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
View Answer play_arrowquestion_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) \[\frac{3\pi }{4}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{{{Q}^{2}}}{2\pi {{\varepsilon }_{0}}a}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{2\sqrt{2mE}}{h}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[3.2\times {{10}^{-15}}\]
View Answer play_arrowquestion_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) \[\frac{2{{\mu }_{0}}ni}{\pi l}\]
View Answer play_arrowquestion_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) \[-Q\]
View Answer play_arrowquestion_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) \[{{r}^{-4}}\]
View Answer play_arrowquestion_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) \[2\times {{10}^{-2}}J\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{10}{2\pi }Hz\]
View Answer play_arrowquestion_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) \[\left[ {{p}^{-1}}v{{t}^{2}} \right]\]
View Answer play_arrowquestion_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) \[\sqrt{\frac{{{m}_{e}}}{2{{m}_{\alpha }}}}\]
View Answer play_arrowquestion_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\[\Omega \]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{L{{i}^{2}}B}{4\pi }\]
View Answer play_arrowquestion_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) \[{{n}^{2}}\frac{h}{2\pi }\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[6\times {{10}^{-3}}/day\]
View Answer play_arrowquestion_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) \[\frac{4}{5}\]
View Answer play_arrowquestion_answer29) Potential gradient is defined as
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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[zero\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{{{v}^{2}}g}{r}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{3}{2}M{{R}^{2}}\]
View Answer play_arrowquestion_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) \[\frac{2\pi }{\omega }\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[108{}^\circ C\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[2,1,-1,+\frac{1}{2}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer46) Which one of the following has a coordinate bond?
A) \[N{{H}_{4}}Cl\]
B) \[AlC{{l}_{3}}\]
C) \[NaCl\]
D) \[C{{l}_{2}}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer48) Cow milk, an example of natural emulsion is stabilised by
A) fat
B) water
C) casein
D) \[M{{g}^{2+}}\]ions
View Answer play_arrowquestion_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) \[{{t}_{1/2}}\propto 1/R_{0}^{2}\]
View Answer play_arrowquestion_answer50) The extraction of which of the following metals involves bessemerisation?
A) \[Fe\]
B) \[Ag\]
C) \[Al\]
D) \[Cu\]
View Answer play_arrowquestion_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) \[Be>Li>B>C\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[{{C}_{6}}{{H}_{5}}N{{(C{{H}_{3}})}_{2}}\]
View Answer play_arrowquestion_answer54) An example of natural biopolymer is
A) Teflon
B) Nylon-66
C) Rubber
D) DNA
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer56) Le-blanc process is employed in the manufacture of
A) baking soda
B) washing soda
C) potash
D) Plaster of Paris
View Answer play_arrowquestion_answer57) Carbon content of
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
View Answer play_arrowquestion_answer58) The IUPAC name of acryldehyde is
A) prop-2-en-l-al
B) propenylaldehyde
C) but-2-en-l-al
D) propenal
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer60) Petrol for aviation purpose must contain
A) straight chain hydrocarbons
B) aromatic hydrocarbons
C) olefinic hydrocarbons
D) highly branched chain paraffins
View Answer play_arrowquestion_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) \[[H{{g}^{2+}}]{{[{{I}^{-}}]}^{2}}\]
View Answer play_arrowquestion_answer62) The number of atoms contained in a fee unit cell of a monoatomic substance is
A) 1
B) 2
C) 4
D) 6
View Answer play_arrowquestion_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) \[1.8\times {{10}^{-3}}{{s}^{-1}}\]
View Answer play_arrowquestion_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\[{{H}_{2}}S{{O}_{4}}\]
View Answer play_arrowquestion_answer65) The substance which does not liberate oxygen on treatment with ozone is
A) \[PbS\]
B) \[HCl\]
C) \[S{{O}_{2}}\]
D) \[Hg\]
View Answer play_arrowquestion_answer66) Which one of the following will undergo meta-substitution on monochlorination?
A) Ethoxybenzene
B) Chlorobenzene
C) Ethyl benzoate
D) Phenol
View Answer play_arrowquestion_answer67) Propyne on passing through red hot copper tube forms
A) benzene
B) toluene
C) mesitylene
D) None of these
View Answer play_arrowquestion_answer68) Which one of the following is mainly responsible for depletion of ozone layer?
A) Methane
B) Carbon dioxide
C) Water
D) Chlorofluorocarbons
View Answer play_arrowquestion_answer69) On warming with silver powder, chloroform is converted into
A) acetylene
B) hexachloroethane
C) 1,1, 2, 2-tetrachloroethane
D) ethylene
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-COOH\]
View Answer play_arrowquestion_answer73) The pH value of 0.001 M aqueous solution of \[NaCl\]is
A) 7
B) 4
C) 11
D) unpredictable
View Answer play_arrowquestion_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) \[N{{H}_{4}}OH+N{{H}_{4}}Cl\]
View Answer play_arrowquestion_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) \[{{C}_{2}}{{H}_{2}}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer78) Graphite is a
A) molecular solid
B) covalent solid
C) ionic solid
D) metallic solid
View Answer play_arrowquestion_answer79) Which one of the following transition metal ions is diamagnetic?
A) \[C{{o}^{2+}}\]
B) \[N{{i}^{2+}}\]
C) \[C{{u}^{2+}}\]
D) \[Z{{n}^{2+}}\]
View Answer play_arrowquestion_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) \[R{{b}_{2}}C{{O}_{3}}\]
View Answer play_arrowquestion_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) \[\frac{63}{62}\]
View Answer play_arrowquestion_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) \[-9\]
View Answer play_arrowquestion_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) \[\frac{a-b}{h}+\frac{8h}{a{{b}^{2}}}=6\]
View Answer play_arrowquestion_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) \[{{\tan }^{-1}}\left[ \frac{3}{5} \right]\]
View Answer play_arrowquestion_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) \[-\frac{3}{2}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[x-y=2\]
View Answer play_arrowquestion_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) \[\frac{1}{2}\log \left| \frac{{{x}^{2}}+x+1}{{{x}^{2}}-x+1} \right|+c\]
View Answer play_arrowquestion_answer89) If\[f(x)=x+2,\]then\[f'(f(x))\]at\[x=4\]is
A) 8
B) 1
C) 4
D) 5
View Answer play_arrowquestion_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) \[y=3x\pm 5\]
View Answer play_arrowquestion_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) \[\frac{\pi }{4}\]
View Answer play_arrowquestion_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) \[\frac{{{(x-2)}^{2}}}{9}+\frac{{{(y-1)}^{2}}}{25}=1\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer94) Equation\[{{x}^{2}}+{{y}^{2}}-2xy+20x+10=0\]represents the curve
A) circle
B) parabola
C) ellipse
D) hyperbola
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[-2\]
View Answer play_arrowquestion_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) \[-3\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer101) The value of amp\[(i\omega )+\]amp\[(i{{\omega }^{2}})\]is
A) \[0\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{2}\]
D) \[\pi \]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[\frac{1}{2}\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_answer110) How many lines can be drawn from 6 points on a circle?
A) 12
B) 15
C) 30
D) 60
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[|A{{|}^{3}}\]
View Answer play_arrowquestion_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) \[k=0\]
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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
View Answer play_arrowquestion_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) \[cos\text{ }x\]
View Answer play_arrowquestion_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) \[\frac{7}{5}\]
View Answer play_arrowquestion_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) \[\frac{4}{7}\]
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