# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

### done Rajasthan PET Solved Paper-2009

• question_answer1) Which of the following equation represents a progressive wave?

A) $y=\,A\cos \,ax\,\sin bt$

B) $y=\,A\,\sin \,bt$

C) $y=\,A\,\cos (ax+bt)$

D) $y=\,A\,\tan (ax+bt)$

• question_answer2) The frequency and velocity of sound wave are 600 Hz and 360 m/s respectively. Phase difference between two particles of medium are$60{}^\circ ,$the minimum distance between these two particles will be

A) 10 cm

B) 15 cm

C) 20 cm

D) 50 cm

• question_answer3) The heat required to increase the temperature of 4 moles of a monoatomic ideal gas from 273 K to 473 K at constant volume is

A) 200 H

B) 400 R

C) 800 J

D) 1200 R

• question_answer4) A solid sphere rolls without slipping on the roof. The ratio of its rotational kinetic energy and its total kinetic energy is

A) 2/5

B) 4/5

C) 2/7

D) 3/7

• question_answer5) A black body at a temperature of 2600 K has the wavelength corresponding to maximum emission 1200$\overset{o}{\mathop{\text{A}}}\,$. Assuming the moon to be perfectly black body the temperature of the moon, if the wavelength corresponding to maximum emission is 5000$\overset{o}{\mathop{\text{A}}}\,$ is

A) 7800 K

B) 6240 K

C) 5240 K

D) 3640 K

• question_answer6) When the light enters from air to glass, for which colour the angle of deviation is maximum?

A) Red

B) Yellow

C) Blue

D) Violet

• question_answer7) Two waves are represent by ${{y}_{1}}=A\sin (kx-\omega t)\,and\,{{y}_{2}}=A\cos \,(kx-\omega t)$ The amplitude of resultant wave is

A) 4A

B) 2A

C) $\sqrt{2}A$

D) A

• question_answer8) Which of the following event, support the quantum nature of light?

A) Diffraction

B) Polarization

C) Interference

D) Photoelectric effect

• question_answer9) The linear momentum of photon is p. The wavelength of photon is $\lambda$, then ($h$is Planck?s constant)

A) $\lambda =hp$

B) $\lambda =\frac{h}{p}$

C) $\lambda =\frac{p}{h}$

D) $\lambda =\frac{{{p}^{2}}}{h}$

• question_answer10) When two coherent monochromatic beams of intensity I and 9l interfere, the possible maximum and minimum intensities of the resulting beam are

A) $9I$ and$I$

B) $9I$and$4I$

C) $16I$and$4I$

D) $16I$and$I$

• question_answer11) An atom of mass M which is in the state of rest emits a photon of wavelength $\lambda$ . As a result, the atom will deflect with the kinetic energy equal to (A is Planck's constant)

A) $\frac{{{h}^{2}}}{M{{\lambda }^{2}}}$

B) $\frac{1}{2}\frac{{{h}^{2}}}{M{{\lambda }^{2}}}$

C) $\frac{h}{M\lambda }$

D) $\frac{1}{2}\frac{h}{M\lambda }$

• question_answer12) Two long straight wires are set parallel to each other Each carries a current i in the opposite direction and the separation between them is 2R. The intensity of the magnetic field midway between them is

A) zero

B) $\frac{{{\mu }_{0}}i}{4\pi R}$

C) $\frac{{{\mu }_{0}}i}{2\pi R}$

D) $\frac{{{\mu }_{0}}i}{\pi R}$

• question_answer13) Charge Q is placed at the diagonal faced comers of a square and charge q is placed at another two corners of square. The condition for net electric force on Q to be zero will be

A) $Q=(-2\sqrt{2)}\,q$

B) $Q=-\frac{q}{2}$

C) $Q=(2\sqrt{2)}\,q$

D) $Q=-\frac{q}{2}$

• question_answer14) The electric potential at centre of metallic conducting sphere is

A) zero

B) half from potential at surface of sphere

C) equal from potential at surface of sphere

D) twice from potential at surface of sphere

• question_answer15) A capacitor of capacity 10 $\mu$F is charged to a potential of 400 Volt. When its both plates are connected by a conducting wire, then heat generated will be

A) $80\text{ }J$

B) $0.8\text{ }J$

C) $8\times {{10}^{-3}}$

D) $8\times {{10}^{-6}}J$

• question_answer16) Magnet moment of bar magnet is M. The work done to turn the magnet by$90{}^\circ$of magnet in direction of magnetic field B will be

A) zero

B) $\frac{1}{2}$MB

C) 2 MB

D) MB

• question_answer17) Voltage V and current$i$in AC circuit are given by \begin{align} & V=50\sin (50\,t)\,volt \\ & i=50\,\sin \,\left( 50t+\frac{\pi }{3} \right)mA \\ \end{align} The power dissipated in circuit is

A) 5.0 W

B) 2.5 W

C) 1.25 W

D) zero

• question_answer18) The maximum voltage in DC circuit is 282 Volt. The effective voltage in AC circuit will be

A) 200 V

B) 300 V

C) 400 V

D) 564 V

• question_answer19) If L, C and R denote inductance, capacitance and resistance respectively, then which of the following combination has the dimension of time?

A) $\frac{C}{L}$

B) $\frac{1}{RC}$

C) $\frac{L}{R}$

D) $\frac{RL}{C}$

• question_answer20) The ratio of momenta of an electron and photon which are accelerated from rest by a potential difference 50 Volt is

A) $\frac{{{m}_{e}}}{{{m}_{p}}}$

B) $\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}$

C) $\frac{{{m}_{p}}}{{{m}_{e}}}$

D) $\sqrt{\frac{{{m}_{p}}}{{{m}_{e}}}}$

• question_answer21) A wire of resistance$18\,\Omega$is divided into three equal parts. These parts are connected in side of triangle, the equivalent resistance of any two corners of triangle will be

A) 18$\Omega$

B) 9$\Omega$

C) 6$\Omega$

D) 4$\Omega$

• question_answer22) Two capacitors of capacity 6 $\mu$F and 12 $\mu$V in series are connected by potential of 150 V. The potential of capacitor of capacity 12 $\mu$F will be

A) 25 V

B) 50 V

C) 100 V

D) 150 V

• question_answer23) A charged particle enters in a magnetic field whose direction is parallel to velocity of the particle, then the speed of this particle

A) in straight line

B) in coiled path

C) in circular path

D) in ellipse path

• question_answer24) Magnetic intensity for an axial point due to a short bar magnet of magnetic moment M is given by

A) $\frac{{{\mu }_{0}}}{4\pi }\frac{m}{{{d}^{3}}}$

B) $\frac{{{\mu }_{0}}M}{4\pi {{d}^{2}}}$

C) $\frac{{{\mu }_{0}}}{2\pi }\frac{\mu }{{{d}^{3}}}$

D) $\frac{{{\mu }_{0}}M}{2\pi {{d}^{2}}}$

• question_answer25) Which of the following transition gives the photon of minimum frequency?

A) n = 2 to n = 1

B) n = 3 to n = 1

C) n = 3 to n = 2

D) n = 4 to n = 3

• question_answer26) lonization energy of He+ ion at minimum position is

A) 13.6 eV

B) 27.2 eV

C) 54.4 eV

D) 68.0 eV

• question_answer27) The half-life period of a radioactive substance is 3 days. Three fourth of substance decays in

A) 3 days

B) 6 days

C) 9 days

D) 12 days

• question_answer28) If the decay constant of a radioactive substance is $\lambda$, then its half-life is

A) $\frac{1}{\lambda }{{\log }_{e}}2$

B) $\frac{1}{\lambda }$

C) $\lambda {{\log }_{e}}2$

D) $\frac{\lambda }{{{\log }_{e}}2}$

• question_answer29) A galvanometer can be converted into a voltmeter by connecting

A) low resistance in parallel

B) low resistance in series

C) high resistance in parallel

D) high resistance in series

• question_answer30) A heater coil cut into two equal parts and one part is connected with heater. Now heat generated in heater will be

A) twice

B) half

C) one- fourth

D) four times

• question_answer31) A particle moves along with x-axis. The position$x$of particle with respect to time t from origin given by $x={{b}_{0}}+{{b}_{1}}t+{{b}_{2}}{{t}_{2}}$. The acceleration of particle is

A) ${{b}_{0}}$

B) ${{b}_{1}}$

C) ${{b}_{2}}$

D) $2{{b}_{2}}$

• question_answer32) One end of string of length$l$is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is

A) zero

B) $T-\frac{m{{v}^{2}}}{I}$

C) $T$

D) $T+\frac{m{{v}^{2}}}{I}$

• question_answer33) If the kinetic energy of a body is increased 2 times, its momentum will

A) half

B) remain unchanged

C) be doubled

D) increase $\sqrt{2}$times

• question_answer34) The moment of inertia of a solid sphere of mass M and radius R about the tangent on its surface is

A) $\frac{7}{5}M{{R}^{2}}$

B) $\frac{4}{5}M{{R}^{2}}$

C) $\frac{2}{5}M{{R}^{2}}$

D) $\frac{1}{2}M{{R}^{2}}$

• question_answer35) Satellites A and B are revolving around the orbit of earth. The mass of A is 10 times to mass of B. The ratio of time period $\left( \frac{{{T}_{A}}}{{{T}_{B}}} \right)$ is

A) $10$

B) $1$

C) $\frac{1}{5}$

D) $\frac{1}{10}$

• question_answer36) A particle of amplitude A is executing simple harmonic motion. When the potential energy of particle is half of its maximum potential energy, then displacement from its equilibrium position is

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

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

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

D) $\frac{A}{\sqrt{2}}$

• question_answer37) A simple wave motion represents by$y=5(\sin 4\pi t+\sqrt{3}\cos 4\pi t)$. Its amplitude is

A) 5

B) 5$\sqrt{3}$

C) $10\sqrt{3}$

D) 10

• question_answer38) A liquid does not wet the sides of a solid, if the angle of contact is

A) obtuse

B) $90{}^\circ$

C) acute

D) zero

• question_answer39) Root means square speed of the molecules of ideal gas is$v$. If pressure is increased two times at constant temperature, then the rms speed will become

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

B) $v$

C) $2v$

D) $4v$

• question_answer40) 1 mole of gas occupies a volume of 200 ml at 100 mm pressure. What is the volume occupied by two moles of gas at 400 mm pressure and at same temperature?

A) 50 mL

B) 100 mL

C) 200 mL

D) 400 mL

• question_answer41) The$s{{p}^{3}}$hybridisation is present on the central atom of

A) $HCHO$

B) $BC{{l}_{3}}$

C) $PC{{l}_{3}}$

D) $S{{O}_{3}}$

• question_answer42) The number of unit cells in the 5.85 g crystals of$NaCl$are

A) $1.5\times {{10}^{23}}$

B) $1.5\times {{10}^{22}}$

C) $3.0\times {{10}^{22}}$

D) $3.0\times {{10}^{23}}$

• question_answer43) The oxidation number of sulphur is -1 in

A) ${{H}_{2}}S$

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

C) $C{{S}_{2}}$

D) $C{{u}_{2}}S$

• question_answer44) For which of the following metals, the electronic configuration of valence shell is not ${{d}^{6}}$?

A) Fe (II)

B) $Mn$(II)

C) Co (III)

D) Ni (IV)

• question_answer45) 68 g sugar$({{C}_{12}}{{H}_{22}}{{O}_{11}})$is dissolved in 1 kg of water. What is the mole fraction of sugar?

A) 0.018

B) 0.036

C) 0.0018

D) 0.0036

• question_answer46) The pH of 0.1 M aqueous ammonia $({{K}_{b}}=1.8\times {{10}^{-5}})$is.

A) 9.13

B) 10.13

C) 11.13

D) 12.13

• question_answer47) From the following mixtures, which is not a buffer (concentration level 0.5 M)?

A) $C{{H}_{3}}COOH+NaOH(2:1)$

B) $HCl+N{{H}_{3}}(aq)(1:2)$

C) $C{{H}_{3}}COOH+NaOH(1:2)$

D) $HCl+N{{H}_{3}}(2:3)$

• question_answer48) How much volume (in litre) of$3M\,NaOH$is obtained from 80 g$NaOH$? (Atomic mass of $Na=23u$)

A) 2.67

B) 1.34

C) 0.67

D) 0.33

• question_answer49) The initial concentration of sugar solution is 0.12 M. On doing fermentation the concentration of sugar decreases to 0.06 M in 10 h and to 0.045 M in 15 h. The order of the reaction is

A) 0.5

B) 1.0

C) 1.5

D) 2.0

• question_answer50) For the decomposition of${{N}_{2}}O$and${{O}_{2}}$in presence of at, the velocity constant, k is $k=5\times {{10}^{11}}{{e}^{-30,000/T}}$ For this, the activation energy is (in kJ$mo{{l}^{-1}}$)

A) 2.494

B) 24.94

C) 249.4

D) 2494

• question_answer51) The following equilibrium establishes on heating 0.2 mole of${{H}_{2}}$and 1.0 mole of sulphur in 1 L vessel at$90{}^\circ C$. ${{H}_{2}}(g)+S(s){{H}_{2}}S(g);$ $K=6.8\times {{10}^{-2}}$ The partial pressure of${{H}_{2}}S$in equilibrium state is

A) 4.20

B) 0.42

C) 0.21

D) 0.042

• question_answer52) An aqueous solution boils at$100.2{}^\circ C$. At which temperature this will freeze. $({{K}_{b}}=0.5{}^\circ C/m,{{K}_{f}}=1.9{}^\circ C/m)$

A) $+0.76$

B) $-0.76$

C) $-0.38$

D) $+0.38$

• question_answer53) The lowest$p{{K}_{a}}$value is for

A) phenol

B) $m-$cresol

C) o-cresol

D) p-cresol

• question_answer54) At room temperature, the least stable compound is

A) $C{{H}_{3}}COCl$

B) $HCOCl$

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

D) ${{(C{{H}_{3}}CO)}_{2}}O$

• question_answer55) For the conversion of$C{{H}_{2}}=C{{H}_{2}}$into$HOOC$. $C{{H}_{2}}C{{H}_{2}}COOH,$the minimum number of steps required are

A) 2

B) 3

C) 4

D) 5

• question_answer56) Which of the following compounds does not give two isomer compounds on reaction with$N{{H}_{2}}OH$?

A) $C{{H}_{3}}CO{{C}_{2}}{{H}_{5}}$

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

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

D) $PhCOC{{H}_{3}}$

• question_answer57) From the following which is not a reactant, reagent or product in Hoffmann reaction?

A) $RCON{{H}_{2}}$

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

C) $B{{r}_{2}},O{{H}^{-}}$

D) ${{H}_{2}}S{{O}_{4}}$

• question_answer58) The total number of isomers for cyclic alcohol ${{C}_{4}}{{H}_{7}}OH$is

A) 2

B) 3

C) 4

D) 5

• question_answer59) The least stable free radical is

A) $\overset{\bullet }{\mathop{C}}\,{{H}_{2}}C{{H}_{2}}CH{{(C{{H}_{3}})}_{2}}$

B) $C{{H}_{3}}\underset{\bullet }{\mathop{C}}\,HCH{{(C{{H}_{3}})}_{2}}$

C) $C{{H}_{3}}C{{H}_{2}}\underset{\bullet }{\mathop{C}}\,{{(C{{H}_{3}})}_{2}}$

D) $\overset{\bullet }{\mathop{C}}\,{{H}_{3}}$

• question_answer60) The suitable reagent for the reduction of ${{C}_{2}}{{H}_{5}}COOH$into${{C}_{3}}{{H}_{7}}OH$is

A) $B{{H}_{3}}/THF$and${{H}_{3}}{{O}^{+}}$

B) $NaB{{H}_{4}}$

C) $Na/EtOH$

D) ${{H}_{2}}/$catalyst

• question_answer61) The blue colour of acidic solution of$C{{r}_{2}}O_{7}^{2-}$is not changed into green by

A) ${{C}_{6}}{{H}_{5}}C{{H}_{2}}OH$

B) ${{(C{{H}_{3}})}_{2}}CHOH$

C) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH$

D) ${{(C{{H}_{3}})}_{3}}COH$

• question_answer62) The reaction of${{C}_{2}}{{H}_{5}}Cl$with$Li$and$CuI$gives mainly

A) 2-butene

C) n-butane

D) n-butyl chloride

• question_answer63) The reagent which does not convert n-butyl chloride into zi-butane is

A) $Zn,\text{ }HCl$

B) $LIAl{{H}_{4}}$

C) $Mg,$Anhydrous ether,${{H}_{2}}O$

D) ${{B}_{2}}{{H}_{6}}$in THF

• question_answer64) The correct order of stability is

A) Pentane < iso-pentane < neo-pentane

B) iso-pentane < neo-pentane < pentane

C) neo-pentane < iso-pentane < pentane

D) Pentane < iso-pentane < iso-pentane

• question_answer65) The correct order of boiling point of ethyl dimethyl amine , n-butyl amine and diethyl amine is

A) $B>C>A$

B) $B>A>C$

C) $A>B>C$

D) $C>B>A$

• question_answer66) Which of the following compounds does not give iodoform test?

A) $C{{H}_{3}}COC{{H}_{2}}COO{{C}_{2}}{{H}_{5}}$

B) $PhC{{H}_{2}}COC{{H}_{3}}$

C) $M{{e}_{3}}C.COC{{H}_{3}}$

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

• question_answer67) The species which acts as both nucleophile and electrophile is

A) $C{{H}_{3}}CN$

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

C) $P{{(C{{H}_{3}})}_{2}}$

D) ${{H}_{2}}$

• question_answer68) The most basic from the following is

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

B) $C{{H}_{3}}N{{H}_{2}}$

C) $N{{F}_{3}}$

D) $N{{(Si{{H}_{3}})}_{3}}$

• question_answer69) The main product of the reaction of benzene with lithium in liquid ammonia and$EtOH$is

A)

B)

C)

D)

• question_answer70) The rate of free radical chlorination of$C{{H}_{4}}$is

A) equal to$C{{D}_{4}}$

B) double the rate of $C{{D}_{4}}$

C) 12 times the rate of$C{{D}_{4}}$

D) less than the rate of$C{{D}_{4}}$

• question_answer71) The first ionisation energy difference is maximum for which pair?

A) $Na,Mg$

B) $K,Ca$

C) $Rb,Sr$

D) $Cs,Ba$

• question_answer72) The ratio of third Bohr orbit radius and second Bohr orbit radius for the hydrogen atom is

A) 0.5

B) 1.5

C) 0.75

D) 2.25

• question_answer73) The principal quantum number of Mn for those valence shell orbits in which electrons are filled

A) 4, 3

B) 4, 4

C) 3, 3

D) 5, 4

• question_answer74) From the generally known oxidation states, the oxidation number is maximum for

A) $Mn$

B) $Cu$

C) $Sn$

D) $Sc$

• question_answer75) The number of molecules in 180 g of heavy water are

A) $6.02\times {{10}^{24}}$

B) $6.02\times {{10}^{22}}$

C) $5.42\times {{10}^{24}}$

D) $5.42\times {{10}^{23}}$

• question_answer76) Which of the following is reduced by${{H}_{2}}{{O}_{2}}$?

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

B) ${{[Fe{{(CN)}_{6}}]}^{4-}}$

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

D) $SO_{3}^{2-}$

• question_answer77) The maximum energy molecular orbit filled by electron in nitrogen molecule is/are

A) $\sigma 2{{p}_{z}}$

B) $\pi 2{{p}_{x}}\approx \pi 2{{p}_{y}}$

C) ${{\pi }^{*}}2{{p}_{x}}\approx {{\pi }^{*}}2{{p}_{y}}$

D) ${{\sigma }^{*}}2{{p}_{z}}$

• question_answer78) Which of the following is correct order for density?

A) $Cs>Rb>K>Na$

B) $Cs>Rb>Na>K$

C) $Rb>Cs>K>Na$

D) $Rb>Cs>Na>K$

• question_answer79) The correct order of dipole moment is

A) $B{{F}_{3}}<{{H}_{2}}S<{{H}_{2}}O$

B) ${{H}_{2}}S<B{{F}_{3}}<{{H}_{2}}O$

C) ${{H}_{2}}O<{{H}_{2}}S<B{{F}_{3}}$

D) ${{H}_{2}}O<B{{F}_{3}}<{{H}_{2}}S$

• question_answer80) Which of the following bond has minimum bond energy?

A) $C-H$

B) $N-H$

C) $O-H$

D) $F-H$

• question_answer81) The intersection point of the normals drawn at the end points of latusrectum of the parabola${{x}^{2}}=-2y$is

A) $\left( -\frac{1}{2},-\frac{3}{2} \right)$

B) $\left( \frac{1}{2},-\frac{3}{2} \right)$

C) $(0,-1)$

D) $\left( 0,-\frac{3}{2} \right)$

• question_answer82) The equation whose roots are reciprocal of the roots of the equation$a{{x}^{2}}+bx+c=0,$is

A) $b{{x}^{2}}+cx+a=0$

B) $b{{x}^{2}}+ax+c=0$

C) $c{{x}^{2}}+ax+b=0$

D) $c{{x}^{2}}+bx+a=0$

• question_answer83) If in the expansion of${{\left( 3x-\frac{2}{{{x}^{2}}} \right)}^{15}},$rth term is independent of$x,$then value of r is

A) 11

B) 10

C) 9

D) 12

• question_answer84) If$f(x)=\left| \begin{matrix} 1+a & 1-ax & 1+a{{x}^{2}} \\ 1+b & 1+bx & 1+b{{x}^{2}} \\ 1+c & 1+cx & 1+c{{x}^{2}} \\ \end{matrix} \right|,$where$a,b,c$ are non-zero Constants, then value of$f(10)$ is

A) $10(b-a)(c-a)$

B) $100(b-a)(c-b)(a-c)$

C) $100\,abc$

D) 0

• question_answer85) If$^{n}{{C}_{12}}{{=}^{n}}{{C}_{8}},$then value of$^{n}{{C}_{19}}$is

A) 1

B) 20

C) 210

D) 1540

• question_answer86) If$\omega$is a complex cube root of unity and$A=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right],$then${{A}^{50}}$is

A) ${{\omega }^{2}}A$

B) $\omega A$

C) $A$

D) $0$

• question_answer87) If sum of$n$terms of an AP is$2n+3{{n}^{2}},$then rth term is

A) $2r+3{{r}^{2}}$

B) $3{{r}^{2}}-4r+1$

C) $6r-1$

D) $4r+1$

• question_answer88) If A and B are square matrices of order$3\times 3,$ then which of the following is true?

A) $AB=0\Rightarrow A=O$or$B=O$

B) $det(2AB)=8\text{ (}detA)\text{ (}detB)$

C) ${{A}^{2}}-{{E}^{2}}=(A+B)(A-B)$

D) $det(A+B)=det(A)+det(B)$

• question_answer89) If geometric mean and harmonic mean between two different numbers are 12 and $\frac{48}{5}$respectively, then one number is

A) 4

B) 6

C) 8

D) 10

• question_answer90) Let a, b, c are in GP and 4a,5b,4c are in AP such that$a+b+c=70,$then value of$b$is

A) 5

B) 10

C) 15

D) 20

• question_answer91) The value of integral$\int_{0}^{4}{|x-1|}dx$ is

A) 4

B) 5

C) 7

D) 9

• question_answer92) If$\frac{x-1}{1+i}+\frac{y-1}{1-i}=i,$where$x$and y are real numbers and$i=\sqrt{-1},$then

A) $x=0$

B) $x<0$

C) $x>0$

D) None of these

• question_answer93) If a pair of two fair dice is thrown, then the probability of getting the sum 5 on both dice is

A) $\frac{5}{36}$

B) $\frac{1}{12}$

C) $\frac{1}{18}$

D) $\frac{1}{9}$

• question_answer94) If a fair coin is tossed 20 times and let we get head n times, then probability that 21 is odd, is

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

B) $\frac{1}{6}$

C) $\frac{5}{8}$

D) $\frac{7}{8}$

• question_answer95) If${{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right),$then value of${{x}_{1}}\,{{x}_{2}}\,\,{{x}_{3}}....$is

A) $i$

B) $1$

C) $-1$

D) $-i$

• question_answer96) If${{\left( \frac{1+\cos \phi +i\sin \phi }{1+\cos \phi -i\sin \phi } \right)}^{n}}=u+iv,$where u and v are real numbers, then u is

A) $n\cos \phi$

B) $\cos n\phi$

C) $\cos \left( \frac{n\phi }{2} \right)$

D) $\sin \left( \frac{n\phi }{2} \right)$

• question_answer97) If square root of $-7+24i$ is $x+iy,$ then $x$ is

A) ?1

B) ? 2

C) ?3

D) ? 4

• question_answer98) If ${{\tanh }^{-1}}(x-iy)=\frac{1}{2}{{\tanh }^{-1}}\left( \frac{2x}{1+{{x}^{2}}+{{y}^{2}}} \right)$ $+\frac{i}{2}{{\tan }^{-1}}\left( \frac{2y}{1-{{x}^{2}}-{{y}^{2}}} \right)x,y\in R,$ then ${{\tanh }^{-1}}(iy)$ is

A) $2\text{ }tan{{h}^{-1}}(y)$

B) $-2\text{ }tan{{h}^{-1}}(y)$

C) $\text{i }ta{{n}^{-1}}y$

D) $\text{-i }ta{{n}^{-1}}(y)$

• question_answer99) If $f:R\to R$ is defined as $f(x)={{(1-x)}^{1/3}}$ then ${{f}^{-1}}(x)$ is

A) ${{(1-x)}^{-1/3}}$

B) ${{(1-x)}^{3}}$

C) $1-{{x}^{3}}$

D) $1-{{x}^{1/3}}$

• question_answer100) If ${{x}^{y}}={{e}^{x-y}},x>0,$ then value of $\frac{dy}{dx}$ at (1,1) is

A) 0

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

C) 1

D) 2

• question_answer101) The value of $\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)}{{{x}^{2}}}$is

A) doesn't exist

B) infinite

C) 0

D) 2

• question_answer102) The value of differentiation of${{e}^{{{x}^{2}}}}$w.r.t. to ${{e}^{2x-1}}$at$x=1$is

A) e

B) 0

C) ${{e}^{-1}}$

D) 1

• question_answer103) If function$f(x),x\in R$is differentiable and $f(1)=1,$then value of$\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)}{{{x}^{2}}}$is

A) 0

B) 1

C) $f'(1)$

D) $\infty$

• question_answer104) The value of integral $\int_{0}^{2a}{\frac{f(x)}{f(x)+f(2a-x)}}dx,$where$f(x)$is a continuous function, is

A) 0

B) 1

C) $a$

D) $2a$

• question_answer105) The area of the region bounded by the curves $y=ex,\text{ y}=lo{{g}_{e}}x$and lines$x=1,\text{ }x=2$is

A) ${{(e-1)}^{2}}$

B) ${{e}^{2}}-e+1$

C) ${{e}^{2}}-e+1-2lo{{g}_{e}}2$

D) ${{e}^{2}}+e-2lo{{g}_{e}}2$

• question_answer106) If$f(x)=sin\text{ }x+cos\text{ }x+1$and $g(x)={{x}^{2}}+x,\text{ }x\in R,$then value of$fog(x)$at $x=0$is

A) 0

B) 1

C) 2

D) 3

• question_answer107) The maximum value of function $f(x)=\sin x(1+\cos x),x\in R$is

A) $\frac{{{3}^{3/2}}}{4}$

B) $\frac{{{3}^{5/3}}}{4}$

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

D) $\frac{{{3}^{7/5}}}{4}$

• question_answer108) The normal at point (1,1) to the curve${{y}^{2}}={{x}^{3}}$is parallel to the line

A) $3x-y-2=0$

B) $2x+3y-7=0$

C) $2x-3y+1=0$

D) $2y-3x+1=0$

• question_answer109) Function$f(x)=|x-1|+|x-2|,x\in R$is

A) differentiable everywhere in R

B) except$x=1$and$x=2$differentiable everywhere in R

C) not continuous at$x=1$and$x=2$

D) increasing in$R$

• question_answer110) If$f(1)=2$and$f'(1)=1,$then the value of$\underset{x\to 1}{\mathop{\lim }}\,\frac{2x-f(x)}{x-1}$is

A) $-1$

B) 0

C) $1$

D) 2

• question_answer111) The distance of the point P (1,2,3) from the line which passes through the point A (4,2,2) and parallel to the vector$2\hat{i}+3\hat{j}+6\hat{k},$is

A) $\sqrt{10}$

B) $\sqrt{7}$

C) $\sqrt{5}$

D) $1$

• question_answer112) Let$\overrightarrow{a}=2\hat{i}+\hat{k},\overrightarrow{b}=\hat{i}+\hat{i}+\hat{k}$and$\overrightarrow{c}=4\hat{i}-3\hat{j}+7\hat{k}$. If r is a vector such that$\overrightarrow{r}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{b}$ and$\overrightarrow{r}.\overrightarrow{a}=0,$then value of$\overrightarrow{r}.\overrightarrow{b}$is

A) 7

B) $-7$

C) $-5$

D) 5

• question_answer113) A unit vector which is coplanar with $\hat{i}+\hat{j}+2\hat{k}$and$\hat{i}+2\hat{j}+\hat{k}$and perpendicular to $\hat{i}+\hat{j}+\hat{k},$ is

A) $\frac{(-\hat{j}+\hat{k})}{\sqrt{2}}$

B) $\frac{(\hat{k}-\hat{i})}{\sqrt{2}}$

C) $\frac{(\hat{i}-\hat{j})}{\sqrt{2}}$

D) $\frac{(\hat{i}-\hat{k})}{\sqrt{2}}$

• question_answer114) If a line is inclined at$45{}^\circ$to both x-axis and$y-$axis, then the angle at which it is inclined to z-axis is

A) $45{}^\circ$

B) $60{}^\circ$

C) $30{}^\circ$

D) $90{}^\circ$

• question_answer115) The equation of plane which passes through the point$(1,2,-1)$and parallel to the plane $x-y+2z=0$is

A) $x-y+2z-3=0$

B) $x-y+2z+3=0$

C) $x-y+2z+6=0$

D) $x-y+2z-7=0$

• question_answer116) Let a plane passes through the point P(-1, -1,1) and also passes through a line joining the points Q (0,1,1) and R(Q,0,2). Then, the distance of plane from the point (0,0,0) is

A) 3

B) 0

C) $1/\sqrt{6}$

D) $2/\sqrt{6}$

• question_answer117) If$f(x)$and$g(x),x\in R$are continuous functions, then value of integral $\int_{-\pi /2}^{\pi /2}{[\{f(x)+f(-x)\}\{g(x)-g(-x)\}]}\,dx$is

A) $\pi$

B) $\pi /2$

C) $1$

D) 0

• question_answer118) The equation of circle which touches the$x-$axis and 7-axis at points (1, 0) and (0, 1) respectively, is

A) ${{x}^{2}}+{{y}^{2}}-4y+3=0$

B) ${{x}^{2}}+{{y}^{2}}-2y-2=0$

C) ${{x}^{2}}+{{y}^{2}}-2x-27+2=0$

D) ${{x}^{2}}+{{y}^{2}}-2x-2y+1=0$

• question_answer119) If lines$4x+3y=1,\text{ }y-x=5$and$kx+5y=1$are concurrent, then value of k is

A) 0

B) 1

C) 3

D) 7

• question_answer120) The equation${{y}^{2}}-8y-x+19=0$represents

A) a parabola whose focus is$\left( \frac{1}{4},0 \right)$and directrix is$x=-\frac{1}{4}$

B) a parabola whose vertex is (3, 4) and directrix is$x=\frac{11}{4}$

C) a parabola whose focus is$\left( \frac{13}{4},4 \right)$and vertex is (0, 0)

D) a curve which is not a parabola