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A pipe of length l1 closed at one end is kept in a chamber of gas of density ρ1.A second pipe open at both ends is placed in a second chamber of gas of density ρ2.The compressibility of both.The gases is equal.If frequency of first overtone in both the cases is equal,the length of the second pipe is

If a,b,c are the number of 4 digited numbers that can be formed using the digits 2,4,5,7,8 that are divisible by 3,4,5 respectively then the ascending order of a,b,c is

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

The number of common tangents to the two circles x2+y2-8x+2y=0 and x2+y2-2x-16y+25=0 is

One side of a rectangle lies along the line 4x+7y+5=0.Two of its vertices are (-3, 1), and (1, 1).Then the equation of the other sides are

If (2,1,1) is the centroid of the triangle for which (3,2,-1), (2,-2,5) are two vertices then the third vertex is

If A and B are mutually exclusive events with P(B)≠1, then P(A/B-)is equal to (Here B- is the complement of the event B)

Orthocentre of the ?le whose vertices are (2,-5), (2, 5), (4, 5) is

The IUPAC name for CH3-CH2-CH(OH)-CH=CH2

The equation of the circle which cuts orthogonally the three circles x2+y2+2x+17y+4=0, x2+y2+7x+6y+11=0 , x2+y2-x+22y+3=0 is

A capacitor of 8 μF is charged to a potential of 1000V. The energy stored in the capacitor is

The angle between the line joining the points (1, -2), (3, 2) and the line x+2y-7=0 is

If A,B,C are collinear points such that A=(3,4), B=(7,7) and AC=10 then C=

In a thermo couple the temperature of the cold junction is 150C.If the temperature of inversion is 4850C,the neutral temperature of the thermo couple is

2 tan h -1 1/2 is equal to

Let A and B be any two points on each of the circles x2+y2-8x-8y+28=0 and x2+y2-2x-3=0 respectively. If d is the distance between A and B then the set of all possible values of d is

C0+4.C1+7.C2+……(n+1) terms =

If 1,-2,3 are the roots of ax3+bx2+cx+d=0 then the roots of ax3+3bx2+9cx+27d=0 are

For an oral test 25 questions a reset of which 5 are easy and 20 are tough. Two questions are given to two candidates A and B in that order(one question to each person). The probability for B to receive easy question is

The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 but using each digit not more than once in each number is…….. The number of these integers that are greater than 3000 is

The line y = m(x + a)+a/m touch the parabola y2= 4a(x+ a) form

Magnetic field induction at the centre of a circular coil of radius 5 cm and carrying a current 0.9 A is (in S.I. units) (ε0 = absolute permittivity of air in S.I. units; velocity of light = 3 x 108 ms-1)

If A lies in the third quadrant and 3 tanA – 4 = 0, then 5 sin2A + 3 sinA + 4 cosA is equal to

Two opposite vertices of a square are (1,-2) and (-5,6) then the other vertices are

The vector equation of the plane passing through A and perpendicular to AB where 3i+j+2k, i-2j-4k are the position vectors of A, B respectively

In a p-n junction the depletion region is 400nm wide and electric field of 5x105Vm-1 exists in it. The minimum energy of a conduction electron, which can diffuse from n-side to the p-side is

The function f(x)= x3-9x2+15x+25 is decreasing in

The cost of a cloth piece is Rs.35/-.If the length of the cloth piece is 4 metres more and each metre costs Rs.1/- less,the cost would remain unchanged.The length of the cloth piece is

The angle subtended by the double double ordinate of length 16 of the parabola y2=8x at its vertex is

cos θ cos (600+ θ) cos (600-θ)=

A bag contains2whit, 3 black and 4greenballs. If2 balls are drawn from it, one after another then the probability that the first one is white and the second one is black is

An aircraft gun can take a maximum of three shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second and third shot are 0.5,0.4,0.3 respectively. The probability that the gun hits the place is

If one roots of the equation 5x2+13x+k=0 is the reciprocal of the other then

Keeping the banking angle sam,to increase the maximum speed with which a vehicle can travel on a curved road by 10 percent the radius of curvature of the road has to be changed from 20m to :

Which one of the following equation is correct for the reaction N2(g)+3H2(g)→2NH3(g)

If tan400= λ then (tan 1400- tan 1300)/(1+ tan 1400 tan 1300) =

If the roots of x3-kx2+14x-8=0 are in G.P then k=

Which of the following is a lyophobic colloidal solution ?

All the three oxygen atoms of ozone are utilized in the oxidation of

The lengths of tangent, sub tangent, normal and subnormal for the curve y = x + x - 1 at (1,1) are A, B, C and D respectively, then their increasing order is

In ΔABC, if a= 26, b=30, cos C=63/65 then r1:r2:r3 =

A body of weight "64N" is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards, if the coefficients of static and dynamic friction are 0.6 and 0.4 respectively, the acceleration of the body is: (acceleration due to gravity = g)

If sin α + sin β =a, cos α + cos β= b, then sin (α + β)cos2((α-β)/2) is equal to:

If A+B+C= 1800 then cos2 A+ cos 2 B - cos2 C=

A stone is projected vertically up to reach maximum height h, The ratio of its kinetic energy to its potential energy, at a height (4/5) h, will be :

A tuning fork A of frequency 384Hz produces 3 beats/second when sounded with a second tuning fork B of unknown frequency.When a is filed a little,the number of beats decreased to 2 beats/second.The frequency of the fork B must be

If α,β,γ are the roots of x3-x-1=0 then the transformed equation having the roots 1+α/1-α,1+β/1-β,1+γ/1-γ is obtained by taking x=

If 15Pr-1 : 16Pr-2 = 3 : 4 then r =

The roots of the equation a(b-c) x2+b(c-a)x +c(a-b) =0 are

For real values of x the expression x2-x+1/x2+x+1 takes values in interval

The vectors i-2j+3k, 2i-3j+4k, i-3j+5k are

Three groups of children contain 3girls and one boy;2 boys; 2 girls and 2 boys. One girl and 3 boys. One child is is selected at random from each group. The probability that three selected consists of 1 girl and 2 boys is

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

The transformed equation of x3+6x2+12x-19=0 by eliminating second term is

If one root of the equation ax2 + bx+ c=0 where a, b, c are integers is √5+3, then the other root is

If α,β,γ are the roots of the equation x3+ax2+bx+c=0 then α-1+β-1+γ-1=

If 5,-7,2 are the roots of lx3+mx2+nx+p=0 then the roots of lx3-mx2+nx+p=0 are

A number n is chosen at random from S = {l,2,3,....,50}. Let A = {n ε S: n + 50/n > 27} and B = { n ε S: n is a prime number} and C = {n ε S: n is a square}.The correct order of their probability is

In the argand plane the area in square units of the triangle formed by the points1 + i, 1 –i, 2i is

The eccentricity of the ellipse 5x2+9y2=1 is

If the lines 3x-4y-7 =0and 2x-3y-5=0 are two diameters of a circle of area 49π sq unit. Then the equation of this circle is

The curve whose subtangent is twice the abscissa of the point of contact and passing through (1,2) is

The polar of the point (t-1, 2t) w.r.t the circle x2 + y2 -4x + 6y +4=0 passes through the point of intersection of the lines

An infinite number of charges each of magnitude q are placed on x-axis at distances of 1, 2, 4, 8, ….. meter from the origin. The intensity of the electric field at origin is

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

The frequency of a tuning fork x is 5% greater than that of standard fork of frequency K.The frequency of another fork y is 3% less than that of K.When x and y are vibrated together 4 beats are heard per second.The frequencies of x and y are

In a coil of area 10cm2 and 10 turns with magnetic field directed perpendicular to the plane and is changing at the rate of 108 gauss/second.The resistance of the coil is 20Ω.The current in the coil will be

If a solid is dispersed in a liquid the colloid is called

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively.Then the point O divides the segment PQ in the ratio

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index 1.5. When the telescope is adjusted to infinity, the separation between the two lenses is 16 cm. If the space between the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses is

If α,β,γ are the roots of x3+3px+q=0 then the equation whose roots are α+1/β+γ–α,β+1/γ+α–β and γ+1/α+β–γ is

If the sum of two of the roots of 4x3+16x2-9x-36=0 is zero then the roots are

If the function y = sin-1 x, then ( 1 - x2 ) d2y / dx2 is equal to :

If α,β and γ are roots of x3+ax2+bx+c=0,then Σα2β=

The two circles (x-a)2+(y-b)2=c and (y-b)2+x2=4c have only one real common tangent then

The focal length of a lens of dispersive power 0.45 which should be placed in contact with a convex lens of focal length 84 cm and dispersive power 0.21 to make the achromatic combination from the two lenses, in cm is

If (9,12) is one end of a focal chord of the parabola y2=16x then the slope of the chord is

Un polarized light of intensity I0 is incident on a polarizer and the emerging light strikes a second polarizing filter with its axis at 450 to that of the first.The intensity of the emerging beam

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 300 with one another is

The equation of the straight line perpendicular to the straight line 3x+2y=0 and passing through the point of intersection of the lines x+3y-1=0 and x-2y+4=0 is

The equations of the tangents to the hyperbola 9x2-16y2 =144 at the ends of latus recta are

If [cos(θ1-θ2)/ cos(θ1+θ2)]+ [cos(θ3+θ4)/ cos(θ3-θ4)] =0, then tan θ3tan θ4=

If the product of two of the roots of x4-5x3+5x2+5x-6=0 is 3 then the roots are

If the parabola y2=-4ax passes through (-3,2) then the length of its latusrectum is

In measuring the circumfrence of a circle, there in an error of 0.05 cm. if with this error the cir cumfence of the circle is measured of the circle is measured as c cm, and then the error in area is

The circumcentre of the triangle formed by the points(1,2,3), (3,-1,5), (4,0,-3) is

The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem ae5 to 4.Thenthe probability that the problem will be solved if both of them try the problem is

75 ml of 0.2 M HCl is mixed with 25 ml of 1 M HCl. To this solution, 300 ml of distilled water is added. What is the pH of the resultant solution

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make the θ1 and θ2 with the axis so that tan θ1 tanθ2 = k is

If A=cos θ+ 2√2 sin θ, then for all real values of θ

The point of intersection of straight lines represented by 6x2 + xy - 40y2 – 35x - 83y + 11 = 0 is:

The equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

1- cos A+ cos B- cos (A+B)/1+cos A- cos B- cos(A+B)=

The locus of the point if the join of the points (-4,2,3), (2,-1,5) subtends a right angle at P is

If the straight line ax+by+c=0 and x cos α+ y sin α=c, enclose an angle π/4 between them and meet the stright line x sin α – y cos α =0 in the same point , then

If 2-cos3 θ=3 sin θ cos θ then θ=

Equation of the tangent to the circle x2+y2=3, which is include at 600 with the x-axis is

The tyre of a motor car contains air at 150C. If the temperature increases to 350C, the approximate percentage increase in pressure is (ignore to expansion of tyre)

cos2(A-B)+ cos2 B- 2cos(A-B)cos A cos B=

C0+C1/2+C2/22+C3/23+.....Cn/2n

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