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JEE Main 2005 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2005Annual, Paper 1

Physics 62Chemistry 57Mathematics 70

Physics

Q5866The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance ofElectromagnetic Induction and Alternating Currents
Q5867A circuit has a resistance of 12 ohm and an impedance of 15 ohm. The power factor of the circuit will beElectromagnetic Induction and Alternating Currents
Q5868The phase difference between the alternating current and emf is (π)/2. Which of the following cannot be the constituent of the circuit?Electromagnetic Induction and Alternating Currents
Q6036A nuclear transformation is denoted by X(n,α) 7 3 Li. Which of the following is the nucleus of element X ?Atoms and Nuclei
Q6076If radius of the 27 13 Al nucleus is estimated to be 3.6 fermi then the radius of 125 52 Te nucleus is estimated to be nearlyAtoms and Nuclei
Q6077Starting with a sample of pure ⁶⁶Cu,7/8 of it decays into Zn in 15 minutes. The corresponding half life isAtoms and Nuclei
Q6078The intensity of gamma radiation from a given source is L. On passing through 36 mm of lead, it is reduced to (I)/8. The thickness of lead which will reduce…Atoms and Nuclei
Q6164A fully charged capacitor has a capacitance 'C'. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific…Electrostatics
Q6165A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is 'C' then…Electrostatics
Q6196A body A of mass M while falling vertically downloads under gravity breaks into two-parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The center of…Rotational Motion
Q6411A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now beCurrent Electricity
Q6412The resistance of hot tungsten filament is about 10 times the cold resistance. What will be resistance of 100 W and 200 V lamp when not in use ?Current Electricity
Q6449A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 - divisions per milliampere and voltage sensitivity is 2 divisions per…Current Electricity
Q6450Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltmeters, equal amount of metals are…Current Electricity
Q6487Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are R₁ and R₂(R₁ > R₁). If the potential…Current Electricity
Q6494An energy source will supply a constant current into the load if its internal resistance isCurrent Electricity
Q6500In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of 2Ω, the balancing length becomes 120…Current Electricity
Q6533If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factorDual Nature of Matter and Radiation
Q6616A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1/2 m away, the number of electrons emitted by…Dual Nature of Matter and Radiation
Q6675A coil of inductance 300 mH and resistance 2 Ω is connected to a source of voltage 2 V. The current reaches half of its steady state value inElectromagnetic Induction and Alternating Currents
Q6858The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap in…Electronic Devices
Q6859In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would beElectronic Devices
Q6893In a common base amplifier, the phase difference between the input signal voltage and output voltage isElectronic Devices
Q6954Two point charges +8q and -2q are located at x=0 and x=L respectively. The location of a point on the x axis at which the net electric field due to these two…Electrostatics
Q6994Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and -q. The…Electrostatics
Q7025A thin glass (refractive index 1.5) lens has optical power of -5 D in air. Its optical power in a liquid medium with refractive index 1.6 will beOptics
Q7091A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm…Optics
Q7129The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much…Gravitation
Q7227A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force…Gravitation
Q7249Average density of the earthGravitation
Q7353A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio Cp/C v of the mixture isThermodynamics
Q7548A smooth block is released at rest on a 45° incline and then slides a distance 'd'. The time taken to slide is 'n' times as much to slide on rough incline…Laws of Motion
Q7549Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped is [ μ k = 0.5 ]Laws of Motion
Q7577A particle of mass 0.3 kg subjected to a force F=-kx with k=15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the…Laws of Motion
Q7633A magnetic needle is kept in a non-uniform magnetic field. It experiences:Magnetic Effects of Current and Magnetism
Q7668Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil…Magnetic Effects of Current and Magnetism
Q7697Two thin, long, parallel wires, separated by a distance 'd' carry a current of 'i' A in the same direction. They willMagnetic Effects of Current and Magnetism
Q7735A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction…Magnetic Effects of Current and Magnetism
Q7736A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle…Magnetic Effects of Current and Magnetism
Q7811A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time isKinematics
Q7841A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to…Kinematics
Q7856A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s². He reaches the ground with a speed of 3 m/s. At…Kinematics
Q7880The relation between time t and distance x is t = ax² + bx where a and b are constants. The acceleration isKinematics
Q8000If S is stress and Y is young's modulus of material of a wire, the energy stored in the wire per unit volume isProperties of Solids and Liquids
Q8006A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water…Properties of Solids and Liquids
Q8064An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two…Rotational Motion
Q8080The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the center isRotational Motion
Q8129The function sin ²(ω t) representsOscillations and Waves
Q8130Two simple harmonic motions are represented by the equations y₁ = 0.1 sin (100π t + (π)/3) and y₂ = 0.1 cos π t. The phase difference of the velocity of…Oscillations and Waves
Q8131If a simple harmonic motion is represented by d²x d t² + α x = 0. its time period isOscillations and Waves
Q8185The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged…Oscillations and Waves
Q8218Out of the following pair, which one does NOT have identical dimensions isUnits and Measurements
Q8388If I₀ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?Optics
Q8389Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which…Optics
Q8410A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen isOptics
Q8456When an unpolarized light of intensity I₀ is incident on a polarizing sheet, the intensity of the light which does not get transmitted isOptics
Q8514An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent…Oscillations and Waves
Q8540When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heated. Now, some tape is attached on the prong of the fork 2…Oscillations and Waves
Q8563A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that…Work, Energy and Power
Q8564The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come…Work, Energy and Power
Q8565A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill…Work, Energy and Power
Q8601A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time is given byWork, Energy and Power

Chemistry

Q2Acid catalyzed hydration of alkenes except ethene leads to the formation ofOrganic Compounds Containing Oxygen
Q3The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one isOrganic Compounds Containing Oxygen
Q143Due to the presence of an unpaired electron, free radicals are:Some Basic Principles of Organic Chemistry
Q226In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-Biomolecules
Q339Lattice energy of an ionic compounds depends uponChemical Bonding and Molecular Structure
Q348Which one of the following species is diamagnetic in nature?Chemical Bonding and Molecular Structure
Q395For the reaction 2NO₂ (g) 2NO (g) + O₂ (g), (K c = 1.8 × 10⁻⁶ at 184^(o)C) (R = 0.0831 kJ/(mol. K)) When K p and K c are compared at 184^(o)C, it is found that:Equilibrium
Q396An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. Pressure. Ammonium hydrogen sulphide…Equilibrium
Q432The exothermic formation of ClF₃ is represented by the equation: Cl₂ (g) + 3F₂ (g) 2ClF₃ (g); Δ H = -329 kJ Which of the following will increase the quantity…Equilibrium
Q462A reaction involving two different reactants can never beChemical Kinetics
Q463t₁/4 can be taken as the time taken for the concentration of a reactant to drop to 3 4 of its initial value. If the rate constant for a first order reaction…Chemical Kinetics
Q484Hydrogen bomb is based on the principle ofChemical Kinetics
Q485The photon of hard gamma radiation knocks a proton out of ₁₂²⁴Mg nucleus to formNuclear Chemistry (historical)
Q521Which one of the following methods is neither meant for the synthesis nor for separation of amines?Organic Compounds Containing Nitrogen
Q582The oxidation state of Cr in [Cr(NH₃)₄Cl₂]⁺ is:Coordination Compounds
Q697The IUPAC name of the coordination compound K₃[Fe(CN)₆] isCoordination Compounds
Q707Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (At. No. Cr = 24, Mn = 25, Fe = 26, Co = 27)Coordination Compounds
Q757The oxidation state of chromium in the final product formed the reaction between K I and acidified potassium dichromate solution is:d- and f-Block Elements
Q800The lanthanide contraction is responsible for the fact that:d- and f-Block Elements
Q801Which of the following factors may be regarded as the main cause of lanthanide contraction?d- and f-Block Elements
Q848On heating mixture of C u₂ O and C u₂ S will give:d- and f-Block Elements
Q849Calomel (H g₂ C l₂) on reaction with ammonium hydroxide gives:d- and f-Block Elements
Q926Aluminium oxide may be electrolysed at 1000^(o)C to furnish aluminium metal (Atomic mass = 27 amu; 1 Faraday = 96,500 Coulombs). The cathode reaction is Al³⁺…Redox Reactions and Electrochemistry
Q927The highest electrical conductivity of the following aqueous solutions is of:Redox Reactions and Electrochemistry
Q928Electrolyte: KCl KNO₃ HCl NaOAc NaCl ^∞ (Sc m² mo l⁻¹): 149.9 145 426.2 91 126.5 Calculate HOAc ^∞ Using appropriate molar conductances of the electrolytes…Redox Reactions and Electrochemistry
Q969For a spontaneous reaction the ∆G, equilibrium constant (K) and E cell ^(o) will be respectivelyRedox Reactions and Electrochemistry
Q1119Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?Gaseous State
Q1134Tertiary alkyl halides are practically inert to substitution by S N 2 mechanism because ofOrganic Compounds Containing Halogens
Q1135Alkyl halides react with dialkyl copper reagents to giveOrganic Compounds Containing Halogens
Q1136Elimination of bromine from 2-bromobutane results in the formation of-Organic Compounds Containing Halogens
Q1176Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds isHydrocarbons
Q11772 methylbutane on reacting with bromine in the presence of sunlight gives mainlyHydrocarbons
Q1184Which types of isomerism is shown by 2,3-dichlorobutane?Hydrocarbons
Q1238Which of the following statements in relation to the hydrogen atom is correct?Hydrogen
Q1278What is the conjugate base of OH⁻?Equilibrium
Q1291Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be:Equilibrium
Q1327The solubility product of a salt having general formula MX₂, in water is: 4 × 10⁻¹². The concentration of M²⁺ ions in the aqueous solution of the salt is:Equilibrium
Q1430During the process of electrolytic refining of copper, some metals present as impurity settle as ‘anode mud’ These areIsolation of Elements
Q1569In which of the following arrangements the order is NOT according to the property indicated against it?Classification of Elements and Periodicity in Properties
Q1629Which of the following oxides is amphoteric in character?Classification of Elements and Periodicity in Properties
Q1670Which of the following is fully fluorinated polymer?Polymers
Q1715Which of the following is a polyamide?Polymers
Q1843Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point:S Block Elements
Q1940An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for…Solid State
Q1953If α is the degree of dissociation of Na₂SO₄, the vant Hoff’s factor (i) used for calculating the molecular mass is:Solutions
Q1975Equimolar solutions in the same solvent haveSolutions
Q1998Benzene and toluene form nearly ideal solutions. At 20 ^(o)C, the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour…Solutions
Q2024Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 ml of 1.2 M second solution. What is…Some Basic Concepts in Chemistry
Q2062If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of the substance willSome Basic Concepts in Chemistry
Q2134Of the following sets which one does NOT contain isoelectronic species?Atomic Structure
Q2135Pick out the isoelectronic structure from the following: (i) C H₃ ⁺ (ii) H₃O⁺ (iii) N H₃ (iv) C H₃ ^ -Atomic Structure
Q2191In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same energy in the absence of magnetic and…Atomic Structure
Q2228The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively, which of the following statements…Surface Chemistry
Q2229The volume of a colloidal particle, V C as compared to the volume of a solute particle in a true solution V S, could beSurface Chemistry
Q2335Consider an endothermic reaction, X → Y with the activation energies E b and E f for the backward and forward reactions, respectively. In general:Chemical Thermodynamics
Q2336Consider the reaction: N₂ + 3H₂ → 2NH₃ carried out at constant temperature and pressure. If Δ H and Δ U are the enthalpy and internal energy changes for the…Chemical Thermodynamics
Q2337If the bond dissociation energies of XY, X₂ and Y₂ (all diatomic molecules) are in the ratio of 1:1:0.5 and Δ H f for the formation of XY is -200 kJ mole⁻¹…Chemical Thermodynamics

Mathematics

Q2387If the angel θ between the line (x + 1)/1 = (y - 1)/2 = (z - 2)/2 and the plane 2x - y + λ z + 4 = 0 is such that sin θ = 1/3 then value of λ is:Three Dimensional Geometry
Q2388If the plane 2ax-3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x² + y² + z² + 6x - 8y - 2z = 13 and x² + y² + z²…Three Dimensional Geometry
Q2389The distance between the line r = 2 i - 2 j + 3 k + λ (i - j + 4k), and the plane r.(i + 5 j + k) = 5 isThree Dimensional Geometry
Q2479The angle between the lines 2x=3y=-z and 6x=-y=-4z is:Three Dimensional Geometry
Q2549The plane x+2y-z=4 cuts the sphere x² + y² + z² - x + z - 2 = 0 in a circle of radiusThree Dimensional Geometry
Q2620Area of the greatest rectangle that can be inscribed in the ellipse (x²)/(a²) + (y²)/(b²) = 1Limit, Continuity and Differentiability
Q2693If the equation a n xⁿ + a n - 1 xⁿ⁻¹ +........... + a₁x = 0 a₁ ≠ 0,n ≥ 2, has a positive root x = α, then the equation n a n xⁿ⁻¹ + (n - 1)a n - 1 xⁿ⁻²…Limit, Continuity and Differentiability
Q2694Let f be differentiable for all x. If f(1) = -2 and f'(x) ≥ 2 for x [ 1,6 ], thenLimit, Continuity and Differentiability
Q2703A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?Limit, Continuity and Differentiability
Q2739A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm ³ /min. When the thickness of ice is 5…Limit, Continuity and Differentiability
Q2740A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of 2 ~cm / s² and pursues the insect which is crawling…Limit, Continuity and Differentiability
Q2753The normal to the curve x = a(cos θ + θ sin θ),y = a(sin θ - θ cos θ) at any point θ ' is such thatLimit, Continuity and Differentiability
Q2795The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If S₁,S₂,S₃ are respectively the areas of…Integral Calculus
Q2877The area enclosed between the curve y = log e (x + e) and the coordinate axes is:Integral Calculus
Q2878Let f(x) be a non - negative continuous function such that the area bounded by the curve y=f(x), x -axis and the ordinates x = (π)/4 and x = β > (π)/4 is (β…Integral Calculus
Q2906If the coefficient of x⁷ in [ a x² + (1/bx) ]¹¹ equals the coefficient of x⁻⁷ in [ ax - (1 b x²) ]¹¹, then a and b satisfy the relationBinomial Theorem and Its Simple Applications
Q2907If the coefficients of r^(t)h, (r+1)^(t)h, and (r + 2)^(t)h terms in the binomial expansion of (1 + y) ^(m) are in A.P., then m and r satisfy the equationBinomial Theorem and Its Simple Applications
Q2961If x is so small that x³ and higher powers of x may be neglected, then ((1 + x)^(3/2) - (1 + 1/2x)³)/((1 - x)^(1/2)) may be approximated asBinomial Theorem and Its Simple Applications
Q2967The value of ⁵⁰C₄ + Σ r = 1 ⁶ ^(56 - r) C₃ isBinomial Theorem and Its Simple Applications
Q3040If the pair of lines a x² + 2(a + b)xy + b y² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the…Coordinate Geometry
Q3062A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is:Coordinate Geometry
Q3104If a circle passes through the point (a, b) and cuts the circle x² + y² = p² orthogonally, then the equation of the locus of its centre is:Coordinate Geometry
Q3116If the circles x² + y² + 2ax + cy + a = 0 and x² + y² - 3ax + dy - 1 = 0 intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through…Coordinate Geometry
Q3208If z₁ and z₂ are two non-zero complex numbers such that | z₁ + z₂ | = | z₁ | + | z₂ |, then arg z₁ - arg z₂ is equal to:Complex Numbers and Quadratic Equations
Q3231If the cube roots of unity are 1, ω, ω ² then the roots of the equation (x - 1)³ + 8 = 0, are:Complex Numbers and Quadratic Equations
Q3248If ω = z/(z - 1/3i) and | ω | = 1, then z lies on:Complex Numbers and Quadratic Equations
Q3282lim n → ∞ [ 1/(n²) sec ²1/(n²) + 2/(n²) sec ²4/(n²).... + 1/n sec ² 1 ] equalsIntegral Calculus
Q3300Let f:R → R be a differentiable function having f(2) = 6, f'(2) = (1/48). Then lim x → 2 ∫₆^(f(x)) (4t³)/(x - 2)dt equals:Integral Calculus
Q3337If I₁ = ∫₀¹ 2^(x²)dx,I₂ = ∫₀¹ 2^(x³)dx, I₃ = ∫₁² 2^(x²)dx and I₄ = ∫₁² 2^(x³)dx thenIntegral Calculus
Q3338The value of ∫ - π ^π (cos ²)/(1 + aˣ)dx, a > 0, isIntegral Calculus
Q3339The value of integral, ∫₃⁶ (x)/(√(9 - x) + x) dx isIntegral Calculus
Q3574The differential equation representing the family of curves y² = 2c(x + c), where c>0, is a parameter, is of order and degree as follows:Differential Equations
Q3578If xdy/dx = y(log y - log x + 1), then the solution of the equation is:Differential Equations
Q3741An ellipse has OB as semi minor axis, F and F ' its focii and theangle FBF ' is a right angle. Then the eccentricity of the ellipse is:Coordinate Geometry
Q3791Let f:(- 1,1) → B, be a function defined by f(x) = tan ⁻¹2x/(1 - x²), then f is both one-one and onto when B is the intervalSets, Relations and Functions
Q3857A real valued function f(x) satisfies the functional equation f(x - y) = f(x)f(y) - f(a - x)f(a + y) where a is given constant and f(0) = 1, f(2a - x) is…Sets, Relations and Functions
Q3983The locus of a point P(α,β) moving under the condition that the line y = α x + β is tangent to the hyperbola (x²)/(a²) - (y²)/(b²) = 1 is:Coordinate Geometry
Q3998∫ ((log x - 1))/(1 + (log x)²) \ ² dx is equal toIntegral Calculus
Q4084If cos ⁻¹x - cos ⁻¹y/2 = α, then 4x² - 4xy cos α + y² is equal to:Trigonometry
Q4172Suppose f(x) is differentiable at x = 1 and lim h → 0 1/hf(1 + h) = 5, then f'(1) equalsLimit, Continuity and Differentiability
Q4173If f is a real valued differentiable function satisfying | f(x) - f(y) | ≤ (x - y)², x, y R and f(0) = 0, then f(1) equalsLimit, Continuity and Differentiability
Q4265Let α and β be the distinct roots of a x² + bx + c = 0, then lim x → α 1 - cos (a x² + bx + c) (x - α)² is equal toLimit, Continuity and Differentiability
Q4307If A = [ 1 0 1 1 ] and I = [ 1 0 0 1 ], then which one of the following holds for all n ≥ 1, by the principle of mathematical induction?Mathematical Induction
Q4436If a₁,a₂,a₃,........,a n,..... are in G.P., then the determinant Δ = | log a n log a n + 1 log a n + 2 log a n + 3 log a n + 4 log a n + 5 log a n + 6 log a n…Matrices and Determinants
Q4437If a² + b² + c² = - 2 and f (x) = | 1 + a²x (1 + b²)x (1 + c²)x (1 + a²)x 1 + b²x (1 + c²)x (1 + a²)x (1 + b²)x 1 + c²x |, then f (x) is a polynomial of degree:Matrices and Determinants
Q4476If A² - A + 1 = 0, then the inverse of A is:Matrices and Determinants
Q4550The system of equations α x + y + z = α - 1 x + α y + z = α - 1 x + y + α z = α - 1 has no solutions, if α is:Matrices and Determinants
Q4693Let P be the point (1, 0) and Q a point on the parabola y² = 8x. The locus of mid point of PQ is:Coordinate Geometry
Q4901Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all…Statistics and Probability
Q4994A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals:Statistics and Probability
Q5015Let A and B two events such that P(A B) = 1/6, P(A B) = 1/4 and P(A) = 1/4, where A stands for complement of event A. Then events A and B are:Statistics and Probability
Q5025If in a Δ ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in:Properties of Triangle
Q5058If both the roots of the quadratic equation x² - 2kx + k² + k - 5 = 0 are less than 5, then k lies in the intervalComplex Numbers and Quadratic Equations
Q5089If the roots of the equation x² - bx + c = 0 be two consecutive integers, then b² - 4c equalsComplex Numbers and Quadratic Equations
Q5116In a triangle PQR, R = (π)/2. If tan (P/2) and tan (Q/2) are the roots of a x² + bx + c = 0, a ≠ 0 thenComplex Numbers and Quadratic Equations
Q5117The value of a for which the sum of the squares of the roots of the equation x² - (a - 2)x - a - 1 = 0 assume the least value is:Complex Numbers and Quadratic Equations
Q5118The value of a for which the sum of the squares of the roots of the equation x² - (a - 2)x - a - 1 = 0 assume the least value isComplex Numbers and Quadratic Equations
Q5278If x = Σ n = 0 ^∞ aⁿ, y = Σ n = 0 ^∞ bⁿ, z = Σ n = 0 ^∞ cⁿ, where a, b, c are in A.P and | a | < 1, | b | < 1, | c | < 1 then x, y, z are inSequence and Series
Q5286The sum of the series 1 + 1/(4.2!) + 1/(16.4!) + 1/(64.6!) +....... ad inf. isSequence and Series
Q5368Let R=\(3,3),(6,6),(9,9),(12,12),(6,12), (3,9),(3,12),(3,6) be a relation on the set A=\3,6,9,12. The relation is:Sets, Relations and Functions
Q5411If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately:Statistics and Probability
Q5422Let x₁, x₂,...........,x n be n observations such that Σ x i ² = 400 and Σ x i = 80. Then a possible value of n among the following isStatistics and Probability
Q5527If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (-1, 2) and (3, 2) then the centroid of the triangle is:Coordinate Geometry
Q5595The line parallel to the x - axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx - 2ay - 3a = 0, where (a, b) ≠ (0, 0) is:Coordinate Geometry
Q5596If non zero numbers a, b, c are in H.P., then the straight line x/a + y/b + 1/c = 0 always passes through a fixed point. That point is:Coordinate Geometry
Q5682If C is the mid point of AB and P is any point outside AB, then:Vector Algebra
Q5683Let a, b and c be distinct non-negative numbers. If the vectors a i + a j + c k, i + k and c i + c j + b k lie in a plane, then c is:Vector Algebra
Q5708Let a = i - k, b = x i + j + (1 - x) k and c = y i + x j + (1 + x - y) k. Then [ a, b, c ] depends on:Vector Algebra
Q5709If a, b, c are non coplanar vectors and λ is a real number then [ λ (a + b) λ ² b λ c ] = [ a b + c b ] for:Vector Algebra
Q5798For any vector a, the value of (a × i)² + (a × j)² + (a × k)² is equal to:Vector Algebra