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The given equation can be rewritten as
x=7 touches the circle x^{2} + y^{2}  4x  6y  12 = 0, then the coordinates of the point of contact are
If ω is a cube root of unity ,then
(1  ω + ω^{2})^{5} + (1 + ω  ω^{2}) is equal to
If z = 2/(1 + √3i),then the value of arg (z) is
The solution of the differential equation cos x sin y dx + sin x cos y dy =0 is
If m and n are integers, then what is the value of sin m x sin n x d x . If m ≠ n
Since sin mx, sin nx is an odd function if m ≠ n, then sin mx . sin nx dx = 0
The value of f(0) so that f (x) is continuous at x = 0 is
If y=sec⁻^{1}[(x+1)/(x1)]+sin⁻^{1}[(x1)/(x+1)], (dy/dx)=
Tangents are drawn from a point P(3,4) to the ellipse (x^{2}/9) + (y^{2}/16) = 1 touching the ellipse in the points Q and R. The angle between PQ and PR is
Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."
A statement is logically equivalent to its contrapositive. To form the contrapositive, switch the "If" and "then" sections of the statement AND insert "NOTs" into each section. Notice in this situation, that inserting "NOTs" turns the thoughts positive (you are negating negative thoughts).
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): Let f(x) and g(x) be two polynomials all of whose coefficients are rational numbers . Suppose f(x) and g(x) have a common irrational root, then g(x) = r f(x) for some rational number.
Reason(R): The common root of the equations ax^{2} + bx + c = 0 and a'x^{2} + b'x + c' = 0 is
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):
Reason(R):
If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is
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):α_{1},α_{2},α_{3},α_{4} are roots of 2x^{4}  2x^{3} + 9x^{2}  x + 12 = 0, then the value of is 21.
Reason(R): 2(xα_{1}) (xα_{2})(xα_{3}) x (xα_{4}) = 2x^{4}  2x^{3} + 3x^{2}  x + 12. Put x = 3 i on both sides and take modulus of both sides
The line 4x + 6y + 9 = 0 touches the parabola y^{2} = 4 x at the point
If A = [(x,y) : x^{2} + y^{2} = 25] and B = [(x,y) : x^{2} + 9y^{2} = 144] and A ∩ B contains
A random variable X has the following distribution
x 1 2 3 4
P ( X = x) c 2c 3c 4c
The value of c is
The plane XOZ divides the join of (1,1,5) and (2,3,4) in the ratio λ:1,then λ is
Since the plane XOZ divides the join of (1, 1, 5) and (2,3,4) in the ratio λ:1.
S o . Y = 0
The angle between the vectors
î  ĵ + k̂ and î + 2ĵ + k̂ is
Alcohol fermentation is brought about by the action of
Which of the following radicals will not be precipitated by passing H₂S in concentrated acid solution?
The wavelength of light having wave number 4000cm^{1} is
Purine derivative among the following bases is
Amongst the following the molecule that is linear is
The correct order of hybridisation of the central room atom in the following species, NH₃, [PtCl₄]^{2}⁻, PCl₅ and BCl₃ is respectively
The types of bonds present in CuSO₄.5H₂O are
Latent heat of vaporisation of a liquid at 500 K and 1 atm pressure is 10.00 Kcal/mol. What will be the change in internal energy (ΔU) of 3 mol of liquid at same temperature ?
Vaporization of 3 moles of H_{2}O vapors is: 3H_{2}O(l) → 3H_{2}O(g)
Δn = 3  0 = 3
Therefore,
ΔU = ΔH  ΔnRT
= (3 x 10)  3(0.002)(500) = 27
change in internal energy is:
ΔU = 27 Kcal
A liquid is in equilibrium with its vapour at its boiling point. The molecules in these two phases will have equal
If 75% of first order reaction is completed in 32 min, then 50% of the reaction would be completed in
The bond dissociation energies of H₂,Cl₂ and HCl are 104, 58 and 103 kcal respectively. The enthalpy of formation of HCl gas will be
The enthalpy and entropy change for a chemical reaction are 2.5 X 10^{3} Jmol⁻^{1} and 7.4 JK⁻^{1}mol⁻^{1} respectively. The reaction at 298 K is
In an endothermic reaction, the value of ∆H 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 atomic radius of elements of which of these would be nearly same
The atomic radii of the d block elements of a given series decrease with increase in atomic number but this decrease becomes small after midway. The decrease in atomic radii in the beginning, is due to an increase in nuclear charge from member to member which tends to reduce the size. At the same time, the addition of extra electrons to (n1)d orbitals also provides the screening effect. As the number of delectrons increases, the screening effect increases. Thus, there are operating two effects namely screening effect and nuclear charge effect which oppose each other. In the midway onwards of the series both these effects become nearly equal and thus, there is no change in atomic radii inspite of the fact that atomic number increases gradually.
Low spin octahedral complexes are maximum distorted in which of the following state?
whenever e_{g} orbitals unsymmetrical, i.e., contain 1,2 or 3 electons in low spin complex strong distortion occurs leading to tetrgonal or square planer complexes. Since the direction of the e_{g} orbitals of the central metals ion correspond with the directions of the ligands disposed octahedrally around the metal ion, the octahedral arrangement of the ligands is likely to be more severely distorted by the dissymmetry of the e_{g} orbitals than that of the t_{2g} orbitals.
Which of the following factors may be regarded as the main cause of lanthanide contraction?
In alkaline medium ClO₂ oxidises H₂O₂ to O₂ and itself gets reduced to Cl⁻.How many moles of H₂O₂ are oxidised by 1 mole of ClO₂ ?
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
50 mL of hydrogen diffues through a small hole from a vessel in 20 min .The time needed for 40 mL of oxygen to diffuses out is
Which one of the following statements ,if any ,regarding hydrogen peroxide is false ?
Reaction C₂H₅I + C₅H₁₁I + 2Na → C₂H₅  C₅H₁₁ + 2NaI is called
When wine is put in air, it becomes sour due to
Arrange the following halides in the decreasing order of S_{N}1 reactivity.
In order to get Bakelite from phenol which of the following reagents is required?
Arrange these compounds in order of increasing S_{N}1 reaction rate :
The Fisher projections shown to the right are
The particles which can be added to the nucleus of an atom without changing its chemical properties are called
The halflife of radium is about 1600 years. If 100 g of radium is existing now, then 25 g will remain unchanged after
Two wires of equal diameters of resistivities ρ_{1} and ρ_{2} and lengths X_{1} and X_{2} respectively are joined in series. The equivalent resistivity of the combination is
Resistance of a coli is 4.2 Ω at 100ºC and the temperature coefficient of resistance of its material is 0.004/ºC. Then its resistance at 0ºC is
In a discharge tube at 0.02 mm, there is formation of
The approximated wavelength of a photon of energy 2.48eV is
According to Maxwell's hypothesis, a changing electric field gives rise to
Two charged spheres separated by a distance 'd' exert some force (F) on each other. If they are immersed in a liquid of dielectric constant 4, then what is the force exerted, if all other conditions are same?
The orbital velocity a satellite near the surface of the earth is 7 kms⁻^{1}. If radius of the orbit is 4 times the radius of earth, then its orbital velocity will be
Two capacitors of capacitances 3 μF and 6 μF are charged to a potential of 12 V each. They are now connected to each other, with the positive plate of each joined to the negative plate of the other. The potential difference across each capacitor will be
If the value of g at the surface of the earth is 9.8 m/sec^{2}, then the value of g at a place 480 km above the surface of the earth will be
On increasing the temperature of a substance gradually, which of the following colours will be noticed by you
When a bus suddenly takes a bend, the passengers are thrown in the outward direction, due to
A moving charge will gain energy due to the application of
A particle is viberating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and kinetic ?
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 combination Y = sinωt + cos 2ωt is not a simple harmonic function even though it is periodic.
Reason(R): All periodic functions satisfy the relation
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 equation y = x + t cannot be true, where x, y are distance and t is time.
Reason(R) : Quantities with different dimensions cannot be added.
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): PT graphs of all gases at low density meet at only one point called absolute zero.
Reason(R): Absolute zero is less than 0ºC in a celsius scale.
According to kinetic theory of gases the absolute temperature of a gas is directly related to the average of
A glass rod is dipped in mercury and withdrawn out, the mercury does not wet the rod because
While viewing a distant object with a telescope, suddenly a housefly sits on objective lens. The correct statement is that
To move a body in a circle, which of the following force is needed?
A long spring when stretched by 'x' cm has a potantial energy V. On increasing the stretching to 'nx' cm the potential energy stroed in the spring will be
To hear an echo, the reflecting surface must be at a minimum distance of
To hear the echo distinctly, the time gap between the two sounds must be 0.1 s.
Let the distance between the listener and the reflecting surface be d
The total distance travelled by the sound = 2d
Thus the minimum distance between the listener and the reflecting surface to hear the echo in air is 16.5 m (when the velocity of sound through air is 330 ms^{1})
For an adiabatic expansion of a perfect monoatomic gas, when volume increases by 24%, what is the percentage decrease in pressure?
A water fall is 84 meters high. If half of the potential energy of the falling water gets converted to heat, the rise in temperature of water will be
If a star is moving towards earth, then the lines are shifted towards
The position of a particle at time 't' is given by the equation . Where V_{0} is constant and A > 0. Dimensions of V_{0} and A respectively are
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