answer66) $12\,\,g$ of a non-volatile solute dissolved in $108\,\,g$ of water produces the relative lowering of vapour pressure of$0.1$. The molecular mass of the solute is

A) $80$

B) $60$

C) $20$

D) $40$

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• question_answer67) Electron gain enthalpy with negative sign of fluorine is less than that of chlorine due to

A) high ionisation enthalpy of fluorine

B) smaller size of chlorine atom

C) smaller size of fluorine atom

D) bigger size of 2p orbital of fluorine

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• question_answer68) Fog is a colloidal solution of

A) liquid particles dispersed in a gas

B) gaseous particles dispersed in a liquid

C) solid particles dispersed in a liquid

D) solid particles dispersed in a gas

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• question_answer69) In the reaction sequence, is

A) cyclohexanone

B) caprolactum

C) $HO{{(C{{H}_{2}})}_{6}}N{{H}_{2}}$

D) hexamethylene diisocyanate

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• question_answer70) The highest calorific value is found in

A) proteins

B) fats

C) vitamins

D) carbohydrates

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• question_answer71) In an electric field, if an amino acid migrate towards cathode, the pH of solution is said to be

A) less than$Pl$

B) More than$Pl$

C) equal to$Pl$

D) $7$

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• question_answer72) Acid anhydrides on reaction with primary amines gives

A) amide

B) imide

C) secondary amine

D) imine

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• question_answer73) Benzene diazonium chloride on reaction with phenol in weakly basic medium gives

A) diphenyl ether

B) p-hydroxyazobenzene

C) chlorobenzene

D) benzene

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• question_answer74) Reagent used for the oxidation of allyl alcohol to acrolein is

A) $KMn{{O}_{4}}$

B) ${{H}_{2}}{{O}_{2}}$

C) active$Mn{{O}_{2}}$

D) $Os{{O}_{4}}$

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• question_answer75) The enol form of acetone, after treatment with ${{D}_{2}}O$ gives

A) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OD \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}$

B) $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{3}}$

C) $C{{H}_{2}}=\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}D$

D) $C{{D}_{2}}=\underset{\begin{smallmatrix} | \\ OD \end{smallmatrix}}{\mathop{C}}\,-C{{D}_{3}}$

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• question_answer76) The compounds $[Co(S{{O}_{4}}){{(N{{H}_{3}})}_{5}}]Br$ and $[CO(S{{O}_{4}}){{(N{{H}_{3}})}_{5}}]Cl$represent

A) linkage isomerism

B) ionisation isomerism

C) coordination isomerism

D) no isomerism

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• question_answer77) $Xe{{F}_{2}}$ on hydrolysis gives

A) $Xe{{O}_{3}}$

B) $XeO$

C) $Xe$

D) $Xe{{O}_{2}}$

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• question_answer78) Sulphur in $+3$ oxidation state is present in

A) dithionous acid

B) sulphurous acid

C) thionous acid

D) phyrosulphuric acid

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• question_answer79) Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with${{t}_{1/2}}=3.00\,\,h$.What fraction of sample of sucrose remains after$8\,\,h$?

A) $1.023\,\,M$

B) $0.8725\,\,M$

C) $0.023\,\,M$

D) $0.1576\,\,M$

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• question_answer80) The osmotic pressure of a $5%(wt./vol)$ solution of cane sugar at ${{150}^{o}}C$ is

A) $3.078\,\,atm$

B) $4.078\,\,atm$

C) $5.078\,\,atm$

D) $2.45\,\,atm$

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• question_answer81) An alloy of $Cu,\,\,Ag,\,\,Au$ is found to have a simple cubic close packed lattice. If the $Ag$ atoms occupy the face centres and $Au$ is present at the body centre, the formula of the alloy will be

A) $C{{u}_{4}}A{{g}_{4}}Au$

B) $CuA{{g}_{3}}Au$

C) $CuAgCu$

D) $C{{u}_{4}}A{{g}_{2}}Cu$

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• question_answer82) Ozone layer of stratosphere requires protection from indiscriminate use of

A) pesticides

B) atomic explosions

C) aerosols and high flying jets

D) balloons

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• question_answer83) An in saturated hydrocarbon $'A'$ adds two molecules of H^ and on reductive ozonolysis gives butane-1, 4-dial, ethanol and propanone. Give the $IUPAC$ name of$A$.

A) 3-methyl octa-2, 6-diene

B) 2-methyl octa-2, 5-diene

C) 2-methyl octa-2, 6-diene

D) 2-methyl octa-3, 5-diene

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• question_answer84) Carborundum is obtained when silica is heated at high temperature with

A) carbon

B) carbon monoxide

C) carbon dioxide

D) calcium carbonate

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• question_answer85) The difference of water molecules in gypsum and plaster of Paris is

A) $\frac{5}{2}$

B) $2$

C) $\frac{1}{2}$

D) $1\frac{1}{2}$

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• question_answer86) Identify disproportionation reaction.

A) $C{{H}_{3}}+2{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}+2{{H}_{2}}O$

B) $C{{H}_{4}}+4C{{l}_{2}}\xrightarrow{{}}CC{{l}_{4}}+4HCl$

C) $2{{F}_{2}}+2O{{H}^{-}}\xrightarrow{{}}2{{F}^{-}}+O{{F}_{2}}+{{H}_{2}}O$

D) $2N{{O}_{2}}+2O{{H}^{-}}\xrightarrow{{}}NO_{2}^{-}+NO_{3}^{-}+{{H}_{2}}O$

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• question_answer87) The solubility product of $A{{g}_{2}}Cr{{O}_{4}}$ is$32\times {{10}^{-12}}$. What is the concentration of $CrO_{4}^{-}$ ions in that solution?

A) $2\times {{10}^{-4}}M$

B) $16\times {{10}^{-4}}M$

C) $8\times {{10}^{-4}}M$

D) $8\times {{10}^{-8}}M$

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• question_answer88) The structure of $I{{F}_{5}}$ can be described as

A)

B)

C)

D) None of these

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• question_answer89) $pH$of ${{10}^{-8}}N$$NaOH$ is

A) $8.0$

B) $6.0$

C) $6.98$

D) $7.04$

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• question_answer90) The heat of neutralisation of a strong acid and a strong alkali is$57.0\,\,kJ\,\,mo{{l}^{-1}}$. The heat released when $0.5$ mole of $HN{{O}_{3}}$ solution is mixed with $0.2$ mole of $KOH$ is

A) $57.0\,\,kJ$

B) $11.4\,\,kJ$

C) $28.5\,\,kJ$

D) $34.9\,\,kJ$

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• question_answer91) The unit and value of rate constant and that of rate of reaction are same for

A) zero order

B) first order

C) second order

D) third order

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• question_answer92) A weak acid HA after treatment with $1.2\,\,ml$ of $0.1\,\,M$ strong base has $\text{a}$$pH$of$5$. At the end point, the volume of same base required is$26.6\,\,mL$. The value of ${{K}_{a}}$ is

A) $8.2\times {{10}^{-6}}$

B) $6.4\times {{10}^{-6}}$

C) $5.3\times {{10}^{-5}}$

D) $2.4\times {{10}^{-6}}$

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• question_answer93) $A$and $B$ are respectively.

A) ${{H}_{2}}/Pt;\,\,LiAl{{H}_{4}}/{{H}_{2}}O$

B) ${{H}_{2}}/Pt;\,\,{{H}_{2}}/Pt$

C) $LiAl{{H}_{4}}/{{H}_{2}}O;\,\,LiAl{{H}_{4}}/{{H}_{2}}O$

D) $LiAl{{H}_{4}}/{{H}_{2}}O;\,\,{{H}_{2}}/Pt$

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• question_answer94) The $IUPAC$ name of

A) 3, 4-dimethylpentanoyl chloride

B) 1-chloro-1 -oxo-2, 3-dimethylpentane

C) 2-ethyl-3-methylbutanoyl chloride

D) 2, 3-dimethylpentanoyl chloride

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• question_answer95) $F{{e}^{2+}}$ reduces $N{{H}_{4}}OH$ to

A) $N{{H}_{3}}$

B) ${{N}_{3}}H$

C) ${{N}_{2}}{{H}_{4}}$

D) ${{N}_{2}}$

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• question_answer96) Proteins when heated with conc.$HN{{O}_{3}}$give yellow colour. This is known as

A) Hoppe's test

B) acid-base test

C) Biuret's test

D) Xanthoprotic test

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• question_answer97) A person was using water supplied by municipality. Due to shortage of water, he started using underground water. He felt laxative effect. Its cause due to high concentration of

A) $C{{O}_{2}}$

B) $SO_{4}^{2-}$

C) $CO_{3}^{2-}$

D) ${{S}^{2-}}$

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• question_answer98) The order of acidic strength of boron dialyses is

A) $B{{F}_{3}}<BC{{l}_{3}}<BB{{r}_{3}}<B{{l}_{3}}$

B) $B{{l}_{3}}<BB{{r}_{3}}<BC{{l}_{3}}<B{{F}_{3}}$

C) $BC{{l}_{3}}<BB{{r}_{3}}<B{{l}_{3}}<B{{F}_{3}}$

D) $BB{{r}_{3}}<BC{{l}_{3}}<B{{F}_{3}}<B{{l}_{3}}$

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• question_answer99) The hardest substance amongst the following is

A) $B{{e}_{2}}C$

B) tritonium

C) ${{B}_{4}}C$

D) graphite

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• question_answer100) The radius of divalent cation ${{M}^{2+}}$ is $94\,\,pm$ and that of divalent anion ${{X}^{2-}}$ is$146\,\,pm$. Thus ${{M}^{2+}}{{X}^{2-}}$ has

A) $NaCl$ structure

B) linear structure

C) $CsCl$ structure

D) $ZnS$ structure

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• question_answer101) If $p,\,\,q,\,\,r$ have truth values $T,\,\,F,\,\,T$ respectively, then which of the following is true?

A) $(p\to q)\wedge r$

B) $(p\to q)\wedge \tilde{\ }r$

C) $(p\wedge q)\wedge (p\vee r)$

D) $q\to (p\wedge r)$

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• question_answer102) If one root of the equation${{z}^{2}}+(a+i)z+b+ic=0$ = 0 is real, when$a,\,\,b\in R$, R, then${{c}^{2}}+b-ac$is equal to

A) $0$

B) $-1$

C) $1$

D) None of these

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• question_answer103) If the slopes of the lines given by$a{{x}^{2}}+2hxy+b{{y}^{2}}=0$are in the ratio $3:1$, then${{h}^{2}}$ is equal to

A) $\frac{ab}{3}$

B) $\frac{4ab}{3}$

C) $\frac{4a}{3b}$

D) None of these

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• question_answer104) If $a\in Z$ and the equation$(x-a)(x-10)+1=0$has integral roots, then the values of a are

A) $10,\,\,8$

B) $12,\,\,10$

C) $12,\,\,8$

D) $18,\,\,10$

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• question_answer105) If the tangent at any point $P$ on the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$meets the tangents at the vertices $A$ and $A'$ in $L$ and $L'$ respectively, then $AL\cdot \text{ }A'L'$is equal to

A) $a+b$

B) ${{a}^{2}}+{{b}^{2}}$

C) ${{a}^{2}}$

D) ${{b}^{2}}$

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• question_answer106) If $z$ is any complex number satisfying$|z-1|\,\,=1$, then which of the following is correct?

A) $\arg (z-1)=2\arg (z)$

B) $2\arg (z)=\frac{2}{3}\arg ({{z}^{2}}-z)$

C) $\arg (z-1)=\arg (z+1)$

D) $\arg (z)=2\arg (z+1)$

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• question_answer107) In a test, there are $n$ questions in which ${{2}^{n-i}}$ students gave wrong answers to atleast $i$ questions, where$i=1,\,\,2,\,\,...n$. If the total number of wrong answers given is $2047$, then $n$is equal to

A) $12$

B) $11$

C) $10$

D) None of these

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• question_answer108) The period of the function$f(x)=\frac{|\sin x|-|\cos x|}{|\sin x+\cos x|}$is

A) $\frac{\pi }{2}$

B) $2\pi$

C) $\pi$

D) None of these

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• question_answer109) Let $[x]$ denotes the greatest integer less than or equal to $x$and$f[x]=[{{\tan }^{2}}x]$. Then,

A) $\underset{x\to 0}{\mathop{\lim }}\,f(x)$ does not exist

B) $f(x)$is continuous at$x=0$

C) $f(x)$ is not differentiate at$x=0$

D) $f'(0)=1$

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• question_answer110) The value of$\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin x\cos x}$is

A) $\frac{2}{5}$

B) $\frac{3}{5}$

C) $\frac{3}{2}$

D) $\frac{3}{4}$

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• question_answer111) If$f(x)=$$\left| \begin{matrix} \sin x+\sin 2x+\sin 3x & \sin 2x & \sin 3x \\ 3+4\sin x & 3 & 4\sin x \\ 1+\sin x & \sin x & 1 \\ \end{matrix} \right|$, then the value of$\int_{0}^{\pi /2}{f(x)}dx$is

A) $3$

B) $2/3$

C) $1/3$

D) $0$

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• question_answer112) If $m$ and $n$ are the order and degree of the differential equation${{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\frac{{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\frac{{{d}^{3}}y}{d{{x}^{3}}}}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1$, then

A) $m=3,\,\,n=3$

B) $m=3,\,\,n=2$

C) $m=3,\,\,n=5$

D) $m=3,\,\,n=1$

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• question_answer113) $\int{\frac{{{\sin }^{3}}x}{({{\cos }^{4}}x+3{{\cos }^{2}}x+1){{\tan }^{-1}}(\sec x+\cos x)}dx}$is equal to

A) ${{\tan }^{-1}}(\sec x+\cos x)+C$

B) ${{\log }_{e}}|{{\tan }^{-1}}(\sec x+\cos x)|+C$

C) $\frac{1}{{{(\sec x+\cos x)}^{2}}}+C$

D) None of the above

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• question_answer114) The solution of the differential equation$({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0$is

A) $\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C$

B) $\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C$

C) $\log \,(xy)=\frac{1}{x}+\frac{1}{y}+C$

D) $\log \,(xy)+\frac{1}{x}+\frac{1}{y}=C$

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• question_answer115) The coefficient of ${{x}^{5}}$ in the expansion of${{(1+x)}^{21}}+{{(1+x)}^{22}}+...+{{(1+x)}^{30}}$is

A) $^{51}{{C}_{5}}$

B) $^{9}{{C}_{5}}$

C) $^{31}{{C}_{6}}{{-}^{21}}{{C}_{6}}$

D) $^{30}{{C}_{5}}{{+}^{20}}{{C}_{5}}$

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• question_answer116) If the direction cosines of line are$\frac{1}{c},\,\,\frac{1}{c},\,\,\frac{1}{c},$ then

A) $0<c<1$

B) $c>2$

C) $c>0$

D) $c=\pm \sqrt{3}$

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• question_answer117) If$0\le x<1$, then$\sin \left\{ {{\tan }^{-1}}\frac{1-{{x}^{2}}}{2x}+{{\cos }^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right\}$is equal to

A) $1$

B) $-1$

C) $0$

D) None of the above

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• question_answer118) Equation of plane passing through the points$(2,\,\,2,\,\,1)$,$(9,\,\,3,\,\,6)$ and perpendicular to the plane $2x+6y+6z-1=0$, is

A) $3x+4y+5z=9$

B) $3x+4y-5z+9=0$

C) $3x+4y-5z-9=0$

D) None of these

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• question_answer119) The length of the shadows of a vertical pole of height$h$, thrown by the sun's rays at three different moments are $h,\,\,2h$ and$3h$. The sum of the angles of elevation of the rays at these three moments is equal to

A) $\frac{\pi }{2}$

B) $\frac{\pi }{3}$

C) $\frac{\pi }{4}$

D) $\frac{\pi }{6}$

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• question_answer120) If${{(1-x+{{x}^{2}})}^{n}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...$$+{{a}_{2n}}{{x}^{2n}}$, then${{a}_{0}}+{{a}_{2}}+{{a}_{4}}+...+{{a}_{2n}}$is equal

A) $\frac{{{3}^{n}}+1}{2}$

B) $\frac{{{3}^{n}}-1}{2}$

C) $\frac{{{3}^{n-1}}+1}{2}$

D) $\frac{{{3}^{n-1}}-1}{2}$

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• question_answer121) If$f:[1,\,\,\infty )\to [2,\,\,\infty )$is given by$f(x)=x+\frac{1}{x}$, then ${{f}^{-1}}(x)$ equals

A) $\frac{x+\sqrt{{{x}^{2}}-4}}{2}$

B) $\frac{x}{1+{{x}^{2}}}$

C) $\frac{x-\sqrt{{{x}^{2}}-4}}{2}$

D) $1+\sqrt{{{x}^{2}}-4}$

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• question_answer122) If$A=\left[ \begin{matrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \\ \end{matrix} \right]$,then $\det (adj(adjA))$is equal to

A) ${{14}^{4}}$

B) ${{14}^{3}}$

C) ${{14}^{2}}$

D) $14$

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• question_answer123) The sum of n terms of the series $1.4+3.04+5.004+7.0004+...$is

A) ${{n}^{2}}+\frac{4}{9}\left( 1+\frac{1}{{{10}^{n}}} \right)$

B) ${{n}^{2}}+\frac{4}{9}\left( 1-\frac{1}{{{10}^{n}}} \right)$

C) $n+\frac{4}{9}\left( 1-\frac{1}{{{10}^{n}}} \right)$

D) None of these

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• question_answer124) Locus of the middle points of all chords of$\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9}=1$, which are at a distance of$2$ units from the vertex of parabola${{y}^{2}}=-8ax$,

A) ${{\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)}^{2}}=\frac{xy}{6}$

B) ${{\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)}^{2}}=\left( \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{81} \right)$

C) $\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)=\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}$

D) None of the above

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• question_answer125) The solution set of the in equation$\frac{|x+3|+x}{x+2}>1$, is

A) $(-5,\,\,-2)\cup (-1,\,\,\infty )$

B) $(-5,\,\,-2)$

C) $(-1,\,\,\infty )$

D) None of these

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• question_answer126) If$f(x)=\frac{1-x}{1+x},\,\,x\ne 0,\,\,-1$and$\alpha =f(f(x))+f(f(1/x))$, then

A) $\alpha >2$

B) $\alpha <-2$

C) $|\alpha |\,\,>2$

D) $\alpha =2$

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• question_answer127) The perimeter of a sector is constant. If its area is to be maximum, then sectorial angle is

A) $\frac{\pi }{6}$

B) $\frac{\pi }{4}$

C) ${{4}^{C}}$

D) ${{2}^{C}}$

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• question_answer128) The values of x for which the angle between $\mathbf{a}=2{{x}^{2}}\widehat{\mathbf{i}}+4x\widehat{\mathbf{j}}+\widehat{\mathbf{k}}$and$\mathbf{b}=7\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+x\widehat{\mathbf{k}}$is obtuse and the angle between b and the $Z-axis$ is acute and less than$\pi /6$, are

A) $a<x<1/2$

B) $1/2<x<15$

C) $x>1/2$or$x<0$

D) None of these

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• question_answer129) The value of a for which the function $f(x)=\left\{ \begin{matrix} {{\tan }^{-1}}a-3{{x}^{2}} & ,0<x<1 \\ -6x & ,x\ge 1 \\ \end{matrix} \right.$has a maximum at$x=1$, is

A) $0$

B) $1$

C) $2$

D) None of these

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• question_answer130) The subtangent at any point on the curve ${{x}^{m}}{{y}^{n}}={{a}^{m+n}}$varies as

A) ${{(abscissa)}^{2}}$

B) ${{(ordinate)}^{2}}$

C) $abscissa$

D) $ordinate$

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• question_answer131) If a is perpendicular to b and r is non-zero vector such that$p\mathbf{r}+(\mathbf{r}\cdot \mathbf{b})=\mathbf{a}=\mathbf{c}$, then r is equal to

A) $\frac{\mathbf{c}}{p}-\frac{(\mathbf{b}\cdot \mathbf{c})\mathbf{a}}{{{p}^{2}}}$

B) $\frac{\mathbf{a}}{p}-\frac{(\mathbf{c}\cdot \mathbf{a})\mathbf{b}}{{{p}^{2}}}$

C) $\frac{\mathbf{b}}{p}-\frac{(\mathbf{a}\cdot \mathbf{b})\mathbf{c}}{{{p}^{2}}}$

D) $\frac{\mathbf{c}}{{{p}^{2}}}-\frac{(\mathbf{b}\cdot \mathbf{c})\mathbf{a}}{p}$

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• question_answer132) If $A$ satisfies the equation${{x}^{3}}-5{{x}^{2}}+4x$$+\lambda =O$, then ${{A}^{-1}}$ exists if

A) $\lambda \ne 1$

B) $\lambda \ne 2$

C) $\lambda \ne -1$

D) $\lambda \ne 0$

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• question_answer133) A person is to count $4500$ currency notes. Let ${{a}_{n}}$ denotes the number of notes he counts in the nth minute. If ${{a}_{1}}={{a}_{2}}=...={{a}_{10}}=150$ and ${{a}_{10}},\,\,{{a}_{11}}...$ are in AP with common difference$-2$, then the time taken by him to count all notes is

A) $12.5\,\,\min$

B) $135\,\,\min$

C) $34\,\,\min$

D) $24\,\,\min$

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• question_answer134) The number of points with integral coordinates that lie in the interior of the region common to the circle ${{x}^{2}}+{{y}^{2}}=16$ and the parabola ${{y}^{2}}=4x$, is

A) $8$

B) $10$

C) $16$

D) None of these

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• question_answer135) In a $GP$ with alternatively positive and negative terms and any term is the $AM$ of the next two terms: Then, the common ratio of the $GP$ is

A) $-1$

B) $-3$

C) $-2$

D) $-1/2$

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• question_answer136) If a curve is given by$x=a\cos t+\frac{b}{2}\cos 2t$ and $y=\sin t+\frac{b}{2}\sin 2t$, then the points for which$\frac{{{d}^{2}}y}{d{{x}^{2}}}=0$, are given by

A) $\sin t=\frac{2{{a}^{2}}+{{b}^{2}}}{3ab}$

B) $\cos t=\frac{{{a}^{2}}+2{{b}^{2}}}{3ab}$

C) $\tan t=a/b$

D) None of the above

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• question_answer137) The weighted mean of first n natural numbers whose weights are equal, is given by

A) $\frac{n+1}{2}$

B) $\frac{2n+1}{2}$

C) $\frac{2n+1}{3}$

D) $\frac{(2n+1)(n+1)}{6}$

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• question_answer138) The area of the region bounded by the parabola${{(y-2)}^{2}}=(x-1)$, the tangent to the parabola at the point $(2,\,\,3)$ and the $X-axis$ is

A) $3$

B) $6$

C) $9$

D) $12$

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• question_answer139) $\frac{d}{dx}\left\{ {{\sin }^{2}}x\left( {{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right) \right\}$equals

A) $-1$

B) $1/2$

C) $-1/2$

D) $1$

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• question_answer140) Total number of words that can be formed using all letters of the word BRIJESH that neither begins with I nor ends with B is equal to

A) 4920

B) 3720

C) 3600

D) 4800

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• question_answer141) Let $A$ and $B$ be two sets defined as given below: $A=\{(x,\,\,y):|x-3|\,\,<1\,\,and|y-3|<1\}$ $B=\{(x,\,\,y):4{{x}^{2}}+9{{y}^{2}}-32x-54y+109\le 0\}$ Then,

A) $A\subset B$

B) $B\subset A$

C) $A=B$

D) None of these

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• question_answer142) A variable plane$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$at a unit distance from the origin cuts the coordinate axes $A,\,\,B$ and$C$. Centroid $(x,\,\,y,\,\,z)$ of $\Delta ABC$ satisfies the equation$\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=k$. The value of$k$is

A) $9$

B) $3$

C) $1/9$

D) $1/3$

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• question_answer143) The set of values of a for which the equation $\sin x(\sin x+\cos x)=a$has real solutions, is

A) $[1-\sqrt{2},\,\,1+\sqrt{2}]$

B) $[2-\sqrt{3},\,\,2+\sqrt{3}]$

C) $[0,\,\,2+\sqrt{3}]$

D) $\left[ \frac{1-\sqrt{2}}{2},\,\,\frac{1+\sqrt{2}}{2} \right]$

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• question_answer144) If$x\sin \theta =y\sin \left( \theta +\frac{2\pi }{3} \right)=z\sin \left( \theta +\frac{4\pi }{3} \right)$ then

A) $x+y+z=0$

B) $xy+yz+zx=0$

C) $xyz+x+y+z=1$

D) None of the above

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• question_answer145) Let$f(x)=2{{\tan }^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)$. Then,

A) $f'(2)=f'(3)$

B) $f'(2)=0$

C) $f'(1/2)=16/5$

D) All of these

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• question_answer146) A plane passes through $(1,\,\,-2,\,\,1)$ and is perpendicular to two planes $2x-2y+z=0$ and$x-y+2z=4$. The distance of the plane from the point $(1,\,\,2,\,\,2)$ is

A) $0$

B) $1$

C) $\sqrt{2}$

D) $2\sqrt{2}$

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• question_answer147) The number of integral triplets $(a,\,\,b,\,\,c)$ such that$a+b\cos 2x+c{{\sin }^{2}}x=0$for all$x,$is

A) $0$

B) $1$

C) $3$

D) infinitely many

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• question_answer148) The point on the line $\frac{x-2}{1}=\frac{y+3}{-2}=\frac{z+5}{-2}$ at a distance of 6 from the point $(2,\,\,-3,\,\,-5)$ is

A) $(3,\,\,-5,\,\,-3)$

B) $(4,\,\,-7,\,\,-9)$

C) $(0,\,\,2,\,\,-1)$

D) $(-3,\,\,5,\,\,3)$

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• question_answer149) If the axes are rotated through an angle of ${{30}^{o}}$ in the clockwise direction, the point $(4,\,\,2\sqrt{3})$ in the new system is

A) $(2,\,\,3)$

B) $(2,\,\,\sqrt{3})$

C) $(\sqrt{3},\,\,2)$

D) $(\sqrt{3},\,\,5)$

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• question_answer150) The range of values of a for which the points $(\alpha ,\,\,2+\alpha )$ and$\left( \frac{3\alpha }{2},\,\,{{\alpha }^{2}} \right)$lie on opposite sides of the line$2x+3y=6$, is

A) $(-2,\,\,1)$

B) $(-\infty ,\,\,-2)\cup (0,\,\,1)$

C) $(-2,\,\,0)\cup (1,\,\,\infty )$

D) $(-1,\,\,0)\cup (2,\,\,\infty )$

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