Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?
[Assume A << A_{0 } (area of tank)]
Which of the following graphs correctly represent the variation of β = −[(dV/dp)/V] with p for an ideal gas at constant temperature?
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What is the potential difference between A and B?
(where A is the centre of left ring and B is the centre of right ring)
Halflife of a radioactive substance A is 4 days. The probability of a nucleus that, from the given sample that it will decay in two halflives is
Which of the following statement is false for electromagnetic waves ?
The voltage of clouds is 4 × 10^{6} V with respect to ground. In a lightning strike lasting 100 ms, a charge of 4 C is delivered to the ground. The average power of lightning strike is (assume complete discharges)
A tuning fork vibrates with a frequency of 256 Hz. Taking the speed of sound to be 345.6 m s^{1} in the air, find the wavelength and the distance, which the sound travels during the time, fork makes 60 vibrations.
If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface would
Three capacitors each of capacity 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by
Six wires of current I_{1} = 1A, I_{2} = 2A, I_{3} = 3A, I_{4} = 1A, I_{5} = 5A and I_{6} = 4A cut the page perpendicularly at the points 1,2,3,4,5 and 6 respectively as shown in the figure. Find the value of integral ∮B→.dℓ around the circular path c.
A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the direction of magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s^{1}. Find the induced emf in the loop when it's radius is 2 cm.
A body executing S.H.M. has amplitude 5 cm and frequency 5 vibrations per second. Calculate the displacement of particle from mean position after 0.32 s.
For network shown in figure, determine V_{0 }and I_{D}. (Where, I_{D} = Current flowing in the diodes)
A particle is projected vertically upwards with a velocity u, from a point O. When it returns to the point of projection, which of the following is incorrect ?
Two blocks each of mass m, lie on a smooth table. They are attached to two other masses as shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces with respect to each other is
An electron is in an excited state in a hydrogen like atom. It has a total energy of 3.4 eV. The kinetic energy is E and its de Broglie wavelength is λλ. Then
Two cylindrical rods of uniform crosssectional area A and 2A, having free electrons per unit volume 2n and n respectively are joined in series. A constant current I flows through them in steady state. The ratio of drift velocity of free electrons in the left rod to that of the right rod is (VL/VR) is:
Uncharged capacitor of capacitance 4 μF4 and a resistance of 2.5 M ΩM Ω are connected in series with 12 V battery at t=0. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, ln (2) = 0.693]
A refrigerator is to maintain the eatables, kept inside it, at 9^{o}C. The coefficient of performance of the refrigerator, if the room temperature is 36^{o}C, is
A ball is projected up an incline of 30o with a velocity of 30 ms^{−1} at an angle of 30^{o} with reference to the inclined plane from the bottom of the inclined plane. If g = 10 ms^{−2}, then the range on the inclined plane is
Three balls A, B and C whose masses are m, km and 4m respectively kept at rest on the horizontal smooth surface, as shown in the figure. The ball A is given velocity v_{0}, rightward and it collides with the ball B elastically. Then ball B collides elastically third ball C. For what value of k, does the third ball C receive the maximum speed?
ABCDECA is a planar body of mass m of uniform thickness and same material. The dimensions are as shown in the figure. The moment of inertia of the body about an axis passing through point A and perpendicular to planar body is 1_{1} and that of about an axis passing through C and perpendicular to planer body is l_{2}. If 1_{1}/1_{2} is k. Find the l value of k.
A body of mass 6.25 kg is travelling in a horizontal straight line with a velocity of 3 m/sec when a horizontal force P is applied to it at right angle to the initial direction of motion. If P varies according to the accompanying graph, remains constant in direction and is the only force acting on the body in its plane of motion, find the magnitude of the velocity of the body when t = 2 sec.
If a car is moving rightward with acceleration rightward as shown in the figure. Find the value of k so that, rod maintains its orientation as shown in the figure. Neglect the friction and mass of the small rollers at A and B.
For identical rods, each of mass m are welded at their ends to form a square, and the corners are then welded to a light metal hoop of radius r. If the rigid assembly of rods and hoop is allowed to roll down the inclined rough surface. If the minimum value of the coefficient of static friction which will prevent slipping is k/10
Find the value of k.
If the nitrogen atom had electronic configuration 1s^{7}, it would have energy lower than that of the normal ground state configuration 1s^{2} 2s^{2 }2p^{3}, because the electrons would be closer to the nucleus, yet 1s^{7} is not observed because it violates
How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca^{2+}
The first orbital of H is represented by where a_{0} is Bohr's radius The probability of finding the electron at a distance r, from the nucleus in the region dV is
20% of N_{2}O_{4} molecules are dissociated in a sample of gas at 27^{∘}C and 760 torr. Mixture has the density at equilibrium equal to:
Which of the following compounds display geometrical isomerism?
Nickel (Z = 28) combines with a uninegative mono dentate ligand X to form a paramagnetic complex [NiX_{4}]^{2}.The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively
The correct stability order of the following resonance structures is?
(i) Tensile strength of vulcanised rubber is almost ten times more than raw rubber.
(ii) Elasticity of raw rubber is very high.
Choose the correct option.
The correct order of reducing ability for the four successive elements Cr, Mn, Fe and Co is: Their Eored values are given below.
An unknown alkyl halide (A) reacts with alcoholic KOH to produce a hydrocarbon (C_{4}H_{8}) as the major product. Ozonolysis of the hydrocarbon affords one mole of propanaldehyde and one mole of formaldehyde. Suggest which organic compound among the following has the correct structure of the above alkyl halide (A)?
Which one of the following reactions of Xenon compounds is not feasible?
One mole of a nonideal gas undergoes a change of state(2.0 atm, 3.0 L, 95 K) ⟶ (4.0 atm, 5.0 L, 245 K) with a change in internal energy, ΔE = 30.0 Latm. The change in enthalpy (ΔH) of the process in Latm
How many moles of KMnO_{4} are needed to oxidise a mixture of 1 mole each of FeSO_{4}, FeC_{2}O_{4} and Fe_{2}(C_{2}O_{4})_{3} completely in acidic medium :
The catalyst used in the manufacture of polyethylene by Ziegler method is
The reagent with which both acetaldehyde and acetone react easily is
Which of the following facts about the complex [Cr(NH_{3})_{6}]Cl_{3} is wrong?
Consider the reaction 2NO(g)+O_{2}(g) ⟶ 2NO_{2}(g) Predict whether the reaction is spontaneous at 298 K. Δ_{f}G(NO) = 86.69kJ/mol,Δ_{f}G(NO_{2}) = 51.84kJ/mol
The pH range of a basic indicator (InOH, pK_{ln}.= 4) is 3.4 to 4.6. For what minimum ratio of does the solution appear in the colour of In+
x moles of phosgene gas is allowed to attain equilibrium with its gaseous decomposition products in a 1 litre vessel. For what value of x; half the chlorine atoms in the equilibrium mixture remain with phosgene. (KC for phosgene decomposition = 3)
If the number of 109°28' angles in the structure of TMS (tetra methyl silane) is x, find x/6.
How many moles of water vapour is evolved when 1 mole of hydrated aluminium chloride dimer (Al_{2}Cl_{6}.12H_{2}O) is strongly heated.
Calculate the energy required (in Joules) to convert all atoms of Mg to Mg^{2+} ions present in 48 mg of Mg vapours. IE_{1} and IE_{2} of Mg are 740 and 1450 kJ mol^{–1} respectively.
The equation of a circle C_{1} is x^{2 }+ y^{2 }− 4x − 2y − 11 = 0. A circle C_{2} of radius 1 unit rolls on the outside of the circle C_{1} touching it externally. The locus of the centre of C_{2} has the equation
Two vertices of a triangle are (3, 2) and (2, 3) and its orthocentre is ( 6, 1). The coordinates of its third vertex are
The equation of the common tangent to the equal parabolas y^{2} = 4ax and x^{2} = 4ay is
A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of zaxis is:
If the fourth term of is equal to 200 and x > 1, then x is equal to
If the line 3x + 2y = 13 divides the area enclosed by the curve, 9x^{2 }+ 4y^{2 }− 18x − 16y − 11 = 0 into two parts then the ratio of the larger area to the smaller area is
The third vertex of the triangle whose centroid is (7,−2, 5) and whose other two vertices are (2, 6, −4) and (4,−2, 3) is
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r is equal to
If a^{3} + b^{6} = 2, then the maximum value of the term independent of x in the expansion of (ax^{1/3} + bx^{1/6})^{9} (a > 0, b > 0) is
The coordinates of the point which divides the line segment joining the points (5,4, 2) and (−1,−2, 4) in the ratio 2 : 3 externally is
The area of an expanding rectangle is increasing at the rate of 48 cm^{2}/sec. The length of the rectangle is always equal to the square of the breadth. At the instant when the breadth is 4.5 cm, The length is increasing at the rate of
If ^{n}P_{r }= 1680 and ^{n}C_{r }= 70, then 69 n + r! is equal to
Consider the straight line ax + by = c, where a, b, c ∈ R^{+ }this line meets the coordinate axes at A and B respectively. If the area of the ΔOAB, O being origin, is always a constant equal to half, then
If for a ΔABC, cot A⋅cot B⋅cot C>0 then the triangle is
The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x^{2 }+ y^{2} = 9 is
The probability of a bomb hitting a bridge is 1/2 and two direct hits are needed to destroy it. Find the least number of bombs required so that the probability of the bridge being destroyed is greater than 0.9.
If sin 3αα= 4 sin αα sin (x+ a) sin (x  αα), then 864 sin^{2} x+ 3620 cos^{2} x is equal to
If points (0,0,9), (1,1,8), (1,0,7) and (2,2, λ) are coplanar, then λ =
357 docs148 tests

357 docs148 tests
