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The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the xaxis is
The 10th term of the expansion of (x1)^{11} (in decreasing powers of x) is
x=7 touches the circle x^{2} + y^{2}  4x  6y  12 = 0, then the coordinates of the point of contact are
The complex numbers 1,1,i√3 form a triangle which is
The volume of a solid which is obtained by revolving area bounded by an ellipse x^{2}+9y^{2}=9 and straight line x+3y=3 about yaxis is
where [x] denotes the greatest integer less than or equal to x, is continuous at x = 2, then the value of a is equal to
If x/a + y/b = √2 touches the ellipse (x^{2}/a^{2}) + (y^{2}/b^{2}) =1, then its eccentric angle θ is equal to
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): In the binomial expansion of (ab)^{n} , n ≤ 5, the sum of the 5th and 6th terms is zero, then
Reason(R): In the expansion of (x+y)^{n}, (r+1) th term from the beginning is called the general term T_{r+1} T_{r+1} = ^{n}C, x^{nr} y^{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):The function
is increasing function.
Reason(R): A function f(x) is said to be an increasing function (or monotonically increasing) at an interval a < x < b, if for any two points x_{1} and x_{2} of the interval f(x_{1}) < f(x_{2}) when x_{1} < x_{2}.
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): A student is allowed to select at the most n books from a collection of (2n+1) books. If the total number of ways in which he can select a book is 63, then n is 3.
Reason(R): By the property of
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): Equation of a straight line through the point (3,1,6) and parallel to each of the two planes 2x  3y + z + 5 = 0 and x + y + 2z = 2 is
Reason(R): The required line will be parallel to the line of intersection of the two planes.
The pole of the straight line x − 2y + 4 = 0 with respect to the parabola y^{2} = 6 x is
The numbers of all words formed from the letters of the word CALCUTTA is
No of letter in the given word is 8
No of repeated word is "C" 2 times, "A" 2 times and "T" 2 times. So the equation is
Minimum area of the triangle formed by any tangent to the ellipse with the coordinate axes is
If log(a + c), log(c  a), log (a  2b + c) are in A.P., then
The angle between two diagonals of a cube is
The correct order of boiling points for primary (1º), secondary (2º) and tertiary (3º) alcohols is
The metal ion which is precipitated when H^{₂}S is passed with HCl is
The most reactive nucleophile among the following is
Although due to +I effect of methyl groups, (CH_{3})_{2} CHO and (CH_{3})_{3} CO are stronger bases but due to steric hindrance both are weaker nucleophiles than CH_{3}O
Further due to resonance, C_{6}H_{5}O
is the weakest nucleophile
CH_{3}O is most reactive (stronger) nucleophile
The molecule which has zero dipole moment is
Which of the following species is paramagnetic?
Which of the following will have the shape of trigonal bipyramid?
PF_{3}Cl_{2} has triogonal bipyramidal geometry. IF_{5}, BrF_{5} and have octahedral geometries with one position occupied by a lone pair of electrons.
The equilibrium between water and its vapour, in an openvessel
In an open vessel, the water vapour diffuse into air and therefore, the concentration of water vapour above water surface is negligible.
The reverse process of condensation of vapour into liquid form is almost absent.
Therefore, evaporation process continues, till the entire water changes into vapour form.
Therefore, in an open vessel, the water vapour system is never in equilibrium.
Finally the whole water will diffuse into air as water vapour.
The heat of combustion of graphite and carbon monoxide respectively are 393.5 kJ mol⁻^{1} and 283 kJ mol⁻^{1}. Thus, heat of formation of carbon monoxide in kJ mol⁻^{1} is
The rate of a reaction can be increased in general by all the factors except by
A Carnot engine has an efficiency of 20%. If energy is fed into the engine at the rate of 1 kW, then the output of the engine is
Which of the following IUPAC names is correct?
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 system has maximum number of unpaired electrons?
Distribution of delectrons in weak field or high spin complex in tetrahedral field for d^{6} ion is thus there are four unpaired electrons.
d^{9} (octahedral) = no of unparied electron is one
d^{4} (octahedral, low spin) no of unpaired electron is one
d^{7} (octahedral, high spin) no of unparied electron is three.
Which of the following has highest first ionization potential?
Nitrogen has highest first ionization potential. This is because N contains exactly halffilled porbitals which is extra stable. hence its first ionisation potential is high.
Electronic configuration of N:
The tendency to form complex compounds is maximum for
Which is the best description of the behaviour of bromine in the reaction: H₂O + Br₂ → HOBr + HBr?
Conductivity (Unit:siemen's S) is directly proportionally to the area of the vessel and the concentration of the solution in it and is inversely proportional to the length of vessel,then the unit of constant of proportionally is
What is the temperature of hydrogen gas, which has the same r.m.s. velocity as that of oxygen at a temperature of 0ºC?
If an isotope of hydrogen has two neutrons in its atoms,its atomic number and atomic mass number will respectively be
Which of the following compounds will be most easily attacked by an electrophile ?
CH_{2}═CHCH_{3}
undergoesfreeradicalsubstitutionusingNBS.Productformedis:
What amount of bromine will be required to convert 2 g of phenol into 2, 4, 6Tribromophenol?
Consider the following statement:
"In a sample of butane at room temperature, none of the molecules will be in the least stable conformation".
The conformations of butane differ in their relative stabiliities. The antiperiplanar has minimum repulsion between the groups attached tetrahedrally to the two carbon atoms. In synclinal (gauche) conformations, methyl groups are so close that they repel each other, as a result is has 3.8 kJmol^{1} more energy than anti conformation. similarly, synperiplanar is least stable having energy 18.4 kJ mol^{−1} than anti conformation. Thus, at room temperature, the more stable ones will have larger populations.
The ratio of minimum to maximum wavelength in Balmer series is
From Bohr's theory for hydrogen atom
In which of the following systems will the radius of the first orbit (n = 1) be minimum?
Identify that set in which all the three sustances are good conductors of electricity
The power of an electric bulb marked as 40 W and 200 V used in a circuit of supply voltage 100 V will be
The curve drawn between velocity and frequency of photon in vacuum will be a
When a charged oil drop moves upwards in an electric field, the electric force acting on the drop is
Out of the folowing statement which is NOT true?
A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
If radius of the earth contracted 2% and its mass remains the same then weight of the body at the earth surface
On gradually, increasing the temperature of a substance, you will notice which of the following colour?
On a cold morning, a metal surface will feel colder to touch than a wooden surface because
A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (vertically). If the acceleration of the system is (g/8), then the ratio of masses is
The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)
A body thrown with an initial speed of 96 ft/sec reaches the ground after (g=32 ft/sec^{2})
A simple pendulum of length l has a bob of mass m, with a charge q on it. A vertical sheet of charge, with surface charge density σ passes through the point of suspension. At equilibrium, the spring makes an angle θ with the vertical. its time period oscillations is T in this poisiton. Then
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 velocitytime graph is a straight line parallel to time axis, then acceleration of body is zero.
Reason(R): Acceleration is equal to rate of change of velocity (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): A ball of mass m fails from a height and bounces back to same height. Contact force is equal to rate of change of momentum.
Reason(R): Contact force is upwards.
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 blocks of masses m_{1} and m_{2} are at rest. They are moving towards each other under the mutual internal force. The velocity of centre of mass is zero.
Reason(R): If no external force acts on the system, then velocity of centre of mass is unchanged but can never be zero.
In a plant a sucrose solution of coefficient of viscosity 0.0015 N s/m^{2} is driven at a velocity of 10⁻^{2}m/s through xylem vessels of radius 2 μ m and length 5 μ m. The hydrostatic pressure difference across the length of xylem vessels, in N/m^{2} is
When red glass is heated in dark room, it will seem
An object of weight W and density ρ is submerged in a fluid of density ρ₁. Its appearent weight will be
A mass M is moving with a constant velocity along a line parallel to xaxis. Its angular momentum with respect to origin or zaxis is
Amplitude of vibration of any particle in a standing wave produced along a stretched string depends on
A spring of force constant K is cut into two equal parts. Then the force constant of each piece is
Water falls from a height of 210 m. Assuming whole of energy due to fall is converted into heat the rise in temperature of water would be (J = 4.3 Joule/cal)
If the door of a refrigerator is kept open, then which of the following is true
The difference in the lengths of a mean solar day and sidereal day is about
Which one of the following properties of light does not support wave theory of light?
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