# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2010

### done Rajasthan PET Solved Paper-2010

• question_answer1) The equation of a stationary wave is$y=0.8cos$ $\left( \frac{\pi x}{20} \right)$sin 200 $\pi$t and t is in sec. The separation between consecutive nodes will be

A) 20 cm

B) 10 cm

C) 40 cm

D) 30 cm

• question_answer2) Two waves of frequencies 20 Hz and 30 Hz travels out from a common point. The phase difference between them after 0.6 s is

A) zero

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

C) $\pi$

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

• question_answer3) When temperature of an ideal gas is increased from$27{}^\circ C$to$227{}^\circ C,$its rms speed changed from 400 m/s to${{v}_{s}}$. Then${{v}_{s}}$is

A) 516 m/s

B) 450 m/s

C) 310 m/s

D) 746 m/s

• question_answer4) One circular ring and one circular disc, both are having the same mass and radius. Then both of their moments of inertia about the axes passing through their centres and perpendicular to their planes, will be in the ratio

A) 1 : 1

B) 2 : 1

C) 1 : 2

D) 4 : 1

• question_answer5) Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperature $127{}^\circ C$and$527{}^\circ C$respectively. The ratio of energy radiated by P and Q is

A) 0.054

B) 0.0034

C) 1

D) 2

• question_answer6) Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge$-Q$ from its centre to infinity is

A) $zero$

B) $\frac{\sqrt{2}\,{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}a}$

C) $\frac{\sqrt{2}\,{{Q}^{2}}}{\pi {{\varepsilon }_{0}}a}$

D) $\frac{{{Q}^{2}}}{2\pi {{\varepsilon }_{0}}a}$

• question_answer7) When light rays from the sun fall on a convex lens along a direction parallel to its axis.

A) Focal length for all colors is the same

B) Focal length for violet color is the shortest

C) Focal length for yellow color is the longest

D) Focal length for red color is the shortest

• question_answer8) Diffraction and interference of light suggest

A) nature of light is electromagnetic

B) wave nature

C) nature is quantum

D) nature of light is transverse

• question_answer9) The de- Broglie wavelength of an electron having kinetic energy E is given by the expression

A) $\frac{h}{\sqrt{2mE}}$

B) $\frac{2h}{mE}$

C) $2mhE$

D) $\frac{2\sqrt{2mE}}{h}$

• question_answer10) If two waves of same frequency and same amplitude respectively, are superimposed on each other produces a resultant disturbance of the same amplitude, then the waves differ in phase by

A) $\pi$

B) 2$\pi$/3

C) $\pi$/2

D) zero

• question_answer11) Ultraviolet radiation of 6.2 eV falls on an aluminium surface (work function 4.2 eV). The kinetic energy in joule of the fastest electron emitted is approximately

A) $3.2\times {{10}^{-21}}$

B) $3.2\times {{10}^{-19}}$

C) $3.2\times {{10}^{-17}}$

D) $3.2\times {{10}^{-15}}$

• question_answer12) The magnetic field at the centre of coil of n turn, bent in the form of a square of side$2l,$carrying current$i,$is

A) $\frac{\sqrt{2}{{\mu }_{0}}ni}{\pi l}$

B) $\frac{\sqrt{2}{{\mu }_{0}}ni}{2\pi l}$

C) $\frac{\sqrt{2}{{\mu }_{0}}ni}{4\pi l}$

D) $\frac{2{{\mu }_{0}}ni}{\pi l}$

• question_answer13) Charges 4Q, q and Q and placed along x-axis at positions $x=0,\text{ }x=1/2$and$x=1$respectively. Find the value of q so, that force on charge Q is zero

A) Q

B) $Q/2$

C) $-Q/2$

D) $-Q$

• question_answer14) Gauss's taw is true only if force due to a charge varies as

A) ${{r}^{-1}}$

B) ${{r}^{-2}}$

C) ${{r}^{-3}}$

D) ${{r}^{-4}}$

• question_answer15) A condenser having a capacity 2.0 $\mu F$ is charged to 200 Volts and then the plates of the capacitor are connected to a resistance wire. The heat produced in joule will be

A) $4\times {{10}^{4}}J$

B) $4\times {{10}^{10}}J$

C) $4\times {{10}^{-2}}J$

D) $2\times {{10}^{-2}}J$

• question_answer16) The intensity of magnetic field is H and moment of magnet is M. The maximum potential energy is

A) MH

B) 2 MH

C) 3 MH

D) 4 MH

• question_answer17) In an AC circuit, V and$i$are given by, $V=100\text{ }sin$ (100 t) Volts, $i=100\,\sin \left( 100\,t+\frac{\pi }{3} \right)mA$ The power dissipated in circuit is

A) 104 W

B) 10 W

C) 2.5 W

D) 5 W

• question_answer18) A resonant AC circuit contains a capacitor of capacitance${{10}^{-6}}F$and an inductor of${{10}^{-4}}H$The frequency of electrical oscillator will be

A) ${{10}^{5}}Hz$

B) 10 Hz

C) $\frac{{{10}^{5}}}{2\pi }Hz$

D) $\frac{10}{2\pi }Hz$

• question_answer19) If pressure p, velocity v and time (are taken as fundamental physical quantities, the dimensional formula of force is

A) $\left[ p{{v}^{2}}{{t}^{2}} \right]$

B) $\left[ {{p}^{-1}}{{v}^{2}}{{t}^{-2}} \right]$

C) $\left[ pv{{t}^{2}} \right]$

D) $\left[ {{p}^{-1}}v{{t}^{2}} \right]$

• question_answer20) The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of 100 V is

A) $1$

B) $\sqrt{\frac{2{{m}_{e}}}{{{m}_{\alpha }}}}$

C) $\sqrt{\frac{{{m}_{e}}}{{{m}_{\alpha }}}}$

D) $\sqrt{\frac{{{m}_{e}}}{2{{m}_{\alpha }}}}$

• question_answer21) The resistor of resistance R is connected to 25 V supply and heat produced in it is 25 J/s. The value of R is

A) 225$\Omega$

B) 1$\Omega$

C) 25$\Omega$

D) 50$\Omega$

• question_answer22) Capacitance of a parallel plate capacitor becomes 4/3 times its original value, if a dielectric slab of thickness $t=\frac{d}{2}$ is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is

A) 8

B) 4

C) 6

D) 2

• question_answer23) A proton (or charged particle) moving with velocity v is acted upon by electric field E and magnetic field B. The proton will move undeflected if,

A) E is perpendicular to B

B) E is parallel to v and perpendicular to B

C) E, B and v are mutually perpendicular and v=$\frac{E}{B}$

D) E and B both are parallel to v

• question_answer24) Current i is carried in a wire of length L. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field B will be

A) $\frac{Li{{B}^{2}}}{2}$

B) $\frac{L{{i}^{2}}B}{2}$

C) $\frac{{{L}^{2}}iB}{4\pi }$

D) $\frac{L{{i}^{2}}B}{4\pi }$

• question_answer25) The angular moment of electron in nth orbit is given by

A) $nh$

B) $\frac{h}{2\pi n}$

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

D) ${{n}^{2}}\frac{h}{2\pi }$

• question_answer26) The minimum energy required to excite a hydrogen atom from its ground state is

A) 13.6 eV

B) $-13.6\text{ }eV$

C) 3.4 eV

D) 10.2 eV

• question_answer27) If half-life of radium is 77 days. Its decay constant in day will be

A) $3\times {{10}^{-3}}/day$

B) $9\times {{10}^{-3}}/day$

C) $1\times {{10}^{-3}}/day$

D) $6\times {{10}^{-3}}/day$

• question_answer28) A radioactive substance has a half-life of 1 year. The fraction of this material, that would remain after 5 year will be

A) $\frac{1}{32}$

B) $\frac{7}{5}$

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

D) $\frac{4}{5}$

A) fall of potential per unit length of the wire

B) fall of potential for unit area of the wire

C) fall of potential between two ends of the wire

D) potential at any one end of the wire

• question_answer30) If two bulb have 40 W and 60 W rating at 220 V then the ratio of their resistances will be

A) 9 : 4

B) 4 : 3

C) 3 : 8

D) 3 : 2

• question_answer31) The position$x$of a particle varies with time t as$x=a{{t}^{2}}b{{t}^{3}}$.The acceleration of the particle will be zero at time t equal to

A) $\frac{a}{b}$

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

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

D) $zero$

• question_answer32) A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point an circular path?

A) 10 m/s

B) 2 m/s

C) 20 m/s

D) $\sqrt{2}$ m/s

• question_answer33) If the over bridge is concave instead of being convex, the thrust on the road at the lowest position will be

A) $mg+\frac{m{{v}^{2}}}{r}$

B) $mg-\frac{m{{v}^{2}}}{r}$

C) $\frac{{{m}^{2}}{{v}^{2}}g}{r}$

D) $\frac{{{v}^{2}}g}{r}$

• question_answer34) A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be

A) 7.46 J

B) 7400 J

C) 7.46 erg

D) 74.6 J

• question_answer35) A solid cylinder has mass M, length L and radius R. The moment of inertia of this cylinder about a generator is

A) $M\left( \frac{{{L}^{2}}}{12}+\frac{{{R}^{2}}}{4} \right)$

B) $\frac{M{{L}^{2}}}{4}$

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

D) $\frac{3}{2}M{{R}^{2}}$

• question_answer36) The instantaneous displacement of a simple pendulum oscillator is given by $x=A\,\cos \left( \omega t+\frac{\pi }{4} \right)$. Its speed will be maximum at time

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

B) $\frac{\pi }{2\omega }$

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

D) $\frac{2\pi }{\omega }$

• question_answer37) The relation between time and displacement for two particles is given by ${{y}_{1}}=0.06\,\sin \,2\pi (0.04t+{{\phi }_{1}})$and ${{y}_{2}}=0.03\,\sin \,2\pi (0.04t+{{\phi }_{2}})$ The ratio of the intensity of the waves, produced by the vibrations of the two particles will be

A) 2 : 1

B) 1 : 2

C) 4 : 1

D) 1 : 4

• question_answer38) To what temperature should the hydrogen at room temperature$(27{}^\circ C)$be heated at constant pressure so, that the rms velocity of its molecules becomes double of its previous value?

A) $1200{}^\circ C$

B) $927{}^\circ C$

C) $600{}^\circ C$

D) $108{}^\circ C$

• question_answer39) The volume of a gas at$21{}^\circ C$temperature and 768 mm pressure is 1 litre. If the density of the gas is $1.2\text{ }g\text{ }d{{m}^{-3}}$ at NTP, then its mass will be

A) 4 g

B) 4.22 g

C) 1.13 g

D) 10 g

• question_answer40) Which of the following statement are true in a case when two water drops coalesce and make a bigger drop?

A) Energy is neither released and nor absorbed

B) Energy is absorbed

C) The surface area of the bigger drop is greater than the sum of the surface area of both the drops

D) The surface area of the bigger drop is smaller than the sum of the surface areas of both the drops

• question_answer41) If the quantum numbers for the 5th electron in carbon atoms are$2,1,1,+1/2,$then for the 6th electron, these values would be

A) $2,1,0,-\frac{1}{2}$

B) $2,0,1,+\frac{1}{2}$

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

D) $2,1,-1,+\frac{1}{2}$

• question_answer42) $C{{H}_{3}}COOH\xrightarrow[{}]{B{{r}_{2}}/P}Y\xrightarrow[(ii)\,{{H}_{3}}{{O}^{+}}]{(i)\,KCN}X$ Here,$X$is

A) glycollic acid

B) $\alpha -$hydroxy propionic acid

C) succinic acid

D) malonic acid

• question_answer43) Acetic anhydride is prepared in the laboratory by heating sodium acetate with

A) ethyl chloride

B) acetyl chloride

C) cone ${{H}_{2}}S{{O}_{4}}$

D) zinc dust

• question_answer44) For the homogeneous reaction, $4N{{H}_{3}}+5{{O}_{2}}4NO+6{{H}_{2}}O$ the equilibrium constant${{K}_{c}}$has the units

A) $cone{{.}^{+10}}$

B) $cone{{.}^{+1}}$

C) $cone{{.}^{-1}}$

D) It is dimensionless

• question_answer45) For the reaction, $N{{H}_{3}}+OC{{l}^{-}}\xrightarrow{{}}{{N}_{2}}{{H}_{4}}+C{{l}^{-}}$ occurring in basic medium, the coefficient of ${{N}_{2}}{{H}_{4}}$in the balanced equation will be

A) 1

B) 2

C) 3

D) 4

• question_answer46) Which one of the following has a coordinate bond?

A) $N{{H}_{4}}Cl$

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

C) $NaCl$

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

• question_answer47) Which of the following would exert maximum osmotic pressure?

A) Decinormal aluminium sulphate

B) Decinormal barium chloride

C) Decinormal sodium chloride

D) A solution obtained by mixing equal volumes of and and filtering

• question_answer48) Cow milk, an example of natural emulsion is stabilised by

A) fat

B) water

C) casein

D) $M{{g}^{2+}}$ions

• question_answer49) For a zero order reaction

A) ${{t}_{1/2}}\propto {{R}_{0}}$

B) ${{t}_{1/2}}\propto 1/{{R}_{0}}$

C) ${{t}_{1/2}}\propto R_{0}^{2}$

D) ${{t}_{1/2}}\propto 1/R_{0}^{2}$

• question_answer50) The extraction of which of the following metals involves bessemerisation?

A) $Fe$

B) $Ag$

C) $Al$

D) $Cu$

• question_answer51) The correct order of decreasing first ionisation energy is

A) $C>B>Be>Li$

B) $C>Be>B>Li$

C) $B>C>Be>Li$

D) $Be>Li>B>C$

• question_answer52) Consider the following reaction, ${{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow[{}]{Sn/HCl}X\xrightarrow[{}]{{{C}_{6}}{{H}_{3}}COCl}Y+HCl$ What is V?

A) Acetanilide

B) Benzinilide

C) Azobenzene

D) Hydrazobenzene

• question_answer53) Which of the following is most basic in nature?

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

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

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

D) ${{C}_{6}}{{H}_{5}}N{{(C{{H}_{3}})}_{2}}$

• question_answer54) An example of natural biopolymer is

A) Teflon

B) Nylon-66

C) Rubber

D) DNA

• question_answer55) Which of the following is known as invert soap?

A) Pentaerythritol monostearate

B) Sodium stearyl sulphate

C) Trimethyl stearyl ammonium bromide

D) Ethoxylated nonyphenol

• question_answer56) Le-blanc process is employed in the manufacture of

A) baking soda

B) washing soda

C) potash

D) Plaster of Paris

A) steel is in between those of cast iron and wrought iron

B) cast iron is in between those of steel and wrought iron

C) wrought iron is in between those of steel and cast iron

D) steel is higher than that of pig iron

• question_answer58) The IUPAC name of acryldehyde is

A) prop-2-en-l-al

B) propenylaldehyde

C) but-2-en-l-al

D) propenal

• question_answer59) The structures${{(C{{H}_{3}})}_{3}}CBr$and$C{{H}_{3}}{{[C{{H}_{2}}]}_{3}}Br$represent

A) chain isomerism

B) position isomerism

C) chain as well as position isomerism

D) functional isomerism

• question_answer60) Petrol for aviation purpose must contain

A) straight chain hydrocarbons

B) aromatic hydrocarbons

C) olefinic hydrocarbons

D) highly branched chain paraffins

• question_answer61) The solubility product of$H{{g}_{2}}{{I}_{2}}$is equal to

A) $[Hg_{2}^{2+}][{{I}^{-}}]$

B) $[H{{g}^{2+}}][{{I}^{-}}]$

C) $[Hg_{2}^{2+}]{{[{{I}^{-}}]}^{2}}$

D) $[H{{g}^{2+}}]{{[{{I}^{-}}]}^{2}}$

• question_answer62) The number of atoms contained in a fee unit cell of a monoatomic substance is

A) 1

B) 2

C) 4

D) 6

• question_answer63) In the first order reaction, 75% of the reactant gets disappeared in 1.386 h. Therate-etaistani of the reaction is

A) $3.0\times {{10}^{-3}}{{s}^{-1}}$

B) $2.8\times {{10}^{-4}}{{s}^{-1}}$

C) $17.2\times {{10}^{-3}}{{s}^{-1}}$

D) $1.8\times {{10}^{-3}}{{s}^{-1}}$

• question_answer64) Moist hydrogen peroxide cannot be dried over cone${{H}_{2}}S{{O}_{4}}$because

A) it can catch fire

B) it is reduced by${{H}_{2}}S{{O}_{4}}$

C) it is oxidised by${{H}_{2}}S{{O}_{4}}$

D) it is decomposed by${{H}_{2}}S{{O}_{4}}$

• question_answer65) The substance which does not liberate oxygen on treatment with ozone is

A) $PbS$

B) $HCl$

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

D) $Hg$

• question_answer66) Which one of the following will undergo meta-substitution on monochlorination?

A) Ethoxybenzene

B) Chlorobenzene

C) Ethyl benzoate

D) Phenol

• question_answer67) Propyne on passing through red hot copper tube forms

A) benzene

B) toluene

C) mesitylene

D) None of these

• question_answer68) Which one of the following is mainly responsible for depletion of ozone layer?

A) Methane

B) Carbon dioxide

C) Water

D) Chlorofluorocarbons

• question_answer69) On warming with silver powder, chloroform is converted into

A) acetylene

B) hexachloroethane

C) 1,1, 2, 2-tetrachloroethane

D) ethylene

• question_answer70) Grignard reagent is not prepared in aqueous medium but prepared in ether medium, because

A) the reagent is highly reactive in ether

B) the reagent does not react with water

C) the reagent becomes inactive in water

D) the reagent reacts with water

• question_answer71) $Argol,$a brown crust, formed during the fermentation of grape juice contains

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

B) fused oil

C) potassium hydrogen tartarate

D) lye

• question_answer72) $C{{H}_{3}}CHO+HCHO\xrightarrow[Heat]{Dil.NaOH}A\xrightarrow[{{H}_{3}}{{O}^{+}}]{HCN}B$ The structure of compound B is

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

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

C) $C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH$

D) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH$

• question_answer73) The pH value of 0.001 M aqueous solution of $NaCl$is

A) 7

B) 4

C) 11

D) unpredictable

• question_answer74) Which buffer solution comprising of the following has its pH value greater than 7?

A) $C{{H}_{3}}COOH+C{{H}_{3}}COONa$

B) $HCOOH+HCOOK$

C) $C{{H}_{3}}COON{{H}_{4}}$

D) $N{{H}_{4}}OH+N{{H}_{4}}Cl$

• question_answer75) Which of the following has$s{{p}^{2}}-$hybridisation?

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

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

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

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

• question_answer76) Hydrogen molecule differs from chlorine, molecule in the following respect.

A) Hydrogen molecule is non-polar but chlorine molecule is polar

B) Hydrogen molecule is polar while chlorine molecule is non-polar

C) Hydrogen molecule can form mtermolecular hydrogen bonds but chlorine molecule does not

D) Hydrogen molecule cannot participate in coordinate bond formation but chlorine molecule can

• question_answer77) The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr orbit is

A) 1/2

B) 1/3

C) 4/9

D) 27/5

A) molecular solid

B) covalent solid

C) ionic solid

D) metallic solid

• question_answer79) Which one of the following transition metal ions is diamagnetic?

A) $C{{o}^{2+}}$

B) $N{{i}^{2+}}$

C) $C{{u}^{2+}}$

D) $Z{{n}^{2+}}$

• question_answer80) Which of the following metal carbonates decomposes on heating?

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

B) $N{{a}_{2}}C{{O}_{3}}$

C) ${{K}_{2}}C{{O}_{3}}$

D) $R{{b}_{2}}C{{O}_{3}}$

• question_answer81) The vertices of a triangle are A(1, 1), B(4, 5), and C(6, 13). Then, the value of cos A is

A) $\frac{63}{65}$

B) $\frac{60}{65}$

C) $\frac{61}{63}$

D) $\frac{63}{62}$

• question_answer82) The value of y, so that the line through (3,y) and (2, 7) is parallel to the line through$(-1,4)$ and (0, 6), is

A) 5

B) $-5$

C) 9

D) $-9$

• question_answer83) If the slope of one of the line represented by $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$be the square of other, then

A) $\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}+6=0$

B) $\frac{a-b}{h}+\frac{8{{h}^{2}}}{ab}+6=0$

C) $\frac{a+b}{h}+\frac{8{{h}^{2}}}{ab}=6$

D) $\frac{a-b}{h}+\frac{8h}{a{{b}^{2}}}=6$

• question_answer84) The angle between the pair of tangents to circle ${{x}^{2}}+{{y}^{2}}+4x+2y-4=0$from the point (1,1/2) is

A) ${{\cos }^{-1}}\left[ \frac{4}{5} \right]$

B) ${{\sin }^{-1}}\left[ \frac{4}{5} \right]$

C) ${{\sin }^{-1}}\left[ \frac{3}{5} \right]$

D) ${{\tan }^{-1}}\left[ \frac{3}{5} \right]$

• question_answer85) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\tan }^{-1}}x-{{\sin }^{-1}}x}{{{x}^{3}}}$equals

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

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

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

D) $-\frac{3}{2}$

• question_answer86) If$f(x)=\frac{1}{{{x}^{2}}-17x+66},$then for what values of$x,f\left( \frac{2}{x-2} \right)$is discontinuous?

A) $2,\frac{7}{3},\frac{25}{11}$

B) $2,\frac{8}{3},\frac{24}{11}$

C) $2,\frac{7}{3},\frac{24}{11}$

D) None of these

• question_answer87) The equation of normal to the curve $y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x)$at$x=0$is

A) $x+y=2$

B) $x+y=1$

C) $x-y=1$

D) $x-y=2$

• question_answer88) The value of$\int{\frac{{{x}^{2}}-1}{{{x}^{4}}+{{x}^{2}}+1}}dx$is

A) $\log ({{x}^{2}}+{{x}^{2}}+1)+c$

B) $\log \left| \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right|+c$

C) $\frac{1}{2}\log \left| \frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} \right|+c$

D) $\frac{1}{2}\log \left| \frac{{{x}^{2}}+x+1}{{{x}^{2}}-x+1} \right|+c$

• question_answer89) If$f(x)=x+2,$then$f'(f(x))$at$x=4$is

A) 8

B) 1

C) 4

D) 5

• question_answer90) Equation of tangent to the hyperbola $2{{x}^{2}}-3{{y}^{2}}=6$which is parallel to the line $y=3x+4,$is

A) $y=3x-4$

B) $y=3x-5$

C) $y=3x+5$

D) $y=3x\pm 5$

• question_answer91) If the eccentricity of hyperbola ${{x}^{2}}-{{y}^{2}}se{{c}^{2}}\alpha =5$is$\sqrt{3}$times the eccentricity of the ellipse${{x}^{2}}\text{ }se{{c}^{2}}\alpha +{{y}^{2}}=25,$then value of $\alpha$is

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

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

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

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

• question_answer92) Determine the locus of that point such that the sum of its distances from$(2,-3)$and (2, 5) is always 10.

A) $\frac{{{(x-2)}^{2}}}{25}+\frac{{{(y-1)}^{2}}}{9}=1$

B) $\frac{{{(x-2)}^{2}}}{25}+\frac{{{(y-1)}^{2}}}{16}=1$

C) $\frac{{{(x-2)}^{2}}}{16}+\frac{{{(y-1)}^{2}}}{9}=1(d)$

D) $\frac{{{(x-2)}^{2}}}{9}+\frac{{{(y-1)}^{2}}}{25}=1$

• question_answer93) Determine the latusrectum of a parabola whose focal chord is PSQ such that$SP=3$and $SQ=2$.

A) $\frac{24}{5}$

B) $\frac{12}{5}$

C) $\frac{6}{5}$

D) None of these

• question_answer94) Equation${{x}^{2}}+{{y}^{2}}-2xy+20x+10=0$represents the curve

A) circle

B) parabola

C) ellipse

D) hyperbola

• question_answer95) Solution of the differential equation $\frac{dy}{dx}=\frac{{{x}^{2}}+{{y}^{2}}+1}{2xy},y(1)=0$is

A) a hyperbola

B) a parabola

C) an ellipse

D) a circle

• question_answer96) If$\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$and$\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k},$ then the vector in the direction of$\overrightarrow{a}$and having magnitude as$|\overrightarrow{b}|$is

A) $7(\hat{i}+2\hat{j}+2\hat{k})$

B) $\frac{7}{9}(\hat{i}+2\hat{j}+2\hat{k})$

C) $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$

D) None of these

• question_answer97) If the vectors$a+\lambda \overrightarrow{b}+3\overrightarrow{c},-2\overrightarrow{a}+3\overrightarrow{b}-4\overrightarrow{c}$and $\overrightarrow{a}-3\overrightarrow{b}+5\overrightarrow{c}$are coplanar, then the value of$\lambda$ is

A) 2

B) $-1$

C) 1

D) $-2$

• question_answer98) If the planes$\overrightarrow{r}.(2\hat{i}+\lambda \hat{j}-3\hat{k})=0$and$\overrightarrow{r}.(\lambda \hat{i}-3\hat{j}+\hat{k})=5$are perpendicular, then value of$\lambda$is

A) 2

B) $-2$

C) 3

D) $-3$

• question_answer99) The distance from the point (3,4,5) to the point where the line$\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ meets the plane$x+y+z=17$is

A) 1

B) 2

C) 3

D) 4

• question_answer100) Which of the following is true?

A) $7+6i>3+2i$

B) $7+2i>6+5i$

C) $3+7i>12+2i$

D) None of these

• question_answer101) The value of amp$(i\omega )+$amp$(i{{\omega }^{2}})$is

A) $0$

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

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

D) $\pi$

• question_answer102) The value of x for which$|x+3|>|2x-1|$is

A) $\left( -\frac{2}{3},4 \right)$

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

C) (0,1)

D) None of these

• question_answer103) Square root of$-2+2\sqrt{3i}$is

A) $\pm (1+\sqrt{3}i)$

B) $\pm (1-\sqrt{3}i)$

C) $\pm (1+\sqrt{3}i)$

D) None of these

• question_answer104) Let${{S}_{n}}$denotes the sum of n terms of an AP. If ${{S}_{2n}}=3{{S}_{n}},$then${{S}_{3n}}:{{S}_{n}}$isequalto

A) 4

B) 6

C) 8

D) 10

• question_answer105) If$x,\text{ }y,\text{ }z$are positive then, minimum value of ${{x}^{\log y-\log z}}+{{y}^{\log z-\log x}}+{{z}^{\log x-\log y}}$is

A) 0

B) 1

C) 2

D) 3

• question_answer106) If$\log (a+c),\log (c-a),\log (a-2b+c)$are in AP.then

A) a,b,c are in AP

B) ${{a}^{2}},{{b}^{2}},{{c}^{2}}$are in AP

C) a,b, care in GP

D) $a,b,c$careinHP

• question_answer107) Roots of the equation$(x-a)\text{ (}x-b)=ab{{x}^{2}}$are

A) real

B) imaginary

C) can?t say

D) None of these

• question_answer108) The value of kfor which the roots of the equation${{x}^{2}}+2(k+1)x+{{k}^{2}}=0$are equal to

A) $-1$

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

C) $1$

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

• question_answer109) Manoj, Mohit, Rohit and Shivani want to give speeches in the class. How many possible ways are for their speeches?

A) 12

B) 24

C) 36

D) 4

• question_answer110) How many lines can be drawn from 6 points on a circle?

A) 12

B) 15

C) 30

D) 60

• question_answer111) The total number of ways of selecting five letters from the letters of the word 'INDEPENDENT' is

A) 72

B) 27

C) 36

D) 64

• question_answer112) If the coefficient of${{x}^{7}}$in${{\left( a{{x}^{2}}+\frac{1}{bx} \right)}^{11}}$. and the coefficient of${{x}^{-7}}$in${{\left( ax-\frac{1}{b{{x}^{2}}} \right)}^{11}}$are equal, then ab is equal to

A) 1

B) 2

C) 3

D) 4

• question_answer113) The roots of the equation$\left| \begin{matrix} x & \alpha & 1 \\ \beta & x & 1 \\ \beta & \gamma & 1 \\ \end{matrix} \right|=0$are independent of

A) $\alpha$

B) $\beta$

C) $\gamma$

D) All of these

• question_answer114) If each element of a$3\times 3$ matrix is multiplied by 3, then the determinant of the newly formed matrix is

A) $3|A|$

B) $9|A|$

C) $27|A|$

D) $|A{{|}^{3}}$

• question_answer115) The system of linearequations $x+y+z=2,$ $2x+y-z=3,$$3x+2y+kz=4$has a unique solution, if

A) $k\ne 0$

B) $-1<k<1$

C) $-2<k<2$

D) $k=0$

• question_answer116) If X and Y are two sets, then$X\cap (Y\cup X)'$is equal to

A) $X$

B) $Y$

C) $\phi$

D) None of these

• question_answer117) If$n(A)=4$and$n(B)=7,$then minimum and maximum value of$n(A\cup B)$are

A) 4, 7

B) 7,11

C) 4, 11

D) None of these

• question_answer118) If$f(x)={{\sin }^{2}}x+{{\sin }^{2}}(x+\pi /3)$$+\cos x\cos (x+\pi /3)$and$g\left( \frac{5}{4} \right)=1,$then$(gof)(x)$is equal to

A) 1

B) 0

C) $sin\text{ }x$

D) $cos\text{ }x$

• question_answer119) The probability that at least one of the events A and B occurs is$\frac{3}{5}.$ If A and B occur simultaneously with probability$\frac{1}{5},$then $P(\overline{A})+P(\overline{B})$is

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

B) $\frac{4}{5}$

C) $\frac{6}{5}$

D) $\frac{7}{5}$

• question_answer120) There are 4 white and 3 black balls in a bag. In another bag there are 3 white j and 4 black balls. If a ball is picked and it is found to be black, then the probability that the ball is drawn from the second bag is

A) $\frac{1}{7}$

B) $\frac{2}{7}$

C) $\frac{3}{7}$

D) $\frac{4}{7}$