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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
The solution of the differential equation cos x sin y dx + sin x cos y dy =0 is
The value of f(0) so that f (x) is continuous at x = 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
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."
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
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
The correct order of hybridisation of the central room atom in the following species, NH₃, [PtCl₄]^{2}⁻, PCl₅ and BCl₃ is respectively
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 ?
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
The atomic radius of elements of which of these would be nearly same
Low spin octahedral complexes are maximum distorted in which of the following state?
Which of the following factors may be regarded as the main cause of lanthanide contraction?
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
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 ?
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
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 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
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?
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
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
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
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
366 docs219 tests

366 docs219 tests
