The area bounded by the curve y = x3, the x-axis and the ordiantes at x = -2 and x = 1 is
The maximum coefficient in the expansion of (1+x)10.
The equation of the circle when touches x-axis at (3,0) and passing through (1,4) is
The order of the differential equation x2+y2+2gx+2fy+c=0, is
The solution of the equation y - x(dy/dx)=a[(y2)+(dy/dx)] is
If f: R → R is defined by f (x) = x − [ x ] , where [x] is the greatest integer not exceeding x, then the set of discontinuities of f is
If and α is constant then the locus of z is
The equation of ellipse in the form (x2/a2) + (y2/b2) = 1, given the eccentricity to be 2/3 and latus rectum 2/3 is
If then f ′ a =
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 P(2a,0) be any point on the axis of parabola, then the chord QPR, satisfies
Reason(R): There exists a point on the axis of the parabola y2 = 4ax such that = constant for all chords QPR of the parabola.
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 , then taking log and differentiating , xx ( 1+ log x) dx = dt .
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 b = 50, c = 63 and ∠B = 54º, then no such triangle exists.
Reason(R): Since , b > c sin B ⇒ no triangle is formed.
The absolute maximum value of y=x3-2x+2 in 0≤x≤2 is
The locus of the point of intersection of the normals at the ends of a focal chord of the parabola y2=4ax is
The probability that a person tossing three fair coins will get either all heads or all tails for the second time on the 5th toss is
In the set W of whole numbers an equivalence relation R is defined as follows :
aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by
If The A.M and G.M. between two distinct positive reals are respectively A and G, then the harmonic mean between the numbers is
In a Poisson variate X, if P (X = 0) = 0.2 then the variance of the distribution is
The value of cot 5º cot 10º.... cot 85º is
If vectors 2λi+j-k and 2j+k are mutually perpendicular, the value of λ is
Which of the following can work as a dehyrating agent for alcohols?
Ions of Ca, Ba and Sr precipitate in fifth group as their
Azimuthal quantum number of last electron of ₁₁Na is
IUPAC name of CH₃-O-C₂H₅ is
The metal present in vitamin B₁₂ is
Hydrogen bonding is maximum in
Specify the coordination geometry around and hybridisation of N and B atoms in a 1 : 1 complex of BF3 and NH3―
The 1 : 1 complex of BF3 and NH3 is represented as-
In this complex both N and B attain tetrahedral geometry with sp3 hybridisation.
Which of the following has maximum dipole moment?
Electronegativity difference between N(3.0) and Cl(3.1) is almost zero and hence N―Cl bonds are non-polar. As a result, the overall μ of NCl3 and its direction is just μ the lone pair of electron. On the other hand N―Br, N―I and N―H bonds are polar. Since the electronegativity difference is highest in case of N―H therefore, NH3 has the highest dipole moment.
The enthalpy of neutralisation of acid acid and sodium hydroxide is -55.4 KJ.What is the enthalpy ionisation of acetic acid ?
In the case of gaseous homogeneous reaction,the active mass of the reactant is obtained by the expression
The unit of second order reaction rate constant is
Consider the following reaction C + O2 → CO2 , ΔH = − 400 kJ ∕ mole 2H2 + O2 → 2 H2O , ΔH = − 570 kJ ∕ mole ; CO2 + 2H2O → CH4 + 2O2 , ΔH = 800 kJ ∕ mole
The heat of formation of methane is
C + O2 → CO2 , ΔH1 = − 400 kJ ∕ mole
2H2 + O2 → 2 H2O , ΔH2 = − 570 kJ ∕ mole
CO2 + 2H2O → CH4 + 2O2 , ΔH3 = 800 kJ ∕ mole
To get enthalpy of CH4, we add all the 3 equations.
C + 2H2 → CH4 ∆H4 = ∆H1+∆H2+∆H3 = -400-570+800 = -170 kJ/mol
The correct answer is -170 kJ/mol.
Which of the following is true for an isochoric processes
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
What is the order of stability for
I.1-butene;II.cis-2-butene;III.trans-2-butene
The properties of the elements are the periodic function of their atomic number. The statement is given by
Which one indicate correct variation of electronegativities
The electronegativity values for the representative elements increase along a period from left to right because of the increase in nuclear charge.
F (4.0) > N (3.0) < O (3.5) > C (2.5).
Which one of the following platinum complexes is used in cancer chemotherapy?
Cis isomer of [PtCl2(NH3)2] is known as cisplatin and is used as an antitumor agent in treatment of cancer.
Low spin complexes are generally formed by the elements of
The unit of electrochemical equivalent is
2.5 Faradays of electricity is passed through solution of CuSO₄.The number of grams equivalents of copper deposited on the cathode would be
If 1.5 moles of O₂ combine with Mg to form MgO, then mass of Mg that has combined is (At.wt. of Mg = 24)
Of the following compounds, the most acidic is
Which one of the following statements ,if any ,regarding hydrogen peroxide is false ?
Which of the following is correct?
Which of the following compound will make precipitate most readily with AgNO₃?
Arrange these compounds in order of increasing SN1 reaction rate :
Which is not the electrophile?
Which of the following molecules is achiral ?
Carbolic acid is
The ratio of the largest to shortest wavelengths in Lyman series of hydrogen spectra is
When the length and area of cross-section both are doubled, then its resistance
The more readily fissionable isotope of uranium has an atomic mass of
A copper wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance
If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same
Particle nature is shown by
Which of the following electromagnetic waves have the smallest wavelength?
The radius of orbit of a planet is two times that of the earth. The time period of planet is
A 4μF capacitor is charged to 400V. Then its plates are joined through a 100 Ω resistor. The heat produced in the resistor is
A capacitor of capacitance 1μF is charged to 1KV. The energy stored in the capacitor in joules is
C = 1μF
V = 1KV
energy stored U = 1/2 (CV2)
= 1/2 x 1 x 12 = 0.5
Gravitational mass is proportional to gravitational
The energy supply being cut-off, an electric element cools down to the temperature of its surrounding. But it will not cool further, because
The energy emitted per second by a black body at 27ºC is 10J. If the temperature of the black body is increased to 327ºC, then energy emitted per second will be
Four charged particles are projected perpendicularly into the magnetic field with equal speed. Which will have minimum frequency?
Four blocks of same mass connected by cords are pulled by a force F on a smooth horizontal surface, as shown in figure. The tensions T1, T2 and T3 will be
A particle starts from rest and has an acceleration of 2m − s⁻2 for 10 s. After that, it travels for 30 s with constant speed and then undergoes a retardation of 4 m − s⁻2 and comes back to rest. The total distance covered by the particle is
A bottle weighing 220 gram and of area of cross-section 50 cm2, and height 4 cm oscillates on the surface of water in vertical position. Its frequency of oscillation 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): All processes in which pressure and volume are proportional, take place at constant temperature.
Reason(R): Work done in a thermodynamical process is path dependent.
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):Doppler effect holds also for electromagnetic waves including microwaves, radio waves and visible light.
Reason(R) : As speed of light is independent of relative motion between source and observer, the formulae for doppler effect are different from that of sound.
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): When we switch on the lights one after the other in our house the main current goes on increasing.
Reason(R): Voltage = current x resistance
Scent sprayer is based on
Atmospheric pressure is measured by
Two discs have same mass and thickness. Their materials have densities d₁ and d₂. The ratio of their moments of inertia about central axis will be
If the period of oscillation of mass M suspended from a spring is one second, then the period of 4 M will be
The intensity ratio of the waves is 1 : 16. The ratio of their amplitudes is
A copper block of mass 4 kg is heated in a furnance to a temperature 425ºC and then placed on a large ice block. The mass of ice that will melt in this process will be (Specific heat of copper=500 J-kg⁻1-ºC⁻1 and heat of fusion of ice = 336 kJ-kg⁻1).
A convex lens of focal length 0.15m is made of a material of refractive index 3/2. When it is placed in a liquid, its focal length is increased by 0.225m. The refractive index of the liquid is
The ratio of the slopes of P-V diagrams of adibatic and isothermal processes is
In young's double slit experiment, the intensity of central maximum is I. It one slit is closed, the intensity at the same place will become
ML⁻1T⁻2 represents
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