If x = a (θ + sinθ), y = a(1 - cosθ), then at θ = π/2, the length of the normal is
Area bounded by parabola y2 = x and st.line 2 y = x is
If w3 = 1 and w ≠ 1, then (1 + w)(1 + w2)(1 + w4)(1 + w8) =
If R → R is continuous such that f (x + y) = f(x) + f(y), ∀ x ∈ R , y ∈ R , and f(1) = 2 then f(100) =
If α and β are real them
The area of the curve |x|+|y|=4 is
If the function f is defined by f(x) = x/1 + | x | then at what points is f differentiable
Which of the following is a solution of the differential equation ( dy/dx )2 - x dy/dx + y = 0
( d/ dx )2 - x . dy/dx + y = 0
y = 2x - 4
∴ dy dx = 2
So, ( dy dx )2 - x . dy dx + y
= (2)2 - x x 2 + 2x - y
= 4 - 2x + 2x - y
The solution of the differential equation cos(x + y)dy = dx is
(d2y/dx2)2 + x(dy/dx)2 is a differential equation of
4[cot-13 + cosec-1(√5)] is equal to
The function f(x) = x3 - 3x2 - 24x + 5 is increasing in the interval
The solution of differential equation 2y sin x(dy/dx)=2 sinx cosx - y2 cosx; x=(π/2), y=1, is
The value of is equal to
If a , b , c are positive then
then a =
The order of the matrix A is 3 x 5 and that of B is 2x3 . The order of the matrix BA is
Which of the following is not a statement in logic ?
1. Earth is planet .
2. Plants are living object .
3. √-3 is rational number .
4. x2 - 5x + 6 < 0, where x ∈ − R
If all the elements of a 3 x 3 matrix A are 1, then A2 → 3 A is
How many words can be formed by taking letters 4 at a time out of letters of the word MATHEMATICS?
A die is thrown 100 times. If getting an even number is considered a success, then the variance of the number of successes is
A card is taken out of a pack of 52 cards numbered 2 to 53. The probability that the number on the card is a prime number less than 20 is
Of cigarette smoking population 70% are men and 30% are women, 10% of these men and 20% of women smoke wills. Probability that a person seen smoking a wills to be male is
If in any ∆ABC, a=(√3+1)cm and ∠B=300, ∠C=450, then the area of triangle is
a, b, c are three unequal numbers such that a, b, c are in A.P. ; b - a, c - b, a are in G.P., then a : b : c : :
Since a, b, c are in A.P.,
∴ b - a = c - b
Also b - a, c - b, a are in G.P
∴ (c - b)2 = (b - a)a
⇒ (b - a)2 = (b - a)a
⇒ b - a = a
⇒ b = 2a
Also c = 2b - a = 2(2a) - a = 3a
∴ a : b : c = a : 2a : 3a = 1 : 2 : 3
The median of 10, 14, 11, 9, 8, 12, 6 is
The mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0, is
If the roots of 4x3 − 12x2 + 11 x + k = 0 are in A.P. then k =
If the roots of the equation (2k+1)x2 - (7k-3)x+k+2=0 are reciprocal of each other, the value of k is
A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be
The equation of the sphere concentric with the sphere
x2 + y2 + z2 - 4x - 6y - 8z - 5 = 0 and which passes through the point (0, 1, 0) is
If tan (cotx) = cot(tanx), then sin2x is equal to
Locus of mid point of the portion between the axes of x cosα + y sinα = p where p is constant is
Two tangents are drawn from the point (-2, -1) to the parabola y2 = 4x. If α is the angle between these tangents, then tan α =
A unit vector perpendicular to each of the vectors (-6î+8k̂), (8î+6k̂) forming a right handed system is
The projection of the vector î - 2 ĵ + k̂ on the vector 4 î - 4 ĵ + 7 k̂ is
A circuit consists of a resistor, an inductor and a capacitor connected in series. If resistance of the resistor is 25 Ω and the value of inductive reactance is equal to capacitive reactance, then net impedance of the circuit will be
The force experienced by the cathode rays when they pass through an electric field of intensity E → is
In photo electric effect the stopping potential is
In the photoelectric effect is that the stopping potential is a function of the frequency of the incident light. As shown in Figure, there is even a cutoff frequency ν0 below which there is no photoelectric effect occurs, regardless of the intensity of the light.
A plot of stopping potential vs. frequency of incident light (Cathode: Sodium ; Cutoff frequency νo =4.39x 1014 Hz
Hence option (A) is correct.
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
The thickness of the foil is negligible
For electroplating a spoon, it is placed in the voltameter at
In short wave communication waves of which of the following frequencies will be reflected back by the ionospheric layer having electron density 1011 per m-3?
N max = 1011 per m-3
Which statement is true ?
(i) Kirchhoff's law is not equally applicable to both AC and DC.
(ii) Semiconductors have a positive temperature coefficient of resistance.
(iii) Meter bridge is least sensitive when the resistance of all the four arms of the bridge are of the same order .
(iv) The emf of a cell depends upon the size and area of electrodes.
The resistance of series combination of two equal resistances is S. When they are joined in parallel, the total resistance is P. If S=nP, then the possible value of n is
A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength 20 Vm-1 and 0.5 T at right angles to the direction of motion of the electrons. What is the velocity of the electrons ?
The internal resistance of a cell is the resistance of
A transformer is employed to
The induced e.m.f. produced in the primary and secondary coils is 2 mV and 5 mV respectively. If the rate of change of current is 20 A-s-1, then coefficient of mutual induction of the secondary coil is
A transformer is having 2100 turns in primary and 4200 turns in secondary. An a.c. source of 120 V, 10 A is connected to its primary. The secondary voltage and current are :
Which of the following has the minimum frequency?
Eight dipoles of charges of magnitude e are placed inside a cube. The total electric flux coming out of the cube will be
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
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
An infinite no. of capacitors with capacitances 1μF, 1/21μF, 1/41μF, 1/81μF, ...etc. are connected in parallel combination. Their equivalent capcitance will be
A point charge Q is placed at a distance d from the centre of an uncharged conduction sphere of radius R. The potential of the sphere is d > R :
A long solenoid has a radius a and number of turns per unit length is n. If it carries a current I, then the magnetic field on its axis is directly propotional to
When P1530 decays to become Si1430 the particle released is
A body of capacity 4 μ F is charged to 80V and another body of capacity 6 μ F is charged to 30V. When they are connected the energy lost by 4 μ F is
E1 = 1/2 C1V2; E2 = 1/2 C2V2
If M(A;Z), M p and M n denote the masses of the nucleus Z A X , proton and neutron respectively in units of u (1u=931.5 MeV/C2) and BE represents its bonding energy in MeV, then
When a beam of light is used to determine the position of an object, the maximum accuracy is achieved if the light is
Fraunhofer spectrum is a
When A is the internal stage gain of an amplifier and β is the feedback ratio, then the amplifier becomes as oscillator if
In a common-base amplifier, the phase difference between the input signal voltage and output voltage is
A common-emitter amplifier is shown in the figure (A).
In this Circuit , the output signal is an amplified version of the input signal and is 180 degrees out of phase with the input signal.
Common emitter Amplifier
Common Base Amplifier
Figure (B) is a common-base amplifier. In this circuit the output signal is an amplified version of the input signal and is in phase with the input signal. In both of these circuits, the output signal is controlled by the base-to-emitter bias. As this bias changes (because of the input signal) the current through the transistor changes.
In a P-N junction diode
To obtain p - type extrinsic semiconductor, the impurity element to be added to Germanium should be of valence
Which of the following statement is true about p-type semiconductors?
When the conductivity of a semiconductor is only due to breaking of covalent bonds, the semiconductor is called
In P-type semiconductor, there is
Bright colours exihibited by spider's web exposed to sun light are due to
When distance between source of light and observer decreases, then the apparent frequency of light
Who was the first to demonstrate the phenomenon of interference of light?
A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is
Which of the following compounds can exist in optically active form?
Treatment of furfural with NaOH yields
When acetaldehyde is treated with Fehling's solution, the following precipitate is formed
Wurtz reaction involves the interaction of alkyl halides in dry ether with
Carbonyl compounds undergo nucleophilic addition because of
1-Butene may be converted to butane by reaction with
The number of atoms contained in 11.2 L of SO₂ at S.T.P. are
The most stable free radical among the following is
Which carbohydrate is used in silvering of mirrors?
Which amino acid is achrial?
Cane sugar on hydrolysis gives
Melting points are normally the highest for
From the following values of dissociation constants of four acids which value represents the strongest acid ?
What is the main reason for the fact that carboxylic acids can undergo ionization?
A reversible reaction is said to have attained equilibrium, when
A reaction reaches a state of chemical equilibrium only when
100cc of 0.1M HCl and 100cc of 0.1 M NaOH solutions are mixed in a calorimeter. If the heat liberated is 'Q' kcal, the heat of neutralization ( Δ H ) (in kcal) of HCl(aq) and NaOH(l) is
Which of the following is an extensive property?
What is the amount of heat liberated (in k.cal) when one mole of aquesous NaOH reacted with one mole of aqueous HCl solution?
Synthetic detergents are sodium salts of long chain
A chiral compound is
In the compound lithium tetrahydroaluminate, the ligands are
In Fe(CO)5 , the Fe ---- C bond possesses
Diazo coupling is useful to prepare
In the presence of acid, the hydrolysis of methyl cyanide gives
The equivalent conductivity of 0.1 M weak acid is 100 times less than that at infinite dilution.The degree of dissociation is
A current liberates 0.504 g of hydrogen in 2 hours, the amount of copper liberated from a solution of CuSO₄ by the same current flowing for the same time would be
Which of the following statements is incorrect?
Ether which is liquid at room temperature is
Which of the following is most dense?
The internal energy of one mole of an ideal gas is given by
A crystal lattice with alternate positive and negative ions has radius ratio 0.524. Its coordination number is
Radius ratio of the given crystal lattice is in the range of 0.414 - 0.732. So the coordination number is 6.
Oxidation state of + 1 for P is found in
While phosphorus forms PCl5, nitrogen does not form NCl5 because
Which acts as both oxidising as well as reducing agent ?
Collodial solution of arsenious sulphide is prepared by
Following configuration of the tartaric acid represents
The + 3 ion of which one of the following has half-filled 4f subshell ?
An important ore of copper is
Find the Antonym of TACTFUL
Fill in the blank with appropriate word.
I.......missed the train this morning as I got up late
Find the synonym of OBSTREPEROUS
Fill in the blanks with the most suitable idiom/phrase.
Let us now _____ and work for the advancement of the country .
Improve the sentence by choosing best alternative for capitalised part of the sentence.
Let's buy a new sari with the annual bonus, CAN WE ?