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sin 100 sin 500 sin 700 sin 900 =

The radius of a circle plate is increasing at the rate of 0.01 cm/s when the radius is at 12 cm . then the rate at which the area increases is

Degenerate electron pressure will not be sufficient to prevent core collapse of 'white dwarf' if its mass becomes n times of solar mass. Value of n is:

If a= 3i+2j+k, b=6i+mj+nk and a, b are collinear, then m, n are

If cos θ+ sin θ=a, then sin 2θ=

2.4+4.7+6.10+….(n-1) terms=

Area of the triangle formed by (a, b+c,(b, c+a), (c, a+b) is

The vertex and focus of a parabola are (-2,2),(-6,6).Then its length of latus rectum is

If (2,-1, 3) is the foot of the perpendicular drawn from the origin to the plane, thenthe equation of the plane is :

If A=sin2θ + cos4θ, then for all values of θ, where

The equation to one asymptote of the hyperbola 14x2+38xy+20y2+x-7y-91=0 is 7x+5y-3=0, then the other asymptote is

a sonometre has 25 forks. Each produces 4 beats with the next one. If the max frequency is 288Hz,which is the frequency of last fork. The lowest frequency is

If θ is the angle of intersection of the curves y2=x3 and y=2x2-1 at (1, 1), then tanθ=

The equation of the tangent to the parabola y2 = 12x at (3, -6) is

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

The radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio

Four numbers are chosen at random from {1, 2, 3, .... 40}. The probability that they are not consecutive, is

A step down transformer has a supply line voltage of 2200V in to 220V. The primary coil has 5000 turns. The efficiency and power transmitted by the transformer are 90% and 8 kilowatt respectively. Then the number of turns in the secondary is

The points (4, -2), (3, b) are conjugate w.r.t x2+y2=24 if b=

The locus of the point z = x + iy satisfying | (z-2i) / (z+2i) | = 1 is

The total pressure of a mixture of 6A of O2 and 5.6 g of N2 present in a 2 litre vessel is 1200 mm. What is the partial pressure (in mm) of nitrogen?

cot(A+150)- tan(A- 150)=

The equation of the tangent to the curve y=x+9/x+5 so that is passes through the origin is

Let O be the origin . A(3, -2), B (1, 2) and C(1, 1). The pair of points which are on different sides of the line 2x+3y=5 are

Which one of the following reactions does not form gaseous product

The locus of the centre of circle which touches the line x cos α+y sin α=p and circle (x-a)2+(y-b)2=c2 is

An isomer of ethanol is

The foot of the perpendicular from the point (3, 4) on the line 3x-4y+5=0 is

A square has two opposite vertices at the points (2,3) and (4,1). Then length of the side is

The length of a narrow closed pipe is L.The possible wavelengths of stationary waves forms in it are

Two dice are rolled simultaneously. The probability of getting an even number and an odd number is

If (1+x+x2)n = a0+a1x+a2x2+……..+a2nx2n then a02-a12+a22-……….+a2n2 =

The equation to the circle touching the y-axis at the origin and passing through(b, c) is

Nitro benzene on reduction with zinc and NH4CI gives

The equation of the asymptotes of the hyperbola 4x2-9y2=36 are

If a point P moves such that its distances from the point A (1, 1) and the line x+ y + 2 = 0 are equal, then the locus of P is

Dry distillation of calcium acetate and calcium formate forms:

The sum of the fourth powers of the roots of the equation x4-x3-7x2+x+6=0 is

The maximum value of 5 cos x+ 3 cos (x- 600)+7 is

If y=e-x cos x then y4=

In the first box there are tickets marked with numbers 1,2,3,4. In the second box there are tickets marked with numbers 2, 4, 6,7,8,9. If a box is chosen and at a ticket is drawn from it at random, the probability for the number of the ticket to be 2 or 4 is

The smallest positive values of x and y which satisfy tan(x-y) =1, sec(x+y) = 2/√3 are

If the tangents at (at12, 2at1) and (at22, 2at2) on the parabola y2=4ax intersect on the axis then

If the bond length and dipole moment of a diatomic molecule are 1.25 A and 1.0D respectively,what is the percent ionic character of the bond

If the latusrectum of a hyperbola subtends an angle 600 at the other focus then its e=

The molar concentrations of A,B and C at equilibrium for the reaction A+2B⇔3C are 2,3 and 4 moles/lit respectively. Its Kc is

If α,β are solutions of a cos 2θ+b sin 2θ=c, then tan α tan β=

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

If the 3rd, 4th and 5th terms of (x+a)n are 720, 1080 and 810 respectively then (x,a,n)=

H2-O2 fuel cell is

A question paper contains 5 questions each having an alternative. The number of ways that a student can answer one or more questions is

In ?ABC, centroid=(2,0). If (1,3) is the midpoint of BC, then A=

If f:[0, ∞)→[0, ∞) defined by f(x)=x2, then f is

The condition for f(x)= x3+px2+qx+r(x R) to have no extreme value, is

The equation of the chord of the hyperbola 3x2-2y2=6 having (4, 3) as its midpoint is ax+by+c=0 then the ascending order of a, b, c is

If the two equations x2-cx+d=0 and x2-ax+b=0 have a common root and the second equation has equal roots,then

The values of ‘a’ for which the function (a+2)x3-3ax2+9ax-1 decreases monotically throughout for all real x are

If b + c = 3a, then cot B/2 cot C/2 is equal to :

If the length of the tangent from (2, 3) to circle x2+y2+6x+2ky-6=0 is equal to 7. Then k=

C1/C0+2. C2/C1+3.C3/C2+....n. Cn/Cn-1=

cos 6900. Sin 8400+ cos 4200 sin 10500=

The angle between the curves y2=x, x2=y at (1, 1) is

A man observes a tower AB of height h from a point P on the ground. He moves a distance ‘d’ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance 3d/4 in the same direction and the angle of elevation is three times that at P. Then 36h2=

The term in the independent of x in the expansion of (3+2x)44, is

One number is selected at random from 1 to 100. The probability that it is a prime number is

If the roots of a(b-c)x2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

If A+B+C =900 then (cot A+cot B+cot C)/(cot A cot B cot C) =

The polars of the points (3, 4),(-5, 12) and (6, t) with respect to a circle are concurrent. Then t=

The equation of the curve in polar coordinates is(1/r) =2sin2(θ/2).Then it represents

The equation of the line dividing the line segment joining the points (2, -3), (1, 2) in the ratio 2:3 and perpendicular to 2x+5y-1=0. Is

If two of the roots of 2x3+7x2+2x-3=0 are differ by 2 then the roots are

If θ is the angle between the curves y=sin x, y =cosx at x=π/4 then tan θ=

An ammeter whose resistance is 180 Ω shows full scale deflection when the current is 2mA.The shunt required to convert into an ammeter reading 20 mA is (in ohm)

The lines 2x+3y = 6,2x+3y = 8 cut the x-axis at A,B respectively.A line L=0 drawn,through the point(2,2) meets the x-axis at C in such a way that abscissa of A,B and C are in the arithmetic progression.Then the equation of L=0 is

If (2, 6) is a centre of similitude for the-circles x2+y2=4 and x2+y2-2x-6y+9=0, the length of the common tangent of circles through it is

The angle between the two line having slopes 3/2 and -2/3

If x4-5x3+9x2-7x+2=0 has a multiple root of order 3 then the roots are

The circle x2+y2-4x+4y-1=0 cuts the positive coordinate axes in A and B respectively. The equation to the diameter of the circle perpendicular to the chord AB is

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

A man on a wharf 20mt above the water level pulls in a rope to which a boat is attached at the rate of 4mt per second. At what rate is the boat approaching the shore, when there is still 25mt rope out…?

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

How many electrons are present in the M shell of an atom of an clement with atomicnumber 24 (Z = 24) ?

The coefficient of x10 in 1-2x+3x2/1-x is

If the equation x2-2mx+7m-12=0 has equal roots then m=

If pr=2(q+s) then among the equations x2+px+q=0 and x2+rx+s=0 have

The normal at P cuts the axis of the parabola y2 = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

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 Q denotes the set of all rational numbers and f(p/q) = (p2 - q2)1/2 for any p/q belongs to R then observe the following statementsI.f(p/q) is real for each p/q belongs to QII..f(p/q) is complex number for each p/q belongs to QThen which of the following is correct

The elementary particles heavier than nucleons are called

A codon has a sequence of A and specifies a particular B that is to be incorporated into aC What areA, B, C

If cosh-1 x = loge (2+√3), then x is equal to

A solid wooden block resting on a frictionless surface is hit by a bullet. The bullet gets embedded. During this process:

A juggler maintains four balls on motion, making each inturn rise to a height 20m from his hand. Where will the other three balls be at the instant when the fourth one is just leaving the hand?

Two identical stringed instruments have a frequency of 100Hz.The tension in one of them is increased by 4%.If they are now sounded together the number of beats per second is

d/dx{x1/x}=

A mixture contains 10 g of oxygen, 28g of nitrogen and 8g of CH4.Total pressure of mixture is 740mm.What is the partial pressure of nitrogen in mm

If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=

Assertion(A): A catalyst has no effect on the state of equilibrium Reason:A catalyst influences the rates of both forward and backward reactions to the same extent

If (x+y)2=ax2 +by2 then dy/dx=

The term independent of x in (x+1/x)6 is

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