1 Crore+ students have signed up on EduRev. Have you? 
An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is
Let the fundamental frequency of organ pipe be f
Case I : f = 200 ± 5 = 205 Hz or 195 Hz
Case II : frequency of 2nd harmonic of organ pipe = 2f (as is clear from the second figure) 2f = 420 ± 10 or f = 210 ± 5 or f = 205 or 215
Hence fundamental frequency of organ pipe = 205 Hz
A vessel of depth 2d cm is half filled with a liquid of refractive index μ1 and the upper half with a liquid of refractive index μ2. The apparent depth of the vessel seen perpendicularly is
Apparent depth = d/μ_{1} + d/μ_{2}
The upper half of an inclined plane with inclination f is perfectly smooth while the lower half is rough.A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
Acceleration of block while sliding down upper half = g sin ф;
retardation of block while sliding down lower half = – (g sin ф  mg cos ф) For the block to come to rest at the bottom, acceleration in I half = retardation in II half. g sin ф = (g sin ф  mg cos ф)
Þ m = 2 tan ф
Alternative method : According to workenergy theorem, W = ΔK = 0 (Since initial and final speeds are zero)
∴ Work done by friction + Work done by gravity = 0
i.e.,
or
A body of density ρ' is dropped from rest at a height h into a lake of density r where ρ > ρ' neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface :
The effective acceleration of the body
Now, the depth to which the body sinks
If the forward voltage in a semiconductor diode is changed from 0.5V to 0.7 V, then the forward current changes by 1.0 mA. The forward resistance of diode junction will be
Forward resistance
The heat generated in a cir cuit is given by Q = I^{2} Rt, where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be
= 2 x 2% + 1% + 1% = 6%.
The r.m.s. velocity of oxygen molecule at 16ºC is 474 m/sec. The r.m.s. velocity in m/s of hydrogen molecule at 127ºC is
A projectile A is thrown at an angle of 30° to the horizontal from point P. At the same time, another projectile B is thrown with velocity v_{2 }upwards from the point Q vertically below the highest point. For B to collide with A, should be
This happen when vertical velocity of both are same.
The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20 m without skidding is (g = 9.8 m/s^{2})
μ mg = mv^{2} / r or v =
or v = = 7 m / s
A boy pushes a toy box 2.0 m along the floor by means of a force of 10 N directed downward at an angle of 60º to the horizontal. The work done by the boy is
W = F s cos θ = 10 × 2 cos 60º = 10 J.
The engine of a truck moving along a straight road delivers constant power. The distance travelled by the truck in time t is proportional to
since both P and m are constants
The escape velocity from a planet is v_{e}. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
In tunnel body will perform SHM at centre V_{max} = Aω (see chapter on SHM)
If the the earth is at onefourth of its present distance from the sun, the duration of year will be
A vessel with water is placed on a weighing pan and it reads 600 g. Now a ball of mass 40 g and density 0.80 g cm^{–3} is sunk into the water with a pin of negligible volume, as shown in figure keeping it sunk. The weighing pan will show a reading
Volume of ball =
Downthrust on water = 50 g.
Therefore reading is 650 g.
In an adiabatic process, the pressure is increased by If γ = 3/2, then the volume decreases by
nearly
PV^{3/2} = K
The equation of a projectile is The angle of projection is given by
Comparing the given equation with we get tan θ = √3
Let mass is displaced towards left by x then force on mass = – kx – 2kx = – 3kx [negative sign is taken because force is opposite to the direction of motion]
Thus it is propotional to
Two wires A and B of the same material, having radii in the ratio 1 : 2 and carry currents in the ratio 4 : 1. The ratio of drift speed of electrons in A and B is
Current flowing through the conductor, I = n e v A. Hence
An instantaneous displacemen t of a simple harmonic oscillator is x = A cos (ωt + π/4). Its speed will be maximum at time
Velocity, = Aω sin (ωt + π/4)
Velocity will be maximum, when
ωt + π/4 = π/2 or ωt = π/2 – π/4 = π/4 or t = π/4ω
The energy of electron in the n th orbit of hydrogen atom is expressed as
The shortest and longest wavelength of Lyman series will be
and
In the circuit given below, the charge in μC, on the capacitor having 5 μF is
Potential difference across the branch de is 6 V. Net capacitance of de branch is 2.1 µF
So, q = CV
⇒ q = 2.1 × 6 µC ⇒ q = 12.6 µ C Potential across 3 µF capacitance is
Potential across 2 and 5 combination in parallel is 6 – 4.2 = 1.8 V
So, q' = (1.8) (5) = 9 µC
A crystal has a coefficient of expansion 13×10^{– 7} in one direction and 231 × 10^{–7} in every direction at right angles to it. Then the cubical coefficient of expansion is
γ = ∝_{1} + ∝_{2} + ∝_{3}
= 13 x 10^{7} + 231 x 10^{7} + 231 x 10^{7} = 475 x l0^{7}
A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
Solid cylin der reaches the bottom first because for solid cylinder and for hollow cylinder, Acceleration down the inclined plane Solid cylin der h as greater acceleration. It reaches the bottom first.
A whistle of frequency 1000 Hz is sounded on a car travelling towards a cliff with velocity of 18 m s^{–1} normal to the cliff. If c = 330 m s^{–1}, then the apparent frequency of the echo as heard by the car driver is nearly
(a) By the concept of accoustic, the observer and source are moving towards each other, each with a velocity of 18 m s–^{1}.
A thin sheet of glass (μ = 1.5) of thickness 6 micron introduced in the path of one of the interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. Then the wavelength of light used is
nλ = (μ  1)t;
M.I of a circular loop of radius R about the axis in figure is
Use theorem of parallel axes.
Three charge q, Q and 4q are placed in a straight line of length l at points distant 0, 1/2
and l respectively from one end. In order to make the net froce on q zero, the charge Q must be equal to
(F_{net} )_{q} =0
In series combination of R, L and C with an A.C. source at resonance, if R = 20 ohm, then impedence Z of the combination is
An electron moves in a circular arc of radius 10 m at a contant speed of 2 × 10^{7} ms^{–1} with its plane of motion normal to a magnetic flux density of 10^{–5} T. What will be the value of specific charge of the electron?
Bqv = mv^{2} /r or q/m = v /rB.
From a 200 m high tower, one ball is thrown upwards with speed of 10 ms^{1} and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to
The ball thrown upward will lose velocity in 1s. It return back to thrown point in another 1 s with the same velocity as second. Thus the difference will be 2 s.
A wheel is rotating at 900 r.p.m. about its axis.When power is cut off it comes to rest in 1 minute.The angular retardation in rad/s^{2} is
Angular retardation,
A particle executing simple harmonic motion along yaxis has its motion described by the equation y = A sin(ω t)+B . The amplitude of the simple harmonic motion is
The amplitude is a maximum displacement from the mean position.
A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere.
The current induced in the loop is
Since the magnetic field is uniform the flux f through the square loop at any time t is constant, because
f = B × A = B × L^{2} = constant
A body of mass 2 kg is placed on a horizontal surface having kinetic friction 0.4 and static friction 0.5. If the force applied on the body is 2.5 N, then the frictional force acting on the body will be [g = 10 ms^{–2}]
Limiting friction = 0.5 x 2 x 10= 10 N
The applied force is less than force of friction, therefore the force of friction is equal to the applied force.
A nucleus splits into two nuclear parts which have their velocity ratio equal to 2 : 1. What will be the ratio of their nuclear radius?
As momentum is conserved, therefore
A charge +q is at a distance L/2 above a square of side L. Then what is the flux linked with the surface?
The given square of side L may be considered as one of the faces of a cube with edge L. Then given charge q will be considered to be placed at the centre of the cube. Then according to Gauss's theorem, the magnitude of the electric flux through the faces (six) of the cube is given by
ф = q/ε_{0}
Hence, electric flux through one face of the cube for the given square will be
A plane electromagnetic wave is incident on a plane surface of area A, normally and is perfectly reflected. If energy E strikes the surface in time t then average pressure exerted on the surface is (c = speed of light)
Incident momentum,
For perfectly reflecting surface with normal incidence
There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be
∵ Both wires are same materials so both will have same Young’s modulus, and let it be Y.
A = area of crosssection of wire Now,
Since load and length are same for both
ΔL_{1} : ΔL_{2}= 4 :1
At steady state the capacitor will be fully charged and thus there will be no current in the 1W resistance. So the effective circuit becomes
Net current from the 6V battery,
Between A and B, voltage is same in both resistances, 2I_{1} = 3I_{ 2} where
I_{1} + I _{2} = I = 1.5
⇒ 2I_{1} = 3(1.5  I_{1} ) ⇒ I_{1} = 0.9A
The potential energy of a satellite of mass m and revolving at a height R_{e} above the surface of earth where R_{e} = radius of earth, is
At a height h above the surface of earth the gravitational potential energy of the particle of mass m is
Where M_{e} & R_{e} are the mass & radius of earth respectively.
In this question, since h = R_{e}
If 0.2 gram of an organic compound containing carbon, hydrogen and oxygen on combustion, yielded 0.147 gram carbon dioxide and 0.12 gram water. What will be the content of oxygen in the substance ?
% of O = 100  (20.045 + 6.666) = 73.29 %
The Lassaigne’s extract is boiled with dil. HNO_{3} before testing for halogens because
Na_{2}S and NaCN, formed during fusion with metallic sodium, must be removed before adding AgNO_{3}, otherwise black ppt. due to Na_{2}S or white precipitate due to AgCN will be formed and thus white precipitate of AgCl will not be identified easily.
Pyridinium chlorochromate selectively oxidises a primary alcohol to an aldehyde
e.g.
Maleic acid and fumaric acids are geometrical isomers.
For which one of the processes represented by the following equations the enthalpy (heat) change is likely to be negative
Gaseous ions, when dissolved in water, get hydrated and heat is evolved (heat of hydration).
Cl^{} (g) + aq → Cl^{} (aq) is such reaction .
A cyclic process ABCD is shown in P–V diagram for an ideal gas. Which of the following diagram represents the same process?
Correct option is (C)
Solution: (C)
In the given fig.,
Process A→B⇒ Isobaric
Process B→C⇒ Isothermal
Process C→D⇒ Isochoric
Process D→A⇒ Isothermal
Hence the process is correctly represented in fig. (C).
In a monoclinic unit cell, the relation of sides and angles are respectively:
Phosphine is not obtained by which of the following reaction?
Red P does not react with NaOH to give PH_{3}.
An ideal gaseous mixture of ethane (C_{2}H_{6}) and ethene (C_{2}H_{4}) occupies 28 litre at 1 atm and 273 K. The mixture reacts completely with 128 g O_{2} to produce CO_{2} and H_{2}O. Mole fraction at C_{2}H_{6} in the mixture is:
C_{2}H_{6} + 3.5O_{2} → 2CO_{2} + 3H_{2}O;
C_{2}H_{4} + 3O_{2} → 2CO_{2} + 2H_{2}O
Let volume of ethane is x litre,
22.4 × 4 = 3.5x + 3(28 – x)
⇒ x = 11.2 litre
at constant T and P, V αx n;
⇒ Mole fraction of C_{2}H_{6} in mixture =
What is the maximum wavelength line in the Lyman series of He^{+} ion?
Acidic character of oxide ∝ Nonmetallic nature of element.
Nonmetallic character increases along the period. Hence order of acidic character is
Cl_{2}O_{7} > SO_{2} > P_{4}O_{10}.
In the reaction 2PCl_{5} PCl_{4}^{+} + PCl_{6}^{} , the change in hybridisation is from
Arrange the following ions in the order of decreasing X – O bond length, where X is the central atom
More will be the electronegativity of X, lesser will be the bond length of XO bond.
Two vessels of volumes 16.4 L and 5 L contain two ideal gases of molecular existence at the respective temperature of 27 °C and 227 °C and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is
Given conditions
V_{1} = 16.4 L, V_{2} = 5 L
P_{1} = 1.5 atm, P_{2} = 4.1 atm
T_{1} = 273 + 27 = 300 K,
T_{2} = 273 + 227 = 500 K
Applying gas equation,
For the combustion reaction at 298 K
2Ag(s) + 1 / 2O_{2} (g ) → 2Ag_{2}O(s)
Which of the following alternatives is correct?
ΔH = ΔU + ΔnRT
Δn = n_{P} – n_{R}
Now,
Thus,
∴ ΔU > ΔH
K_{P} = K_{C} ( RT)^{Δn}_{g}
For the reaction
A solution of NH_{ 4}Cl and NH_{ 3} has pH = 8.0.Which of the following hydroxides may be precipitated when this solution is mixed with equal volume of 0.2 M of metal ion.
pH = 8, pOH = 6; [OH^{ } ] = 10^{ 6} M;
Ionic product of Fe(OH)_{2} = 0.2 × (1 x10 ^{6} )^{ 2}
2 x 10^{ 13} > K_{ sp} (= 8.1 x 10^{16} )
Which of the following is not a disproportionation reaction?
Disproportionation involves simultaneous oxidation and reduction of the same atom in a molecule.
The amount of H_{2}O_{2} present in 1 litre of 1.5 N H_{2}O_{2} solution, is :
Molecular weight of H_{2}O_{2} = 34
Equivalent weight of H_{2}O_{2} = 17
∴ 1 L of 1 N H_{2}O_{2} has = 17 g of H_{2}O
∴ 1 L of 1.5 N H_{2}O_{2} has = 1.5 × 17 = 25.5 g of H_{2}O_{2}
BeF_{2} is soluble in water whereas fluorides of other alkaline earth metals are insoluble because of
Be^{2+} being small in size is heavily hydrated and heat of hydration exceeds the lattice energy.
Hence BeF_{2} is soluble in water.
The hydrolysis of Trialkylchlorosilane R_{3} SiCl yields dimer :
The alcohol product(s) of the reduction of 2methyl3pentanone with LiAlH_{4} is (are)
The resulting compound is C_{3}H_{7}CH(OH)C_{2}H_{5} which is optically inactive and reaction leads the racemisation
Br^{•} will abstract which of the hydrogen most readily?
Bromine is more selective
∴ abstract that hydrogen which forms stable free radical
∴
The vapour pressure of two pure liquids A and B that form an ideal solution, are 400 and 800 mm of Hg respectively at a temperature t°C. The mole fraction of A in a solution of A and B whose boiling point is t°C will be (a) 0.4 (b) 0.8 (c) 0.1 (d) 0.2
V.P. of solution at t°C = 760 mm
[at b.p., V.P. of solution =atompheric pressure]
Thus = P_{A}°.x_{A} + P_{B}°.x_{B}
or P = P_{A}°.x_{A} + P_{B}°.(1 – xA) [∵x_{A} + x_{B} = 1]
or 760 = 400X_{A} + 800(1 – X_{A}) [∵ P = 760 mm of Hg]
or – 800 + 760 = – 400 x_{A}
or – 40 = – 400 xA
Thus mole fraction in solution is 0.1
On reaction with sodium, 1 mol of a compound X gives 1 mol of H_{2}. Which one of the following compounds might be X?
Since 1 mole of compound X reacts with Na to evolve 1 mole of H2 gas, therefore the compound should have 2 active hydrogen atoms per mole which is possible only in option d.
CH_{ 2}OHCH_{ 2}CH_{2}CH_{2}OH + 2 Na → NaOCH _{2}CH_{2}CH_{2}CH_{2}ONa+ 2H
LiAlH_{4} will give the desired compound.
Green house gases such as CO_{2}, ozone, methane, the chlorofluorocarbon compounds and water vapour form a thick cover around the earth which prevents the IR rays emitted by the earth to escape. It gradually leads to increase in temperature of atmosphere.
Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25°C. For this process, which of the following statement is correct?
The adsorption of methyene blue on activated charcoal is an example of physiosorption which is exothermic, multilayer and does not have energy barrier.
What is the product of the following reaction ?
Only –CHO group reacts with CN– ion and the reaction is
The delectron configurations of Cr^{2+}, Mn^{2+}, Fe^{2+} and Co^{2+} are d^{ 4}, d^{ 5}, d^{ 6} and d^{ 7} respectively.Which one of the following will exhibit the lowest paramagnetic behaviour?
(Atomic no. Cr = 24, Mn = 25, Fe = 26, Co = 27).
Electronic No. of unpaired configuration electrons
∴ Sin ce Co^{2+} ha s lowest no. of unpaired electrons hence lowest paramagnetic behaviour is shown by [Co(H_{2}O)_{6}]^{2+}
An organic compound with the formula C_{6}H_{12}O_{6} forms a yellow crystalline solid with phenylhydrazine and gives a mixture of sorbitol and mannitol when reduced with sodium. Which among the following could be the compound?
Since the compound forms a yellow crystalline solid, i.e. osazone with phenylhydrazine, it may be an aldohexose or a ketohexose. Further, since on reduction, compound forms a mixture of sorbitol and mannitol, it must be a ketohexose, i.e. fructose.
Recall that glucose on reduction gives only one alcohol glucitol (Sorbitol)
When structures I and II are C–2 epimers, it implies that these are epimers and diastereomers too.
Which is not the correct statement?
(At. nos. Ce = 58, Lu = 71, La = 57, Yb = 70)
Option (a) is incorrect as Yb^{3+} is colorless.
Which of the following reactions will not give N, N dimethyl benzamide ?
(a) C_{6} H5COOC _{2} H_{5} + (CH3 )2NH → C6H_{5}CON(CH _{3 }) _{2} + C_{2}H _{5}OH
(b) C_{6}H_{5}CONH _{2} + CH_{3}MgI → C_{6}H_{5}CO NH MgI + CH _{4}
(c) C_{6} H 5COCl + (CH_{3} )2NH → C6H_{5}CON(CH_{3})_{2} + HCl
(d) C_{6}H_{5}CO.O.COC_{6}H_{5} +
(CH_{3} )_{2}NH → C_{6}H5CON(CH _{3} ) _{2}
+ C_{6}H_{5}COOH
Here X is polytetrafluoroethylene. So, none of these i.e., option (d) is correct choice.
Bacteriostatic drugs inhibit the growth of organisms while bactericidal drugs kill the microorganisms.
Δ_{f}G^{–} vs T plot in the Ellingham diagram slopes downward for the reaction
Hence, as the temperature increases, TΔS increases and hence ΔG (ΔH – TΔS) decreases.
In other words, the slope of the curve for formation of CO decreases. However, for all other oxides, it increases.
A radioactive isotope having a half  life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope?
Given t_{1/2} = 3
Total time T = 12
No. of half lives (n) =
N = 48 g
DIRECTIONS: Select the most appropriate option to fill in the blank.
One of them would keep a lookout on the road behind to warn us _______ approaching vehicles.
Warn a person of possible danger or a potential problem.
Warn a person against a fault.
Hence out of all four prepositions in options, ‘of’ is the correct choice.
DIRECTIONS: Select the most appropriate option to fill in the blank.
The top ranking manager _________ his success in the profession to his managing director’s guidance.
Attributes means regard something as being caused by.
DIRECTIONS: Some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error.
Mother Teresa asked a building where she and her workers could care for the poor people always.
Write ‘asked for ’.
DIRECTIONS: Some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error.
You may not realize it but the weather in Barbados during Christmas is like New York in June.
Write ‘that in’ after ‘like’.
DIRECTIONS : Some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error.
The parents decided it was worth the risk because these children would have succumbed their disease before adulthood.
Use preposition ‘to’ after ‘succumbed’.
Verb ‘Succumb’ is characterized by preposition ‘to’. Moreover, ‘Succumb to something’ is an idiomatic expression which means to yield to something, especially a temptation, fatal disease, a human weakness, etc.
DIRECTIONS : Read the following passage carefully and choose the best answer to each question out of the four given alternatives.
Harold, a professional man who had worked in an office for many years, had a fearful dream. In it, he found himself in a land where small sluglike animals with slimy tentacles lived on people’s bodies. The people tolerated the loathsome creatures because after many years they grew into elephants which then became the nation’s system of transport, carrying everyone wherever he wanted to go.
Harold suddenly realized that he himself was covered with these things, and he woke up screaming. In a vivid sequence of pictures his dream dramatized for Harold what he had never been able to put into words; he saw himself as letting society feed on his body in his early years so that it would carry him when he retired. He later threw off the ‘security bug’ and took up freelance work.
Q. The statement that ‘he later threw off the security bug’ means that
Harold succeeded in overcoming the need for security
DIRECTIONS : Read the following passage carefully and choose the best answer to each question out of the four given alternatives.
Harold, a professional man who had worked in an office for many years, had a fearful dream. In it, he found himself in a land where small sluglike animals with slimy tentacles lived on people’s bodies. The people tolerated the loathsome creatures because after many years they grew into elephants which then became the nation’s system of transport, carrying everyone wherever he wanted to go.
Harold suddenly realized that he himself was covered with these things, and he woke up screaming. In a vivid sequence of pictures his dream dramatized for Harold what he had never been able to put into words; he saw himself as letting society feed on his body in his early years so that it would carry him when he retired. He later threw off the ‘security bug’ and took up freelance work.
Q. Which one of the following phrases best helps to bring out the precise meaning of ‘loathsome creatures’?
Slimy tentacles and sluglike animals
DIRECTIONS : Read the following passage carefully and choose the best answer to each question out of the four given alternatives.
Harold, a professional man who had worked in an office for many years, had a fearful dream. In it, he found himself in a land where small sluglike animals with slimy tentacles lived on people’s bodies. The people tolerated the loathsome creatures because after many years they grew into elephants which then became the nation’s system of transport, carrying everyone wherever he wanted to go.
Harold suddenly realized that he himself was covered with these things, and he woke up screaming. In a vivid sequence of pictures his dream dramatized for Harold what he had never been able to put into words; he saw himself as letting society feed on his body in his early years so that it would carry him when he retired. He later threw off the ‘security bug’ and took up freelance work.
Q. In his dream, Harold found the loathsome creatures
In a different land
DIRECTIONS : Read the following passage carefully and choose the best answer to each question out of the four given alternatives.
Harold, a professional man who had worked in an office for many years, had a fearful dream. In it, he found himself in a land where small sluglike animals with slimy tentacles lived on people’s bodies. The people tolerated the loathsome creatures because after many years they grew into elephants which then became the nation’s system of transport, carrying everyone wherever he wanted to go.
Harold suddenly realized that he himself was covered with these things, and he woke up screaming. In a vivid sequence of pictures his dream dramatized for Harold what he had never been able to put into words; he saw himself as letting society feed on his body in his early years so that it would carry him when he retired. He later threw off the ‘security bug’ and took up freelance work.
Q. Harold’s dream was fearful because
In it he saw slimy creatures feeding on people’s bodies
DIRECTIONS: In questions, choose the word opposite in meaning to the given word and mark it in.
Q. Subdued
Subdued Lacking in vitality, intensity, or strength
DIRECTIONS: In questions, choose the word opposite in meaning to the given word and mark it in.
Q. Fervent
Fervent having or displaying a passionate intensity. Dispassionate not influenced by strong emotion, and so able to be rational and impartial.
DIRECTIONS: In questions, choose the word opposite in meaning to the given word and mark it in.
Q. Scrupulous
Scrupulous (of a person or process) diligent, thorough, and extremely attentive to details.
DIRECTIONS: In questions no. 26 to 28, out of the four alternatives, choose the one which best expresses the meaning of the given word and mark it.
Q. Onslaught
Onslaught a fierce or destructive attack.
Invasion an instance of invading a country or region with an armed force.
DIRECTIONS: In questions no. 26 to 28, out of the four alternatives, choose the one which best expresses the meaning of the given word and mark it.
Q. Ignominy
Ignominy public shame or disgrace.
DIRECTIONS: In questions no. 26 to 28, out of the four alternatives, choose the one which best expresses the meaning of the given word and mark it.
Q. Tryst
Tryst An agreement (as between lovers) to meet
Which of the option figures bear s the closest resemblance to the question figure?
Question Figure:
Option Figures:
Closest Resemblance is mirror image of question figure.
In the following questions a piece of paper is folded and punched as shown in problem figures and four answer figure marked (a), (b), (c), (d) are given. Select the answer figure which indicates how the paper will appear when open (unfolded).
Question Figure:
Answer Figures:
Which answer figure complete th e form in question figure ?
Question Figure:
Answer Figures:
From the answer figure choose the box that is similar to the box formed by folding the question figure.
Question figure:
Answer figures:
Only cube (4) can be formed.
In each of the following question select the missing number from the given responses.
(100 + 12) – (28 + 25) = 59
Similarly,
(102 + 52) – (36 + 28) = 90
A clock with only dot markings 3, 6, 9 and 12 positions has been kept upside down in front of a mirror. A person reads the time in the reflections of the clock as 12 : 30 the actual that will be
In this time 12 : 30 we subtract that time from 17 : 90 – 12 : 30 = 5 : 60 = 6 : 00
Six friends  A, B, C, D, E and F are sitting in a circle facing center. F is to the immediate left of A and B is sitting opposite to F, E and D are sitting opposite to each other. Who is sitting third right to A?
So, C is sitting third right to A
Ganesh cycles towards SouthWest a distance of 8 m. Then he moves towards East a distance of 20 m. From there he moves towards NorthEast a distance of 8 m, then he moves towards West a distance of 6m. From there he moves towards NorthEast a distance of 2 m. Then he moves towards West a distance of 4 m and then towards SouthWest 2 m and stops at that point. How far is he from the starting point ?
Ganesh is 10m. far from the starting point
If in a code language, LAPTOP is written as PNSOZL and NOTEBOOK and KNNADSNN, then which letter will be there in first and seventh letter from left after coding MEDICINE in the same way?
So, required answer = ED
Find the next term in the following series: X24C, V22E, T20G, ______
Let [x] denote the greatest integer £ x. If f (x) = [x] and g (x) = x, then the value of
Given that, f (x) = [x] and g (x) = x
If a chord of the circle x2 + y2 = 8 makes equal intercets of length a on the coordinate axes, then
Since the chord makes equal intercepts of length a on the coordinate axes. So, its equation can be written as x ± y = ±a . This line meets the given circle at two distinct points.
So, length of the perpendicular from the centre (0, 0) of the given circle must be less than the radius.
In the given figure, the equation of the larger circle is x^{2} + y^{2} + 4 y  5 = 0 and the distance between centres is 4. Then the equation of smaller circle is
We have x^{2} + y^{2} + 4y – 5 = 0. Its centre is C_{1} (0, – 2) ,
r1 = Let C_{2} (h, k) be the centre of the smaller circle and its radius r_{2}. Then C_{1}C_{2} = 4.
⇒ r_{2} = 1
But k = r_{2} = 1 [it touches xaxis]
∴ From eq (1), 4 =
⇒ 16 = h_{2} + 9 ⇒ h_{2} = 7 ⇒ h = ± √7
Since h > 0 ∴ h = √7
Hence, required circle is
(x  √7 )^{2} + (y 1)^{2} = 1
The equation sin^{ 4} x  (k + 2) sin^{ 2} x  (k + 3) = 0 possesses a solution if
We have,
sin ^{4} x  (k + 2) sin ^{2} x  (k + 3) = 0
⇒ sin ^{2} x = k + 3 (∵ sin^{2}x = – 1 is not possible)
Since 0 < sin^{ 2} x ,< 1,
∴ 0 < k +3 < 1or  3 < k < 2
If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils.The number of ways of distributing the pencils is
Required number of ways
= coeff. of x^{16} in (x^{3} + x^{4} + x^{5} + x^{6} + x^{7})^{4}
If a, b, c are positive numbers, then least value of (a + b + c) is
AM > HM
If and are nonzero constant vectors and the scalar b is chosen such that  + b is minimum, then the value of  b ^{2} +  + b^{2} is equal to
For minimum value  + b = 0.
Let and sr are antiparallel so bsr =
∴ b ^{2} +  + b ^{2} =  ^{2} +   ^{2}= ^{2} .
Statement1 : If the general equation x^{2} + y^{2} + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then  g >2 .
Statement2 : The equation ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af^{2} – bg^{2} – ch^{2} = 0.
The equation represents a pair of lines if 1×1×4 + 2× f ×g×11×f ^{2} 1×g ^{2}  4×1^{2} = 0
⇒ (f  g) ^{2} = 0 ⇒ f=g
The equation becomes (x + y)^{2} + 2g(x + y) + 4 = 0 Which represents pair of parallel lines, which are real provided (2g)^{ 2}  4 × 4 ×1 > 0 Þ g  > 2.
If  z_{1}  =  z_{2}  =  z_{n}  = 1. then the
value of  z_{1}  +  z_{2}  + z_{n} I 
In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is
Let R be the set of families having a radio and T the set families having a T.V., then n (R ∪ T) = The number of families having at least on of the radio and T.V. = 1003 – 63 = 940 n(R) = 794 and n(T) = 187 Let x families have both a radio and a T.V.
Then number of families who have only radio = 794 – x
And the number of families who have only T.V. = 187 – x From Venn diagram, 794 – x + x – 187 – x = 940
⇒ 981 – x = 940 or x = 981 – 940 = 41 Hence, the required number of families having both a radio and a T.V. = 41
For f (x) to be defined, we must have
∴ x^{2} > 1 – x^{2} or
Also, 1 – x^{2} > 0 or x^{2} < 1.
Now,
Also, x^{2} < 1 ⇒ (x – 1) ( x + 1) < 0
⇒ –1 < x < 1
Thus, x > 0, x^{2} > and x^{2 }< 1
If the coordinates at one end of a diameter of the circle x^{2} + y^{2} – 8x – 4y + c = 0 are (–3, 2), then the coordinates at the other end are
The centre of the given circle is C º (4, 2) Let A ≡ (3, 2)
If (α, β) are the coordinates of the other end of the diameter, then, as the middle ploint of the diameter is the centre,
Thus, the coordinates of the other end of diameter are (11, 2)
[∵ sin(nπ + θ) = (1)^{ n} sin θ]
∴ sin[(1)^{ n} θ] = (1) n sin θ]
The number of possible outcomes in a throw of n ordinary dice in which at least one of the dice shows an odd number is
Total number of ways = 6 × 6 × ..... to n times = 6^{n}.
Total number of ways to show only even number = 3 × 3 × ...... to n times = 3^{n}.
∴ required number of ways = 6^{n} – 3^{n}.
We know that
keeping x = 2, we get
The given equation is
The solution is
Consider the function f(x) = x – 1/x^{2}, then f (x) is
Clearly, f (x) is continuous for all x ∈ R except at x = 0.
f '(x) > 0 ⇒ x< 0 or 1 < x < 2
f '(x) < 0 ⇒ 0 < x <1 or x > 2
Hence, f (x) is increasing in (∞, 0)∪ (1, 2) and decreasing in (0, 1) ∪ (2,∞).
A straight rod of length 9 units slides with its ends A, B always on the X and Yaxis respectively.Then the locus of the centroid of Δ OAB is :
Let end A is (a, 0) and end B is (0, b) then a ^{2} + b ^{2} = 81 …(1) If centroid is (x, y) then
putting in (1) we get the locus as x^{2} + y^{2} = 9
The given relation is xy + y^{2 }= tan x + y.
Differentiating both sides with respect to x, we get
Th e probability th at certain electr on ic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is
Probability that the electronic component fails when first used is P(F) = 0.10. Therefore, P(F') = 1 – P(F) = 0.90
Let E be the event that a new component will last for one year.
[total probability theorem]
= 0.10 × 0 + 0.90 × 0.99 = 0.891.
Let x +y = 3  cos4θ and x y = 4 sin2θ then the greatest of xy is
∴ xy = (1  sin ^{2} 2θ)^{2} = cos^{4} 2θ < 1
Total number of ways of selecting 2 white squares on a normal chess board if the squares are not from the same row or column is equal to
2 white squares can be selected in ^{32}C_{2} ways If they belong to some row or same column then 2(8.^{4}C_{2}) ways.
The length of the latus rectum of the parabola which has focus at (–1, 1) and the directrix is 4x + 3y – 24 = 0 is
Length of latus rectum = 2 × distance of focus from directrix
In the interval
A student read common difference of an A. P. as – 2 instead of 2 and got the sum of first 5 terms as – 5. Actual sum of first five terms is
∴ Actual sum =
The number of real solution s of the equation ( x – 1) ^{2} + ( x – 2) ^{2} + ( x – 3)^{ 2} = 0 is
Equation holds if and only if x – 1 = 0, x – 2 = 0 and x – 3 = 0 simultanesouly, which is not possible.
The least positive nonintegral solution of the equation sin p(x ^{2} + x) = sin πx^{ 2} is
We have, sin p( x ^{2} + x) = sin πx ^{2}
⇒ p(x ^{2} + x ) = np + (1) ^{n} πx ^{2}
∴ Either x ^{2} + x = 2m + x ^{2} ⇒ x = 2m ∈ I
or x ^{2} + x = k  x ^{2} , where k is an odd integer
⇒ 2x^{2} +x k =0 ⇒ x =
For least positive nonintegral solution is x 1/2, when k = 1
ABC is a triangular park with AB = AC = 100 m. A TV tower stands at the midpoint of BC. The angles of elevation of the top of the tower at A, B, C are 45°, 60°, 60° respectively. The height of the tower is
Where PQ is tower and ABC is the park, with Q being mid point of the side BC and PQ = h
Also, AQ^{2} + BQ^{2} = 100^{2}
⇒ h^{ 2} + h^{ 2} cot^{ 2} 60° = 100^{2}
If x, y and z are real numbers, then
x^{ 2 }+ 4 y^{ 2} + 9 z^{ 2} – 6yz –3zx – 2xy is always
x^{2} + 4y^{2} + 9z^{2} – 6yz – 3zx – 2xy
= x^{2 }+ (2y)^{2} + (3z)^{2} – (2y) (3z) – (3z)(x) – x (2 y) > 0 x, y, z
[∵ a^{2} + b^{2} + c^{2}  ab  bc  ca > 0]
A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is
Selection of 6 guests = 10C6 Permutation of 6 on round table = 5!
Permutation of 4 on round table = 3!
Then, total number of arrangements = 10C6.5!.3!
If a > 0, b > 0, c > 0 and a, b, c are distinct, then (a + b) (b + c) (c + a) is greater than
AM > GM
So, (a + b)(b + c)(c + a ) > 8abc
The equation of the tangent to the curve y = be^{– x/a} at the point where it crosses the yaxis is
y = be^{ x /a} meets the yaxis at (0, b). Again,
Therefore, required tangent is
Putting x + y + 1 = u, we have du = dx + dy and the given equation reduces to u(du – dx) = dx
⇒ log(x + y + 2) = y + constant
⇒ x + y + 2 = Ce ^{y}
If y = 3x + 6x^{2} + 10x^{3} + ........ ∞, then
is equal to
We have y = 3x + 6x 2 + 10x ^{3} + .......
⇒ 1 + y = 1 + 3x + 6x ^{2} + 10x ^{3} + .....
⇒ 1+ y = (1 x)^{3} ⇒ 1 x = (1+ y)^{1/3}
⇒ x = 1  (1 + y)^{ 1 / 3}
Suppose p, q, r ≠ 0 and system of equation
(p + a)x + by + cz = 0,
ax + (q + b) y + cz = 0 , ax + by + (r + c)z = 0 has a nontrivial solution,
then value of is
Since the system is homogeneous and has a nontrivial solution
using R_{1} → R_{1}  R_{2} and R_{2} → R_{2}  R_{3} .
Expanding along C_{1} we get
⇒ p[q(r + c) + br ] + aqr = 0
⇒ pqr + pqc + prb + qra = 0
⇒
If a, c, b are in G.P., then the area of the triangle formed by the lines ax + by + c = 0 with the coordinates axes is equal to
Area of the triangle
[∵ a, c, b are in G.P. ⇒ c^{2} = ab]
Suppose that f(0) = –3 and f '(x) £5 for all values of x.
Then, the largest value which f(2) can attain is
Using LMVT in [0, 2]
The maximum value of z = 6x + 8y subject to constraints 2x + y < 30, x + 2y < 24 and x > 0, y > 0 is
Here, 2x + y < 30, x + 2y < 24, x, y > 0 The shaded region represents the feasible region, hence z = 6x + 8y. Obviously it is maximum at (12, 6).
Hence z = 12 × 6 + 8 × 6 = 120
If a, b, c are three natural numbers in AP and a + b + c = 21 then the possible number of values of the ordered triplet (a, b, c) is
Let a = b – d and c = b + d, then a + b + c = 21
⇒ b = 7 So, the equation is a + c = 14
∴ No. of solution = coeff. of x^{14} in (x + x^{2} + .....) = ^{13}C_{12} = 13
The line is It will touch the ellipse if
∴ The function is not continuous at x = 1.
The line y = mx bisects the area enclosed by lines x =0, y = 0 and x = 3/2 and the curve y = 1 + 4x – x^{2}.
Then the value of m is
y = 1 + 4x  x^{ 2} = 5  (x  2)^{ 2}
We have
On solving we get
There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers are
Let the last three numbers in A.P. be a, a + 6, a + 12, then the first term is also a + 12.
But a + 12, a, a + 6 are in G.P.
∴ a ^{2} = (a +12) (a + 6) ⇒ a ^{2} = a ^{2} +18a + 72
∴ a = –4.
∴ The numbers are 8, –4, 2, 8.
The distance from the point (3, 4, 5) to the point where the line meets the
plane x + y + z = 17 is
Any point on the line is ( r + 3, 2r + 4, 2r + 5).
It lies on the plane x + y + z = 17,
∴ (r + 3) + (2r + 4) + (2r + 5) = 17 i.e r = 1
Thus the point of intersection of the plane and the line is (4, 6, 7) Required distance = distance between (3, 4, 5) and (4, 6, 7)
2 videos15 docs70 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
2 videos15 docs70 tests









