When the function f(x) = sin 2x(1 + cos 2x) has a maximum, one value of x is equal to
The area bounded by the curve y = x3 , x-axis and two ordinates x = 1 to x = 2 is equal to
The roots of the equation
If A, B, C are represented by 3 + 4i, 5 - 2i, -1 + 16i respectively, then A, B, C are
If α , β are two different complex numbers such that | α | = 1, | β | = 1, then the expression | β − α /1 − α β | equals
is continuous at π/4 , then a =
Consider f (x) = x2 /| x | , x ≠ 0, f(x) = 0, x = 0
The area bounded by the curve y = x2 - 4x, x-axis and line x = 2 is
Find the degree of (y2)2 − √y1 = y3
The solution of differential equation (xdy/dx)=y+x2 is
The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively
The differential equation of the family of curves y2=4a (x+a) is
If x=a(t-sint) and y=a(1-cost), (dy/dx)=
If f(x) is an odd periodic function with period 2, then f(4) equals :
∫tan-1x dx =
If tan-1x + tan-1y + tan-1z = π, then x+y+z is equal to
A function f(x) is defined as f (x) = [ 1 − x2 ] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because
The sentence "____ if and only if x + x = 3x" is TRUE.
"if and only if" is TRUE when both conditions are the SAME truth value. Since "x + x = 3x" is false, the first condition must also be false. 2x - x = 2x is false.
A and B are square matrices of the same order. Which is correct?
If A and B are two matrices such that AB=B and BA=A, then A2+B2=
If nPr=840, nCr=35, then n=
A biased coin with probability p,0<p<1 of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is 2/5, then p equals
In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are
In four schools B₁, B₂, B₃, B₄ the percentage of girls students is 12, 20, 13, 17 respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is B₂, is
If the side of a triangle are 13, 14, 15, then the radius of the incircle is
The fourth ,seventh and tenth of a G.P. are p,q,r respectively then
Two numbers within the brackets denote the ranks of 10 students of a class in two subjects - (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is
The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1, 2 and 6, the other two observations are
The one roots of the equation 2x5-14x4+31x3-64x2+19x+130=0 is
The equation of the sphere concentric with the sphere x2+y2+z2-4x-6y-8z=0 and which passes thro' (0.1,0) is
If α , β , γ are the roots of the equation x3 − 6 x2 + 11 x + 6 = 0, then Σ α2 β + Σ α β2 =
The locus of the point of intersection of tangents to the circle x = a cos θ, y = a sin θ at the points, whose parametric angles differ by π/2 is
The radius of the circle
3x (x - 2) + 3y (y + 1) = 4 is
In three dimensional space, the equation 3y+4z=0 represents
If vectors 2i+j+k and i-4j+λk are perpendicular, then λ=
If the solution for θ of cospθ + cosqθ = 0, p > 0, q > 0 are in A.P., then the numerically smallest common difference of A.P. is
Given cospθ = - cosqθ = cos (π + qθ)
⇒ pθ = 2nπ (π + qθ), n ∈ I
⇒ θ = (2n + 1)π/p - q or (2n - 1)π/p + q , n ∈ I
Angle θ = (2n + 1)π p - q given us an AP with common
difference 2π/p - q and θ = (2n - 1)π/p + q gives also an AP with common difference 2π/p + q
Then, certainly, 2π/p + q < | 2π/p - q |
∴ The smallest common difference is 2π/p + q
The projection of the vector î - 2 ĵ + k̂ on the vector 4 î - 4 ĵ + 7 k̂ is
Sodium has body centred packing. Distance between two nearest atoms is 3.7 Å . The lattice parameter is:
For series LCR circuit, wrong statement is
The closest distance of approach of an α - particle travelling with a velocity 'V' to a certain nucleus is 'x'. The distance of closest approach of α - particle travelling with a velocity 3V to the same nucleus is
A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitors becomes
On removing the oil, the capacitance of the capacitor will become.
C ′ = C/K = C/2
A steady current of 1.5 A flows through a copper voltameter for 10 min. If the electrochemical equivalent of copper is 30 x 10-5 g C-1 , the mass of copper deposited on the electrode will be
A laser beam is used for carrying out surgery because it
As the laser beam is highly monochromatic, directional and coherent, it can be sharply focussed.
Therefore it is used for carrying out surgery
EMF is most closely related to
Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be
Taking the internal resistance of the battery as negligible, the steady state current in the 2 Ω resistor shown in the figure will be
If two identical heaters of 220 V, 1000 W are placed parallel to each other across 220 V lines, then the combined power of the heaters is
In a D.C. motor induced e.m.f will be maximum
The approximated wavelength of a photon of energy 2.48eV is
A 5 cm long solenoid having 10 cm resistance and 5 mH inductance is joined to a 10 V battery. At steady state, current through solenoid is
At steady state, inductance is ineffective
I = V/R = 10/10 = 1A
When the current in a coil is changed from 10 A in one direction to 10 A in opposite direction in 0.5 s, an e.m.f. of 1 V is induced in it. Self-inductance of the coil is
Out of the folowing statement which is NOT true?
If the electric flux entering and leaving an enclosed surface respectively is φ₁ and φ₂, the electric charge inside the surface will be
Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given by
Two equal charges, q each are placed at a distance of 2a, and a third charge -2q is placed at the mid point. The potential energy of the system is
The capacitance of a parallel plate capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/2 is inserted between the plates (where d is separation between the plates). The dielectric constant of the slab is
If an unchanged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is
The inward and outward electric flux of a closed surface are 8x103 C and 4x103 C respectively. The net charge inside the closed surface is
A 10 A ammeter has a resistance of 0.09 Ω. What resistance of the shunt will enable it to read up to 100 A?
The first atomic reactor was constructed by
The half life period of radio - active isotope is 5 minutes. The fraction of isotope, that will be remaining after 30 minutes is
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:
When a metallic surface is illuminated by a monochromatic light of wavelength λ, then the potential difference required to stop the ejection of electrons is 3V₀. When the same surface is illuminated by the light of wavelength 2λ, then the potential difference required to stop the ejection of electrons is V₀. Then for photoelectric effect, the threshold wavelength for the metal surface will be
The work function of a metal is 2.8 eV. Its threshold wavelength will be
A telescope consists of two thin lenses of focal lengths 0.3 m and 3 cm respectively. It is focused on moon which subtends an angle of 0.50 at the objective. Then, the angle subtended at the eye by the final image will be
Ultra-violet rays are detected by
In the middle of the depletion layer of a reverse-biased p-n junction, the
The method of connecting the negative pole of battery to p - material and positive pole to n - material of a p - n junction is called
Rectifier is used to convert
The band gap in Germanium and silicon in eV respectively is
When germanium atoms is doped with equal no. of antimony atoms, we get a/an
Suitable impurities are added to a semiconductor depending on its use. This is done to
At room temperature, a p-type semiconductor has
In interference pattern, the energy is
Young's double slit experiment gives interference fringes of width 0.3mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes
Which one of the following properties of light does not support wave theory of light?
If ratio of amplitude of two waves is 4:3, then ratio of maximum and minimum intensity is
Ethyl alcohol can be used for preparation of which of the following?
Aldol condensation will not be observed in
The base-catalysed aldol condensation will not occur with
Which of the following reaction cannot be used for the conversion RCO → RCH₂
Tetrabromomethane on treatment with Zn gives
The product formed by the action of chlorine on ethene in saturated solution of KBr is/are
In the following reaction, which choice has value twice that of the equivalent mass of the oxidising agent SO₂ + H₂O → 3S + 2H₂O
Which species represents the electrophile in aromatic nitration?
Chargaff's rule states that in an organism
Ethyl alcohol reacts with acetyl chloride to form
A certain compound gives negative test with ninhydrin and positive test with Benedict's solution. The compound is
Rancidity of butter is due to the formation of
From the following values of dissociation constants of four acids which value represents the strongest acid ?
The chemical equilibrium of a reversible reaction is not influenced by
In the case of gaseous homogeneous reaction,the active mass of the reactant is obtained by the expression
The internal energy of a subtance does not depend upon
A compound with molecular formula C₇H₁₆ shows optical isomerism , the compound will be
Which of these is a hypnotic?
The heat of formation of the compound in the following reaction is H₂(g) + Cl₂(g) → 2HCl(g) + 44 kcal
Calculate Δ H in KJ for the following reaction C(s) + O2 g → CO2 g Given that
H2O g + C g → CO g + H2 g , Δ H = + 131 k J
CO g + 1/2 O2 g → CO2 g , Δ H = − 282 k J
H2g + 1/2 O2 g → H2O g , Δ H = − 242 k J
The complex CoCl₃.3NH₃ ionises to give
The oxidation state of Cr in [ Cr (NH3)4 Cl 2 ] + is :
Which of the following is produced by reaction of RCN in sodium and alcohol ?
Diazo coupling is useful to prepare
Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN⁻ ion towards metal species is
Calculate the amount of change flowing in 2 minute in a wire of resistance 10 Ω when a potential difference of 20 V is applied
On heating quick lime with coke in an electric furnace, we get
Diethyl ether can be decomposed by
The standard reduction potential at 298 K for the following half cell reaction are given below
Zn2+ + 2e- → Zn E0 = − 0.762 V
Cr+3 + 3 e- → Cr E0 = − 0.740 V
2 H+ + 2 e- → H2 E0 = − 0.0 V
Fe+3 + e- → Fe+2 E0 = − 0.770 V
Which one is the strongest reducing agent?
Lead sulphate is souble in
The largest bond angle is in
If the pressure and absolute temperatre of 2 litres of CO₂ are doubles, the volume of CO₂ would become
Which one of the following is pyrophosphoric acid?
Which substance is serving as a reducing agent in the following reaction? 14H⁺ + Cr₂O₇2- + 3Ni → 2Cr+3 + 7H₂O + 3Ni+2
Following compounds are respectively ... geometrical isomers
A face-centred cubic element has a edge length of 400 pm. What is its density? At. weight of element= 60)
The adsorption of hydrogen by palladium is called
Colourless solutions of the following four salts are placed separately in four different test tubes and a strip of copper is dipped in each one of these. Which solution will turn blue ?
Highest oxidation state of transition element is
Find the antonym of CORPULENT
Fill in the blank with appropriate word.
You will have to face some practical problems when you start.........this plan.
Find the Synonym of LANGUISHING
Choose the alternative which best expresses the meaning of the idiom/phrase.
To be under a cloud
Improve the sentence by choosing best alternative for capitalised part of the sentence.
He has very good command ON English.