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For the curve x = t^{2}  1, y = t^{2}  t tangent is parallel to xaxis where
If ω is a complex cube root of unity ,then the value of ω ^{99} + ω ^{100} + ω^{101} is
The differential equation representing the family of curves y^{2}=2c(x+√c), where c is a positive perimeter, is of
and A_{1} , B_{1} , C_{1} etc are cofactors of a 1 , b 1 , c 1 , then
If c is parameter then the differential equation whose solution is y = c^{2} + c/x is
If cot^{1}[(cos α)^{1/2}]  tan^{1}[(cot α)^{1/2}] = x, then sin x =
where [x] denotes the greatest integer not exceeding x, then
Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?
To form the INVERSE of a statement, insert "NOT" into the "If" and the "then" sections of the sentence.
A and B are square matrices of the same order. Which is correct?
If A represents the determinant of a square matrix of order 3 then (2A)=
From a box containing 10 cards, numbered 1, 2,3,......,10. Four cards are drawn together, what is the probability of their sum is even ?
The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies is
A committee of 6 members is to formed from 8 gentlemen and 4 ladies by taking
(i) 3 lady out of 4 and 3 gentlemen out of 8
(ii) 4 lady out of 4 and 2 gentlemen out of 8
In case (i) the number of ways = ^{4}c_{3} x ^{8}c_{3}
= 4 x 56 = 224
In case (ii) the number of ways = ^{4}c_{4} x ^{8}c_{2}
= 1 x 28 = 28
Hence, the required number of ways = 224 + 28 = 252
The probabilites of solving a problem by three students A, B, C independently are 1/3 , 1/4 , 1/5 . The probability that the problem will be solved is
If A and B are two mutually exclusive events such that P(B) = 2P(A) and A ∪ B = S. Then P(A) is equal to
The harmonic mean of the roots of the equation (5 + √2)x^{2}  (4 + √5)s + 8 + 2√5 = 0 is
⇒ cos (A/2) = cos [(B  C)/2]
⇒ A/2 = (B  C)/2
⇒ A = B  C
⇒ A + C = B
⇒ B = 90^{0}.
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
If the roots of the equation x^{2}+2mx+m^{2 }2m+6=0 are equal, then the value of m is
If there is a multiple root of order 3 for the equation x^{4} − 2x^{3} + 2 x − a = 0 , then the other roots is
The line (p + 2q) x + (p  3q) y = p  q for different values of p and q passes through the fixed point
In a three dimensional space, the equation 3x  4y = 0 represents
If the pair of lines ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 intersect on the yaxis then
If sin(xy) = cos(x+y) = 1/2, the value of x and y lying between 0^{0} and 180^{0}, are given by
If A(1,2,3),B(1,1,1) and C(2,1,3) are points in a plane, the unit vector perpendicular to the plane AB is
In a transformer, current and e.m.f. in the output is 10 A and is 220 V respectively. If ratio of no. of turns in secondary and primary coil 50:10, then current in the primary coil 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 charged particale accelerated through a P.D. of 100 volt passes throught the uniform electric and magnetic fields so as to experience no deflection. If E = 15 x 10^{6} V m^{1} and B = 5 x10^{3} T , then the specific charge of the particle is
A parallel plate capacitor of plate area A and the plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates and work done by the system in question, in the process of inserting the slab, then select the incorrect relation from the following :
The relation between Faraday constant F, electron charge e, and Avogardo Number N is
Consider telecommunication through optical fibres. Which of the following statements is not correct
Two wires of same material have length L and 2L and crosssectional areas 4A and A respectively. The ratio of their specific resistance would be
Two nonideal batteries are connected in parallel. Consider the following statements.
(i)The equivalent emf is smaller than either of the two emfs.
(ii)The equivalent internal resistance is smaller than either of the two internal resistances.
There are three voltmeters of the same range but of resistances 10000 Ω, 8000 Ω and 4000 Ω respectively. The best voltmeter among these is the one whose resistance is
In a H  atom an electron makes 6.6x10^{15} rev/sec around the nucleus. Then its equivalent current is
A charge q is placed at the corner of a cube of side l. The electric flux passing through the cube is
Eight cubes, each side l, are required to form a Gaussian surface
So that the charge q at the corner of a small cube appears at the centre of the bigger cube
According to Gauss's law, the electric flux through the bigger cubes = q/∈_{0}
Hence the electric flux through the given small cube = q/8∈_{0}
The core of transformer is laminated to reduce the effect of
On moving a charge of 20 C by 2 cm, 2 joule of work is done, then the potential difference between the points is
W = QV
∴ V = W/Q = 2/20 = 0.1 volt
A loop of area 0.1 m^{2} rotates with a speed of 60 rps perpendicualr to a magnetic field of 0.4 T. If there are 100 turns in the loop, maximum voltage induced in the loop is
The time in seconds required to produce a potential diference of 20V across a capacitor of 1000 μ F when it is charged at the steady rate of 200 μ C/s is
Equal charges are given to two conducting spheres of different radii. The potential will
Two point charges +q and q are held fixed at (d,0) and (d,0) respectively of a xy coordinate system. Then
When two deuterium nuclei fuse together, in addition to tritium, we get a
Current is flowing in two long parallel conductors in the same direction. The conductors
The radius of an electron orbit in a hydrogen atom is of the order of
The decay constant of a radio active substance is λ . Its half life is
A parallel plate air condenser has certain capacity. When 2/3 of the distance between the plates is filled with a dielectric, the capacity is found to increase by a factor of 2.25. The dielectric constant is
Two radiations containing photons of energy twice and five times the work function of the metal are incident successively on the metal surface. The ratio of the maximum velocities of the emitted electrons in the two cases will be
The far point of a myopic eye is 1.5 m. To correct this defect of the eye, the power of lens is
A plano convex lens is made refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
The function of base layer in a transistor is similar to that  in a vacuum triode.
The electric circuit used to get smooth d.c. output from a rectifier circuit is called
The ratio of work function and temperatures of two emitters are 1:2, then the ratio of current densities obtained by them will be
In intrinsic semiconductor at room temperature, number of electrons and holes are
Two waves of intensities I and 4 I superimpose, then maximum and minimum intensities are
If a star is moving towards earth, then the lines are shifted towards
In Huygen's wave theory, the locus of all points oscillating in the same phase is called a
Carbonyl compounds undergo nucleophilic addition because of
The cyanohydrin of a compound X on hydrolysis gives lactic acid; The X is
How many monochlorobutanes will be obtained on chlorination of nbutane?
Which of the following reactions can be used for the synthesis of an alkene
In the following reaction, which choice has value twice that of the equivalent mass of the oxidising agent SO₂ + H₂O → 3S + 2H₂O
The hormone which controls the processes of burning of fats, proteins and carbohydrates to librates energy in the body is
The αamino acids, usually, exist in the form of zwitter ions. It means they consist of
On heating with conc. HNO₃, proteins give yellow colour. This test is called
Which of the following does not contain a carboxyl group?
The reaction,SO₂ + Cl₂ → SO₂Cl₂ is exothermic and reversible.A mixture of SO₂(g),Cl₂(g) and SO₂Cl₂ (l) is at equilibrium in a closed container.Now a certain quantity of extra SO₂ is introduced into the container , the volume remaining the same.which of the following is/are true ?
when a catalyst is added to a reversible reaction in equilibrium state, the value of equilibrium constant
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)
= ( 68x2) + ( 94)  ( 213) = 17Kcal
Given C(s) + O₂(g) → CO₂(g) ; ∆H = −395kJ, S(s) + O₂(g) → SO₂(g);∆H = −295kJ , CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g) ; ∆H = −1110kJ. The heat of formation of CS₂(l) is
Detergents are prepared by the action of H₂SO₄ followed by neutralization by starting with
In which of the following complex ion, the central metal ion is in a state of sp^{3} d^{2} hybridisation?
During the electrolysis of a solution of AgNO₃, 9650 C of charge passes through the electroplating bath, the mass of silver deposited on the cathode will be
The standard reduction potentials of 4 elements are given below.Which of the following will be the most suitable reducing agent?
I = 3.04 V, II = 1.90 V, III =0 V, IV = 1.90 V
The internal energy of one mole of an ideal gas is given by
Which of the following is used in the preparation of aerated water (soda)?
Which of the following contains a coordinate covalent bond ?
In the conversion Br₂ → BrO₃^{} the oxidation state of bromine changes from
The blue complex formed on addition of conc. NH₄OH solution to a Cu^{2+} salt solution has the structure?
Two moles of an aldehyde react with concentrated solution of sodium hydroxide and produce one mole of acid and one mole of alcohol. The aldehyde is
During extraction of silver, which of the following is formed ?
Fill in the blank with appropriate word.
The miser gazed.........at the pile of gold coins in front of him.
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
He does not like to be friendly with Sarita; he always GIVES HER A COLD SHOULDER.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
No one could explain how a calm and balanced person like him could PENETRATE such a mindless act on his friends.
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