A to Z Exams

Tan-1 2+ Tan-1 3 =

The solution of x log x (dy/dx)+y=2 log x is

A sample of gas has a volume of 0.2 lit. measured at 1 atm. pressure and 00C. At the same pressure, but at 2730C its volume will become

cos A+sin(2700+A)-sin(2700-A)+cos(1800-A)=

In a triangle, the orthocentre and the circumcentre are (-4, 0), (8, 6 ) respectively; the centroid is

The parabola x2=py passes through (12,16).Then the focal distance of the point is

The equation of the line passing through the point P (1, 2) such that P bisects the part intercepted between the axes is

The tangents at (3, 4), (4, -3) to the circle x2+y2=25 are

The distance of (1, -2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is

Three persons A, B, C in order toss a die. The persons who first throws 1 or 2wins.The ratio of the probabilities of their success is

The equation of the normal at the positive end of the latus rectum of the hyperbola x2-3y2=144 is

I: If a=3i-2j+k, b=2i-4j-3k, c=-i+2j+2k then a+b+c=4i-4j II: If a=i-j+2k, b=2i+3j+k, c=i-k, then magnitude of a+2b-3c is √78

Two pillars of equal height stand at a distance of 100 mt. At a point between them, the elevations of their tops are found to be 300 and 600. The height of the pillars and the position of the point of observation are

In measuring the vertical angle  of the sector of acircle of radius  30cms, an error of  10 is made. The error in the area of the sector is

What is the temperature at which the kinetic energy of 0.3 moles of Helium is equal to the kinetic energy of 0.4 moles of Argon at 400 K ?

The equation to the sides of a triangle are x-3y=0, 4x+3y=5, 3x+y=0. The line 3x-4y=0 passes   through

The incentre of the triangle formed by (-36,7) , (20,7) and (0,-8) is

The equation of the circle passing through the points (4, 1), (6, 5) and having the centre on line 4x+y-16=0 is

The approximate change in y, when y=x2+2x, x=3, δx=0.01 is

A: The angle between the tangents drawn from origin to the circle x2+y2-14x+2y+25=0 is π/2 R: If θ is the angle between the pair of tangents drawn from (x1, y1) to the circle S=0 of radius r then tanθ/2=r/√S11

The length of tangent from (0,0) to the circle 2(x2+y2)+x–y+5=0,is:

For the circle2x2+2y2-5x-4y-3=0, the point (4, 2)

The points at which the tangent to the circle x2 + y2=13 is perpendicular to the line 2x + 3y +21=0 is:

Two charges each of 100 micro coulomb are separated in a medium of relative permittivity 2 by a distance of 5cm.The force between them is

The locus of the poles of chords of  the ellipse x2/a2+y2/b2=1 which touch The locus of the poles w.r.t the ellipse x2/α2+y2/β2=1 is

1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =

d/dx { log√(cosec x+1)-√(cosec x-1)}=

A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase area is

the equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y  =2, 2x –y = 4 is

Aniline when heated with NaNO2 and HCl at 0.50C the product formed is:

1+(1+2)/2!+(1+2+22)/3!+(1+2+22+23)/4!+ ....... =

If PM is that perpendicular from P(2, 3) onto the line x+y=3,then the coordinates of  M are

If y = sin (logex) then x2 (d2y/dx2) + x (dy/dx) =

The equation of the circle passing through the point (1, -2) and having its centre on the line 2x-y-14=0 and touching the line4x+3y-23=0 is

When an unknown resistance and a resistance of 4Ω are connected in the left and right gaps of a meterbridge, the balance point is obtained at 50cm. The shift in the balance point if a 4Ω resistance is now connected in parallel to the resistance in the right gap is

An iron block of sides 50 cm x 8 cm x 15 cm has to be pushed along the floor. The force required will be minimum when the surface in contact with ground is:

If A= cos2 3π/5+ cos2 4π/5, b= cos2 π/8+ sin2 3π/8, C= cosec 100- √3 sec 100 then

Sum of the product of the binomial coefficients C0,C1,C2,…….Cn taken two at a time is

In Youngs double slit experiment the separation between the slits is halved and the distance between the slits and screen is doubled .The fringe width is

The extreme values of  4 cos(x2) cos(π/3  + x2 ) cos(π/3 - x2) over IR are

In measuring the circumfence of a circle, there in an error of 0.05 cm. if with this error the circufence of the circle is measured of the circle is measured as c cm, then the percentage error in area is

The solution set of (5+4cosθ)(2cosθ+1) = 0 in the interval [0,2π],is

If the equations x2-x-p=0 and x2+2px-12=0 have a common root,then that root is

If tan 690+ tan 660- tan 690 tan 660= 2k, then the values of k is

A radio isotope has a half life 10 days.If today there is 125g of it left,what was its weight 40 days earlier?

If u=(x-y) (y-z) (z-x) then ux+uy+uz=

If the tangent from a point P to the circle x2+y2=1 is perpendicular to the tangent from P to the circle x2+y2=3, then the locus of P is

The domain of √1-3x+Cos-1 3x-1/2 is

Chloroethane reacts with Y to form NaCl and Z. One mole of Z reacts with two moles of HI to form water and iodo ethane. Which of the following is Y

The point (3, -4) lies on both the circles x2+y2-2x+8y+13=0 and x2+y2-4x+6+11=0. Then the angle between the circles is

The ends of the base of an isosceles triangle are (2a, 0) and (0, a). The equation of one side is x=2a.the equation of the base is

If X is a poission variable such that p(X=0)=0.1,p(X=2)=0.2 then the parameter λ is

If vibrating tuning fork of frequency 255Hz is moving with a velocity 4 ms-1 towards the wall the number of beats heard per second is (speed of found in air = 340 ms-1)

The equation of the circle which touch the y-axis at a distance 4 from the origin and make an intercept 6 on the x-axis is

The equation of the tangent to the circle x2+y2+2x+2y-7=0 which makes 450 with the x axis is

The elementary particles heavier than nucleons are called

If A,B,C are the minimum values of 2x3-3x2-12x+5, x3-9x2+24x-12,x3-6x2+9x+1 then the ascending order of A,B,C is

If α,β,γ,δ are the roots of 3x4-8x3+x2-10x+5=0 then the equation whose roots are –α,-β,-γ,-δ is

A stone is projected vertically upwards with an initial velocity 112 ft/sec and moves such that s=112t-16t2 where s is the distance from the starting point and t is the time. The greatest height reached by the stone is

If A12/x-a1+A22/x-a2+.... Ak2/x-a k=m and ai,AI,m are rational then the equation has

d/dx{Tan-1√(1+x2)+√(1-x2)/(√(1+x2)-√(1-x2))}=

In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to

3 faces of a fair die are yellow, two faces red and one blue. The die is tossed 3 times. The probability that the colours yellow, red and blue appear in the second and third tosses respectively is

If the earth suddenly stops rotating, the value of g at equator would :

How many different combination of 5 can be formed 6 men and 4 women on which exact 3 men and 2 women serve

If the length of the unit cell is 5 Ao. the smallest distance in Ao between the two neighbouring metal atoms in a face centred cubic lattice is

The direction of the magnetic field produced by straight current carrying conductor is given by

There are three events A,B and C one of which and only one can happen. The odds are 7 to 3 against A and 6 to 4 against B.The odds against C are

If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=

A:The radical centre of the circles x2+y2=4,x2+y2-3x=4,x2+y2-4y=4 is (0,0) R:Radical centre of three circles whose centers are non collinear is the point of concurrence of the radical axes of the circles taken in pairs

A parallel plate capacitor has a capacity 80x10-6 when air is present between the plates.The volume between the plates is then completely filled with a dielectric slab of dielectric constant 20. The capacitor is now connected to a battery of 30 V by wires. The dielelctric slab is then removed. Then, the charge that passes now through the wire is

If 3x2+8xy-ky2+29x-3y+18 is resolvable into two linear factors then k=

3√1003 -3√997

If 5x2+λy2=20 represents a rectangular hyperbola, then λ is equal to

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of 0.5ms-1 at an angle of 1200 with the direction of flow of water.The speed of water in the stream, in ms-1, is:

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

Which of the following elements has least number of electrons in its M shell ?

From a well shuffled pack of 52 playing cards two cards are drawn at random, one after another without replacement. The probability that 1st one is a king and second one is queen is

y-axis divides the line segment joining (3,5), (-4,7) in the ratio

If one of the root x4-5x3+10x2-20x+24=0 is purely imaginary then the roots are

sin 1200 cos 1500-cos 2400 sin 3300 is equal to :

Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocenter of the triangle is the origin, then the third vertex is

If sin α+ sin β= a, cos α+ cos β = b then sin(α+β)=

The range of sinn-1 √x is

The area bounded by x=0,x=6+5y-y2 is

If α,β are the roots of 6x2-6x+1=0 then 1/2(a+bα+cα2+dα3)+1/2(a+bβ+cβ2+dβ3)=

If α,β are the roots of x2+ax-b=0 and γ,δ are the roots of x2+ax-b=0 then (α-γ)(β-γ)(α-δ)(β-δ)=

The number of normals to the hyperbola [(x2/a2)-(y2/b2)]=1 from an external point is

cos α+ cos β+ cosγ+ cos(α+β+γ)=

sin2 52 (1/2)0- sin2 22 (1/2)0=

A charge of 4 μC is placed in a uniform electric field of intensity 100N/C. The force acting on the charge is

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

The angle between the vectors 6i+2j+k, 2i-9j+6k is

If sin A= 1/√10, sin B=1/√5 where A and B are positive and acute, then A+B=

The tangents are drawn to the ellipse x2/a2+y2/b2=1 at point where it is intersected by the line lx+my+n=0. The point of intersection of tangents at these points is

The fourth vertex of the square whose consecutive vertices are (4,5,1), (2,4,-1), (3,6,-3) is

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

The centre and radius of the sphere 2x2+ 2y2 + 2z2 – 2x +4y + 2z + 1=0

The value of m for which one of the roots of x2-3x+2m=0 is double of one of the roots of x2-x+m=0 is

A line which makes an acute  angle ? with the possitve direction f x-axis is drawn through the point P(3, 4) and cuts the curve =4x at Qand R . The lengths of the segments  PQ and PR  are numerical values of the roots of the equation