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[(1 + √(3))/2]^{3n} +[(1  √(3))/2]^{3n} is equal to
The area of the triangle formed by joining the origin of the points of intersection of the line x √5 + 2y = 3√5 and the circle x^{2} + y^{2} = 10 is
The area bounded by the xaxis and the curve y = 4x − x^{2} − 3 is
y = 0, y = 4x  x^{2}  3
⇒ 4x  x^{2}  3 = 0
⇒ x^{2}  4x + 3 = 0
⇒ (x  1) (x  3) = 0
⇒ x = 1, 3
If f: R → R defined by f x is continuous function, then
The radius of the circle passing through the foci of the ellipse ((x^{2}/16) + (y^{2}/9) = 1), and having its centre (0,3) is
If c is parameter then the differential equation whose solution is is
Sneha says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Sneha is thinking of is
This sentence contains the word "or" (disjunction). A disjunction is only false if BOTH conditions are false. The only number that is not divisble by 2 and is not divisible by 3 is 11.
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 n and r are positive integers such that 1 ≤ r ≤ n, then
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): Two dice are thrown simultaneously . The probability of obtaining a total score of 5 is 0.11 .
Reason(R): A subset of the sample space S which contains more than one elements is called mixed events.
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 slope of the line whose equation is 5x + 6y = 7 is − 5/6 and the yintercept is 7/6
Reason(R): The equation of straight line which makes an angle θ with xaxis and intercept c on the yaxis is y = mx  c, where m = tan θ
If A is a nonzero column matrix of order m x 1 and B is a nonzero row matrix of order 1 x n, then rank of AB is equal to
Minimum area of the triangle formed by any tangent to the ellipse with the coordinate axes is
Which of the following relations among the locations parameters does not hold?
Two tangents are drawn from the point (2,1) to the parabola y^{2}=4x. If α is the angle between them, then tan α =
A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is
In a Poisson distribution the variance is m. The sum of the terms is odd places in this distribution is
2R ― OH + 2Na → 2RONa + H₂. In the above reaction the reactivity of different alcohols is
A chloride dissolves appreciably in cold water. When placed on a platinum wire in Bunsen flame no distinctive colour is noticed, the cation would be
The configuration of X is 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{10} 4s^{2} 4p^{3}. Its properties are similar to
The effect of atoms or groups loosing electrons towads a carbon atom is called
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 correct order of the O―O bond length in O_{2}, H_{2}O_{2} and O_{3} is___
The bond length of O―O bond in O_{3} (1.278Å) is intermediate that for a single bond in H_{2}O_{2} (1.48 Å) and for a double bond in O_{2} (1.121 Å).
Which of the following compound has a linear structure?
The enthalpies of combustion of carbon and carbon monoxide are 393.5 and 283 KJ mol⁻^{1} respectively .The enthalpy of formation of carbon monoxide per mol is
A chemical reaction is catalyzed by a catalyst X. Hence X
The activation energy of a reaction can be determined by
Heat of combustion ΔH for C(s), H_{2}(g) and CH_{4}(g) are 94, 68 and 213 cal/mol. Then ΔH for C(s) + 2H_{2}(g) → CH_{4}(g) is
CH_{4} + 2O_{2} = CO_{2} + 2H_{2}O
ΔH = 213 cal/mol .....(1)
C + O_{2} = CO_{2}
ΔH =  94 cal/mol .....(2)
H_{2} + (1/2) O_{2} = H_{2}O
ΔH =  68 cal/mol .....(3)
ΔH for C(s) + 2H_{2}(g) → CH_{4}(g)
= 2(eq 3) + (eq 2)  (eq 1)
= ( 68 x 2) + ( 94)  ( 213) = 17Kcal
In the reaction CH_{2}COOH_{aq} + OH_{(aq)} → CH_{3}COO^{} + H_{2}O_{(l)} ; ΔH = 55.2kJ mol^{1} What is the heat of dissociation (in kJ mol^{1}) of acetic acid?
ΔH = 55.2 KJ.mol^{1}
[H^{+} _{(aq)} + OH^{} _{(aq)} → H_{2}O_{(l)} ΔH = 57.3 KJ .mol^{1}]]
CH_{2}COOH_{aq} → CH_{3}COO^{} _{(aq)} + H^{+} _{(aq)} ΔH = ?
CH_{2}COOH_{(aq)} + OH^{} _{(aq)} → CH_{3}COO^{} _{(aq)} + H_{2}O_{(l)} ΔH = 55.2 KJ .mol^{1}
H^{+} + OH^{} _{(aq)} →  H_{2}O_{(l)} ΔH = + 57.3KJ .mol^{1}
CH_{3}COOH_{(aq)} → CH_{3}COO^{} _{(aq)} + H^{+}_{(aq)} ΔH = 2.1 KJmol^{1}
Which of the following is an example of intensive property?
Which of the following is an isomers of propanal ?
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.
Which of the following is the correct order of ionic radii?
Na^{+}, Mg^{2+}, Al^{3+} and Si^{4+} are isoelectronic cations with 10 electrons, but when we go from Na^{+} to Si^{4+}, one unit nuclear charge increases. Thus, the ionic size of isoelectronic species is compared on the basis of their atomic number/number of electrons, i.e. Z/e ratio. Smaller the value of Z/e, larger the size of the species. For example,
Among the following complexes, optical activity is possible in__
Optical isomers of [Co(NH_{3})_{2}(H_{2}O)_{2}Cl_{2}] are
Which of the following belongs to the actinide series?
The charge required to liberate 112 ml of hydrogen from acidified water is
In electrorefining of copper a minor percentage of gold accumulates in
A gaseous mixture of three gases A, B and C has a pressure of 10 atm. The total number of moles of all the gases is 10. If the partial pressures of A and B are 3.0 and 1.0 atm respectively and if C has a mol. wt. 2.0. What is the weight of C in gms present in the mixture?
In which of the following reactions, H₂O₂ acts as a reducing agent?
Which of the following compounds does not exist ?
Which of the following possesses highest melting point?
When ethylene glycol is heated with acidified potassium permanganate, the main organic compound obtained is:
Relatives stabilites of the following carbocation will be in order :
In the addition of HBr to propene in presence of peroxide, most stable free radical formed is :
Increasing order of acid strength among pmethoxyphenol, pmethylphenol and pnitrophenol is
Electron withdrawing groups increase the acid strength while electron releasing groups decrease the acid strength of the phenol.
NO_{2} group is strongly withdrawing group while CH_{3} is mildly releasing and OCH_{3} is strongly releasing group. Thus, pmethoxyphenol is the weakest acid while pnitrophenol is the strongest acid among the given compounds.
The molecule which shows optical isomerism is
The decay constant λ of the radioactive sample is the probability of decay of an atom in unit time, then
A radioactive substance decays to 1/16th of its initial activity in 40 days. The halflife of the radioactive substance is
By increasing the temperature, the specific resistance of a conductor and a semiconductor
On increasing the temperature of a conductor, its resistance increases because
An electron and a proton have same deBroglie's wavelength. The kinetic energy of an electron is
During Xray formation if voltage is increased
An electromagnetic wave of frequency 3 MHz passes from vacuum into a medium with dielectric constant k = 4. Then
Minimum no. of 8 μF and 250 V capacitors, used to make a combination of 16 μF and 1000 V, is
If 1000 droplets each of charge q and radius r are mixed to form a big drop, then the potential of big drop, as compared to small droplet will be
If the value of potential on each small drop be V and potential on each small drop be V ^{'}
V ^{'} = n ^{2/3} V
⇒ V ^{'} = 1000 ^{2/3} V
The gravitational potential energy of a body (in earth's field) is minimum
If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is
A black body, at a temperature of 227ºC, radiates heat at a rate of 84 Jm⁻^{2}s⁻^{1}. When its temperature is raised to 727ºC, the heat radiated by it in Jm⁻^{2}s⁻^{1} will be
The energy spectrum of a black body exhibits a maximum around a wavelength λ₀. The temperature of the black body is now changed such that the energy is maximum around a wavelength 3λ₀/4. The power radiated by the black body will increase by a factor of
If 10% of the current passes through a moving coil galvanometer of resistance 99 ohm, then the shunt resistance will be
A particle under the action of a constant force moves from rest upto 20 seconds. If distance covered in first 10 seconds is s₁ and that covered in next 10 seconds is s₂, then
Two simple pendulums of length 0.5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed... oscillations
In the following question, a Statement1 is given followed by a corresponding Statement2 just below it. Read the statements carefully and mark the correct answer
Statement1:
If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.
Statement2:
The linear momentum of an isolated system remains constant
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 principle of homogeneity of dimensions state that dimensions on both sides of equation must be same
Reason (R) : An equation which is dimensionally correct is also practically correct
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): Two spherical conductors A and B having different potentials are separated by a long distance so that they can be considered as isolated. Then charge flown through the wire, to equilize the potentials of A and B as a result some current flows through connecting wire for sometime. During this time over Ampere's loop is zero.
Reason(R) : According to Ampere's circuital law, over any closed path is equal to the number of times the net current enclosed by the loop provided the electric field over the region of ampere's loop is remains constant.
The upper end of wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle an angle of 30º. Then angle of shear is
Motion of a liquid in a tube is described by
The distance between eye lens and cross wire in Ramsden eye piece which has a field lens of focal length 1.2 cm is .......cm.
A body having moment of inertia about its axis of rotation equal to 3 kgm^{2} is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed of
When the potential energy of a particle executing simple harmonic motion is onefourth of the maximum value during the oscillation, its displacement from the equilibrium position in terms of its amplitude a is
The internal energy of a gas, during isothermal expansion
If the ratio of the densities of two monoatomic gases is 16 : 9, the ratio of the velocities of sound in them is
An ideal gas A and a real gas B have their volumes increased from V to 2V under isothermal conditions. The increase in internal energy
In Huygen's wave theory, the locus of all points oscillating in the same phase is called a
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