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A horizontal force, just sufficient to move a body of mass 4kg lying on a rough horizontal surface is applied on it. The coefficients of static and kinetic friction between the body and the surface are 0.8 and 0.6 respectively. If the force continues to act even after the block has started moving, the acceleration of the block in ms^{−2} is [g = 10 m s − ^{2} ]
What will be the ratio of de Broglie wavelengths of proton and αparticle of same energy
The pressure and temperture of an ideal gas in a closed vessel are 720 kPa and 40^{o}C respectively. If 1/4th of the gas is released from the vessel and the temperature of the remaining gas is raised to 353^{o}C, the final pressure of the gas is
A spherical drop of water has 1 mm radius. If the surface tension of water is 70 x 10⁻^{3} Nm⁻^{1}, then difference of pressures between inside and outside of spherical drop is
How much force is required to produce an elongation of 0.2% in the length of a brass wire of diameter 0.6 mm? (Take Young's modulus for brass = 0.9 x 10^{11} Nm⁻^{2})
A body falls from rest in the gravitational field of the earth. The distance travelled in the fifth second of its motion is (g=10 m/s^{2})
A boy having a mass equal to 40 kilograms is standing in an elevator. The force felt by the feet of the boy will be greatest when the elevator (g=9.8 metres/sec^{2})
If a spring extends by x on loading then energy stored in the spring is (if T is the tension and k is the force constant of the spring)
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along
The angular momentum of an electron present in the excited state of hydrogen is 1.5h/ π . The electron is present in
The number of atoms contained in 11.2 L of SO₂ at S.T.P. are
(ΔH  ΔU) for formation of carbon monoxide (CO) from its elements at 298 K is (R = 8.314 KJ^{1} mol^{1})
A compound contains atoms of three elements A, B and C. If the oxidation number of A=+2, B=+5 and C= 2, the possible formula of the compound is
The aqueous solution containing which of the following ions will be colourless?
Among the following compounds (IIII), the correct order in reaction with electrophile is
Benzene on treatment with a mixture of conc.HNO₃ and conc.H₂SO₄ at 100^{o}C gives
The product of the concentration of hydronium ions and hydroxyl ion in pure water or in any acidic or basic solution is constant at a particular temperature.
It is known as ionic product of water.
It is designated as K_{w}
The value of K_{w} increases with the increase in temperature
If two moles of an ideal gas at 546 K occupy volume of 44.8 L, then pressure must be
If x<1, then the coefficient of x^{n} in expansion of (1+x+x^{2}+x^{3}+...)^{2} is
If the line 2x  y + k = 0 is a diameter of the circle x^{2} + y^{2} + 6x 6y + 5 =0, then k is equal to
The degree of the differential equation d^{2}y/dx^{2}+(dy/dx)^{2}+6y=0 is
The solution of the equation (cosecx logy)dy+(x^{2}y)dx=0 is
If f(x)=cosx, 0≤x≤(π/2), the value of 'c' for which f(x) satisfies Mean Value theorem is
For real values of x the minimum value of [(1x+x^{2})/(1+x+x^{2})] is
The area enclosed between the curve y^{2} = 4x and the line y = x is
If f g (x) dx = g (x), then f g (x) (f(x) + f'(x)) dx is equal to
The number of normals to the hyperbola x^{2} ∕ a^{2} − y^{2} ∕ b^{2} = 1 from an external point is
If A and B are square matrices and A⁻^{1} and B⁻^{1} of same order exists, then (AB)⁻^{1}is equal to
If A and B are two matrices such that AB = B and BA = A, then A^{2} + B^{2} =
If ω is an real cube root of unity, then (a+b)(a+bω)(a+bω^{2}) is
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 =
The angle between the tangents drawn from the origin to the parabola y^{2}=4z(xa) is
There are 16 players in a cricket team in which 5 are ballers and 2 are wicket keepers. How many ways of 11 players can be made from them which have 3 ballers and 1 wicket keeper?
We are to choose 11 players, including at least 3 bowlers and 1 wicket keeper.
out of 16 players, number of bowlers = 5 and the number of wicket keepers = 2
others = 16  (5 + 2) = 9
now the required selection can be done in following manner:
3B + 1W + 7Ot (i) case or 3B + 2W + 6Ot (ii) case or 4B + 1W + 6Ot (iii) case or 4B + 2W + 5Ot (iv) case
or 5B + 1W + 5Ot (v) case or 5B + 2W + 4Ot (vi) case
= ^{5}C_{3} . ^{2}C_{1} . ^{9}C_{7} + ^{5}C_{3} . ^{2}C_{2} . ^{9}C_{6} + ^{5}C_{4} . ^{2}C_{1} . ^{9}C_{6} + ^{5}C_{4} . ^{2}C_{2} . ^{9}C_{5} + ^{5}C_{5} . ^{2}C_{1} . ^{9}C_{5} + ^{5}C_{5} . ^{2}C_{2} . ^{9}C_{4}
= 10 * 2 * 36 + 10 * 1 * 84 + 5 * 2 * 84 + 5 * 1 * 126 + 1 * 2 * 126 + 1 * 1 * 126
= 720 + 840 + 840 + 1008 = 3408
A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
The total number of ways in which 5 person can be chosen out of 9 person is ^{9}C_{5} = 126
The couple serves the committee in ^{7}C_{3} * ^{2}C_{2} = 35 ways
The couple does not serve the committee in
^{7}C_{5}  ^{7}C_{2} = 21 ways
Since the couple will either be together or not at all
∴ favourable number of cases = 35 + 21 = 56
∴ required porbability = 56/126 = 4/9
In Δ A B C , if the line joining the circumcentre 'O' and the incentre I is parallel to BC ,then cosB + cosC =
The quadratic equation whose roots are three times the roots of the equation 3 ax^{2} + 3 bx + c = 0 is
if the 10th term of a G.P.is 9 and 4th term is 4, then its 7th term is
The terms of a G.P. are of form a, ar, ar^{2}, ar^{3} ,.... ar^{9} = 9
So, r^{9} = 9 a .....(1)
ar^{3} = 4 .....(2)
Cubing both sides of (2), we get,
a^{3}r^{9} = 64
putting value of r^{9} in this, we get,
[(2 sinθ tanθ(1tanθ)+2 sinθ sec^{2}θ)/(1+tanθ)^{2}]=
Let a=(1,1,1),c=(1,1,0) be two vectors, then the vector b which satisfies a*b=c and a.b=1 is
If a,b,c are three noncoplanar vectors, then [a+b,b+c,c+a]=
Group the following figures into three classes on the basis of identical properties.
3,5,8 have similar designs (four leaves placed close to a small circle and forming a symmetrical design at the centre of the figure).
2,6,9 have similar designs (three of the corner of the main figure are shaded blace and there is a pattern formed around a '+' sign at the centre of the figure).
1,4,7 have similar designs (there are four small circles at the corners of the main figure and there is a wheal shaped element at the centre of the figure).
'As a farmer , I was determined that we should get on the computer bandwagon ', says Krishnappa Jagannath, the 40year old head of the Gram Panchayat who initiated the whole process three years ago. With tips from a computersavvy brother in the US, Jagannath drew up a plan and convinced others of its merit. Within no time, he was able to raise Rs.65,000 from the public, enough for the purchase of two assembled Pentium II computers . That was easy enough. But who would operate these machines ? Jagannath decided that it had to be the villagers themselves.He got in touch with a software company , which agreed to train the villagers . Although wary initially, the people knew it was worth a try. As they realised it was not so difficult, more and more villagers joined in . Those like T.S.Shobha who showed a greater aptitude were sent for extensive training.
Q. Initially Krishnappa Jagannath raised Rs. 65,000
'As a farmer , I was determined that we should get on the computer bandwagon ', says Krishnappa Jagannath, the 40year old head of the Gram Panchayat who initiated the whole process three years ago. With tips from a computersavvy brother in the US, Jagannath drew up a plan and convinced others of its merit. Within no time, he was able to raise Rs.65,000 from the public, enough for the purchase of two assembled Pentium II computers . That was easy enough. But who would operate these machines ? Jagannath decided that it had to be the villagers themselves.He got in touch with a software company , which agreed to train the villagers . Although wary initially, the people knew it was worth a try. As they realised it was not so difficult, more and more villagers joined in . Those like T.S.Shobha who showed a greater aptitude were sent for extensive training.
Q. Krishnappa Jagannath is a
'As a farmer , I was determined that we should get on the computer bandwagon ', says Krishnappa Jagannath, the 40year old head of the Gram Panchayat who initiated the whole process three years ago. With tips from a computersavvy brother in the US, Jagannath drew up a plan and convinced others of its merit. Within no time, he was able to raise Rs.65,000 from the public, enough for the purchase of two assembled Pentium II computers . That was easy enough. But who would operate these machines ? Jagannath decided that it had to be the villagers themselves.He got in touch with a software company , which agreed to train the villagers . Although wary initially, the people knew it was worth a try. As they realised it was not so difficult, more and more villagers joined in . Those like T.S.Shobha who showed a greater aptitude were sent for extensive training.
Q. Initially the major problem which confronted the villagers was
'As a farmer , I was determined that we should get on the computer bandwagon ', says Krishnappa Jagannath, the 40year old head of the Gram Panchayat who initiated the whole process three years ago. With tips from a computersavvy brother in the US, Jagannath drew up a plan and convinced others of its merit. Within no time, he was able to raise Rs.65,000 from the public, enough for the purchase of two assembled Pentium II computers . That was easy enough. But who would operate these machines ? Jagannath decided that it had to be the villagers themselves.He got in touch with a software company , which agreed to train the villagers . Although wary initially, the people knew it was worth a try. As they realised it was not so difficult, more and more villagers joined in . Those like T.S.Shobha who showed a greater aptitude were sent for extensive training.
Q. T.S.Shobha was sent for the extensive training because she
Select the correct mirrorimage of the Figure (X) from amongst the given alternatives.
Select the correct mirrorimage of the Figure (X) from amongst the given alternatives.
Each of the following questions consists of five Problem figures marked 1,2,3,4 and 5 followed by five Answer figures marked A,B,C,D and E . Select a figure from the Answer figures which will continue the same series as given in the Problem figures.
The symbol gets vertically inverted and laterally inverted alternately. It also moves in ACW direction through distances equal to two halfsides (of square boundary) and three halfsides alternately.
Each of the following questions consists of five Problem figures marked 1,2,3,4 and 5 followed by five Answer figures marked A,B,C,D and E . Select a figure from the Answer figures which will continue the same series as given in the Problem figures.
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