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A physical quantity P is described by the relation P a^{1/2} b^{2} c^{3} d^{−4 }If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be:
A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s^{2} and the car has acceleration 4 m/s^{2}. The car will catch up with the bus after a time of:
Two particles A and B of equal mass M are moving with the same speed v as shown in the figure. They collide completely inelastically and move as a single particle C. The angle θ that the path of C makes with the Xaxis is given by:
The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If theroller is moving towards right at a constant speed, the weight moves up with a:
A conical pendulum of length 1 m makes an angle θ=45^{o} w.r.t. Zaxis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g=10 ms^{−2})
A circular hole of radius R/4 is made in athin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is:
The mass density of a spherical body is given by ρ (r) = k/r for r ≤ R and ρ (r)=0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is:
A steel rail of length 5 m and area of crosssection 40cm^{2} is prevented from expanding along its length while the temperature rises by 10^{o}C. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10^{−5} K^{−1} and 2×10^{11} Nm^{−2} respectively, the force developed in the rail is approximately :
F = yA∝ Δt
= 2 × 10^{11} × 40 × 10^{4} × 1.2 × 10^{5} × 10
= 9.6 × 10^{4} = 1 × 10^{5} N
Two tubes of radii r_{1} and r_{2}, and lengths l_{1} and l_{2}, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P_{1} and P_{2} are pressure differences across the two tubes.
If P_{2} is 4P_{1} and l_{2} is l_{1}/4 , then the radius r_{2} will be equal to:
For the PV diagram given for an ideal gas,
out of the following which one correctly represents the TP diagram?
N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?
A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm^{−1} and oscillates in a damping medium of damping constant 10^{−2} kg s^{−1}. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :
A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by y(x,t) = 0.5 sin cos(200 πt). What is the speed of the travelling wave moving in the positive x direction? (x and t are in meter and second, respectively.)
Four closed surfaces and corresponding charge distributions are shown below.
Let the respective electric fluxes through the surfaces be Φ_{1}, Φ_{2}, Φ_{3} and Φ_{4}. Then:
A combination of parallel plate capacitors is maintained at a certain potential difference.
When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.
A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r/2. The resistance of new wire will be:
The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P_{1}, P_{2} and P_{3} respectively, then:
A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :
A uniform magnetic field B of 0.3 T is along the positive Zdirection. A rectangular loop (abcd) of sides 10 cm×5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium?
A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 Ω, L=25 mH and C=1000 µF. The total impedance, and phase difference between the voltage across the source and the current will respectively be :
The electric field component of a monochromatic radiation is given by cos kz cos ωt
In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:
A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 Å and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is:
a = 0.1 mm = 10^{–4}
λ = 6000 × 10^{10}
= 6 × 10^{7}
D = 0.5 m
for 3^{rd} dark
a sin θ = 3λ
A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are:
[Take Planck’s constant h=6.62×10^{−34} Js]
The acceleration of an electron in the first orbit of the hydrogen atom (n=1) is :
Imagine that a reactor converts all given mass into energy and that it operates at a power level of 10^{9} watt. The mass of the fuel consumed per hour in the reactor will be: (velocity of light, c is 3×10^{8} m/s)
The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 mA, collector current is :
A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated P_{eff} will be given respectively as:
(K is a constant of proportionality)
In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P=4 Ω and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is :
In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r_{1} and r_{2}. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10^{−4} s, the difference in radii, r_{1}−r_{2} is best given by:
An ideal gas undergoes isothermal expansion at constant pressure. During the process :
50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_{b} of ammonia solution is 4.75, the pH of the mixture will be:
The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 211.6 pm. This transition is associated with :
At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen (N_{2}) at 4 bar. The molar mass of gaseous molecule is :
What quantity (in mL) of a 45% acid solution of a monoprotic strong acid must be mixed with a 20% solution of the same acid to produce 800 mL of a 29.875% acid solution?
To find the standard potential of M^{3+}/M electrode, the following cell is constituted : Pt/M/M^{3}+(0.001 mol L^{−1})/Ag+(0.01 mol L^{−1})/Ag The emf of the cell is found to be 0.421 volt at 298 K. The standard potential of half reaction M^{3+}+3e^{−}→ M at 298 K will be :
(Given E_{Ag}+_{/Ag} at 298 K = 0.80 Volt)
A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5 J and 8 J, respectively. Now gas is brought back to A by another process during which 3 J of heat is evolved. In this reverse process of B to A:
Adsorption of a gas on a surface follows Freundlich adsorption isotherm. Plot of log x/m versus log p gives a straight linewith slope equal to 0.5, then:
(x/m is the mass of the gas adsorbed pergram of adsorbent)
The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is: (Assume activation energy and preexponential factor are independent of temperature; ln 2=0.693; R=8.314 J mol^{−1} K^{−1})
A solution is prepared by mixing 8.5 g of CH_{2}Cl_{2 }and 11.95 g of CHCl_{3}. If vapour pressure of CH_{2}Cl_{2} and CHCl_{3} at 298 K are 415 and 200 mmHg respectively, the mole fraction of CHCl_{3} in vapour form is: (Molar mass of Cl=35.5 g mol^{−1})
The electronic configuration with the highest ionization enthalpy is:
The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:
Fe_{2}O_{3}(s)+3 CO(g) ⇌ 2 Fe(l)+_{3} CO_{2}(g)
Using the Le Chatelier’s principle, predict which one of the following will not disturb the equilibrium?
Which one of the following is an oxide?
Which of the following is a set of green house gases?
The group having triangular planar structures is:
XeF_{6} on partial hydrolysis with water produces a compound ‘X’. The same compound ‘X’ is formed when XeF_{6} reacts with silica. The compound ‘X’ is :
The number of P −OH bonds and the oxidation state of phosphorus atom in pyrophosphoric acid (H_{4}P_{2}O_{7}) respectively are :
Which of the following ions does not liberate hydrogen gas on reaction with dilute acids?
The correct sequence of decreasing number of πbonds in the structures of H_{2}SO_{3}, H_{2}SO_{4} and H_{2}S_{2}O_{7} is :
[Co_{2}(CO)_{8}] displays :
A compound of molecular formula C_{8}H_{8}O_{2} reacts with acetophenone to form a single crossaldol product in the presence of base. The same compound on reaction with conc. NaOH forms benzyl alcohol as one of the products. The structure of the compound is :
Which of the following compounds is most reactive to an aqueous solution of sodium carbonate?
In the following structure, the double bonds are marked as I, II, III and IV
Geometrical isomerism is not possible at site (s) :
The major product of the following reaction is:
The incorrect statement among the following is:
Which of the following is a biodegradable polymer?
The increasing order of the boiling points for the following compounds is :
Which of the following compounds will show highest dipole moment?
In the following reaction sequence :
The compound I is :
Among the following compounds, the increasing order of their basic strength is :
The function f : N → N defined by f(x) = x5 [x/5], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :
The sum of all the real values of x satisfying the equation 2(x−1)(x^{2}+5x−50)=1 is :
The equation
represents a part of a circle having radius equal to :
For two 3 × 3 matrices A and B, let A+B=2B' and 3A+2B=I_{3}, where B' is the transpose of B and I_{3} is 3×3 identity matrix. Then :
If x=a, y= b, z =c is a solution of the system of linear equations
x+8y+7z=0
9x+2y+3z=0
x+y+z=0
such that the point (a, b, c) lies on the plane x+2y+z=6, then 2a+b+c equals:
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B_{1} and a particular girl G_{1} never sit adjacent to each other, is:
The coefficient of x^{−5} in the binomial expansion of where x ≠ 0, 1, is :
If three positive numbers a, b and c are in A.P. such that abc=8, then the minimum possible value of b is :
Let
If 100 Sn=n, then n is equal to:
The value of k for which the function
is continuous at x = π/2, is:
If and then λ+k is equal to:
The function f defined by f(x)=x^{3}−3x^{2}+5x+7, is :
Let f be a polynomial function such that f (3x)=f'(x) ⋅ f''(x), for all x ∈ R. Then :
If and f (x) dx = A log 1 − x + Bx + C, then the ordered pair (A, B) is equal to :
(where C is a constant of integration)
If for some positive real number a, then a is equal to :
A tangent to the curve, y= f(x) at P(x, y) meets xaxis at A and yaxis at B. If AP : BP=1 : 3 and f(1)=1, then the curve also passes through the point :
A square, of each side 2, lies above the xaxis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30^{o} with the positive direction of the xaxis, then the sum of the xcoordinates of the vertices of the square is :
A line drawn through the point P(4, 7) cuts the circle x^{2}+y^{2}=9 at the points A and B. Then PA⋅PB is equal to :
The eccentricity of an ellipse having centre at the origin, axes along the coordinate axes and passing through the points (4, −1) and (−2, 2) is:
If y=mx+c is the normal at a point on the parabola y^{2}=8x whose focal distance is 8 units, then c is equal to:
If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ∆ABC is :
If the line, lies in the plane, 2x−4y+3z=2, then the shortest distance between this line and the line, is :
If the vector is written as the sum of a vector parallel to and a vector perpendicular to then is equal to:
From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is:
Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2, then a value of P(E) / P(F) is :
The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :
A value of x satisfying the equation sin[cot^{−1}(1+x)]=cos[tan^{−1}x], is :
The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60^{o}. If the area of the quadrilateral is 4√3 , then the perimeter of the quadrilateral is:
Contrapositive of the statement
‘If two numbers are not equal, then their squares are not equal’, is:
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