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The area bounded by the parabola y^{2} = 8x, the xaxis and the latus rectum is
If the coefficients of rth, (r+1)th and (r+2)th terms in the binomial expansion of (1+y)^{m} are in A.P., then m and r satisfy the equation
Coefficient of the rth term is ^{m}C_{r  1}
According to the given condition ^{m}C_{r  1} + ^{m}C_{r + 1} = 2(^{m}C_{r})
⇒ r^{2} + r + (m  r) (m + 1  r) = 2(m + 1  r) (r + 1)
⇒ r^{2} + r + m^{2} + (1  2r) m  r(1  r) = 2m (r + 1) + 2(1  r^{2})
⇒ m^{2}  m(4r + 1) + 4r^{2}  2 = 0
Given that the function f defined by is continuous . Then the value of k is
The equation of the circle passing thro' (1,0) and (0,1) and having smallest possible radius is
The differential equation of the family of curves y^{2}=4a (x+a) is
The differential equation obtained by eliminating the arbitrary constants a and b from xy = ae^{x} + be^{−x} is
The eccentric angles of the extremities of the latusrectum intersecting positive xaxis of the ellipse ((x^{2}/a^{2}) + (y^{2}/b^{2}) = 1) are given by
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): If M is a n x n matrix with rank n  1, then M can be made nonsingular by changing one element.
Reason(R): An n x n matrix with rank n  1 has a nonvanishing minor of order n  1.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Solution of
Reason(R): xdx + ydy =
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A):If A and B are two independent events such that
Reason(R):
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): If
Reason(R): We know that
If α , β are the roots of the quadratic equation x^{2} − (a − 2) x − (a + 1) = 0 , where a is a variable, then the least value of α^{2} + β^{2} is
If I₃ is the identity matrix of order 3, then I₃⁻^{1} is
If the parabola y^{2}=4ax passes thro' the point (1,2), then the tangent at this point is
If log(a + c), log(c  a), log (a  2b + c) are in A.P., then
If f (x) = {2x  3, x ≤ 2} {x, x < 2} then f (1) is equal to
If the range of a randon variable X is {0, 1, 2, 3, 4 ...} with , then a =
The ratio in which the line joining the points (a,b,c) and (a,c,b) is divided by the xyplane is
Let λ:1 be the ratio in which the line joining the points (a,b,c) and (a, c, b) is divided by xy plane.
So Z = 0
If 'S' is stress and 'Y' is Young's modulus of material of a wire, then the energy stored in the wire per unit volume is
Three separate samples of a solution of a single salt gave these results. One formed a white ppt. with excess ammonia solution, one formed a white ppt. with dil. NaCl solution and one formed a black ppt. with H₂S. The salt could be
The atoms of different elements, having same number of neutrons, but different mass numbers and atomic numbers, are called
Which one of the following compounds in most acidic
The compound in which C uses sp^{3} hybrid orbitals for bond formation is
Homolytic fission of C  C bond in ethane (CH₃  CH₃) gives an intermediate in which carbon atom is
If an endothermic reaction is nonspontaneous at freezing point of water and becomes feasible at its boiling point, then
A gas bulb is filled with NO₂ gas and imersed in an ice bath at 0ºC which becomes colourless after sometime. This colourless gas will be
For the reaction A→B, the rate law expression is rate = k[A]. Which of the following statements is incorrect?
Which of the following gas molecule has the maximum specific heat at constant pressure?
Increasing order of stability among the three main conformations(i.e.,Eclipse,Anti,Gauche) of 2fluorethanol is
Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them ekaaluminium and ekasilicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.
The I.P. of sodium is 5.14eV. The I.P. of potassium could be
The ionisation potential keep on decreasing regularly as we move down a group from one element to the other. Because on moving down the group the atomic size increases gradually due to the addition of one new principal energy shell at each succeeding element. As a result, the force of attraction by the nucleus for the valence electrons decreases and the shielding effect increases. Consequently, ionisation potential also decreases.
then the formation constant of [Ag(NH_{3})_{2}]^{+} is :
Which of the following oxide of vanadium is most basic?
The electrode potentials of halfcell reactions are: Zn → Zn^{2}⁺ + 2e⁻ ; E = 0.76 V and Fe → Fe^{2}⁺ + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe^{2}⁺ + Zn → Zn^{2}⁺ + Fe is
The electronic configuration of an element is 1s₂2s₂2p₆3s₂3p₆3d₁₀4s₂4p₃. Its properties would be similar to which of the following elements?
A helium molecule is two times heavier than a hydrogen molecule at 298 K. The kinetic energy of the helium molecule is
Replacement of Cl of chlorobenzene to give phenol requires drastic conditions but chlorine of 2,4dinitrochlorobenzene is readily replaced. This is because
NO_{2} is an electron withdrawing group and it withdraws e ^{} from ortho/para positions. That's why it facilitate nucleophilic substitution reactions.
Which of the following will not be soluble in sodium bicarbonate?
Increasing order of p k a values (pKa =  log k_{a}) pka of H_{2}O,CH_{3}OH and C_{6}H_{5}OH is :
p k a
value of H_{2}O is 15.7, C_{6}H_{5}OH is 9.95 and CH_{3}OH is 16 so C_{6}H_{5}OH< H_{2}O <CH_{3}OH
In order to get Bakelite from phenol which of the following reagent is required?
If a carbon is bonded to two hydrogens and replacing each of them in turn with deuterium (or another group) creates a pair of diastereomers, the hydrogens are called diastereotopic hydrogens.
If we know the bond of NO and NO^{+}, then which of the following statement is true for these two species?
Bond order of NO is 2.5 while that of NO^{+} is 3. Bond length is inversely proportional to the bond order.
The ratio of th efrequencies of the long wavelength limits of the Lyman and Balmer series of hydrogen is
What was the fissionable material used in bomb dropped at Nagasaki in the year 1945 ?
When a resistance of 2 ohm is connected across the terminals of a cell, the current is 0.5 A;but when the resistance across the cell is 5 ohm, the current is 0.25 A. The e.m.f. of the cell is
The potential difference between two electrodes of a galvanic cell, in an open circuit, is known as
If we consider electrons and photons of the same wavelength, then they will have the same
The work function of sodium is 2.3eV. The threshold wavelength of sodium will be
Which one of the following electromagnetic radiations have the smallest wavelength?
The capacitor of a parallel plate capacitor with no dielectric substance and a separation of 0.4 cm is 2 μF. The separation is reduced to half and it is filled with a substance of dielectric value 2.8. The new capacity of the capacitor is
Two similar point charges at a certain distance experience a force of 80 N. Each charge is halved in magnitude and distance between them is doubled. The new electrostatic force between them would be
Which of the following statements is correct in respect of a geostationary satellite ?
We consider the radiation emitted by the human body. Which of the following statements is true
A calorimeter of mass 0.2 kg and specific heat 900 J/kgK. Containing 0.5 kg of a liquid of specific heat 2400J/kgK. Its temperature falls from 60ºC to 55ºC in one minute. The rate of cooling is
A mass m falls freely from rest. The linear momentum, after it has fallen through height h, is
u = 0; since it falls freely from rest
To convert a 800mV range millivoltmeter of resistance 40 Ω into a milliammeter of 100mA range, the resistance to be connected as shunt is
A stone is thrown up with a velocity of 4.9 m−s−^{1} from a bridge. It falls down in water after 2 s. The height of the bridge is
Which one of the following is ture for a small iron ball when placed just at the centre of the horizontal pole pieces of a strong electromagnet and then released ?
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Orbiting satellite or body has K.E. of always less than that of Potential energy.
Reason(R): For any bound state, the magnitude of potential energy is always twice that of kinetic energy (K.E.)
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): The Lorentzian force acts like a torque on the charge moving with a velocity.
Reason(R) : As any torque is I α , the Lorentzian force produces acceleration.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Pure rolling may be produced when there is sufficient friction to prevent slipping.
Reason(R) : Friction opposes the translatory motion of the rolling body.
The substance which shows practically no elastic after effect is
A flywheel has a moment of inertia 0.5 kgm^{2}. What torque is required to increase its velocity from 2π rads⁻^{2} to 15 π rads⁻^{2} in 8 s?
The time period of a simple pendulum is T. When the length is increased by 10cm, its period is T_{1}. When the length is decreased by 10cm, its period is T_{2}. Then relation between T, T_{1} and T_{2} is
Let V_{s} be the speed of the source emitting sound waves, 'n' the actual frequency of the source of sound, 'V' the speed of sound, and ' n_{1} ' the frequency of sound waves as perceived by a stationary observer to whom the source is approaching. The formula for calculating n 1 is
With respect to the figures of above question, no heat exchange between the gas and the surroundings will take place, if the gas is taken along curve
How many times is diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half?
If C and R denote the capacitance and resistance respectively, then the dimensional formula for CR is same as that fore
CR is time constant of CR circuit
If Young's double slit experiment of light, interference is performed in water, which one of the following is correct?
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