A to Z Exams

The circumcentre of the triangle with vertices at A(5, 12),B(12, 5), c (2√(13 ) ,3√(13 )) is

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

When a circular oil drop expands on water, its area increases at the uniform rate of 40sq. cm per minute. The rate of increase in the radius when the radius 5 cm is

The wave length of the Kαline for an element of atomic number 43 is λ.Then the wavelength of the Kαline for an element of atomic number 29,is

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

A flask is filled with 1.3 g of an ideal gas at 270C and its temperature is raised to 520C The mass of the gas that has to be released to maintain the temperature of the gas in the flask at 520C and the pressure remaining the same is

An organic compound X on treatment with pyridinium chloro chromate in dichloromethane gives compound 'Y". Compound Y reacts with I2 and alkali to form triiodomethane. The compound 'X' is

The solution of extan y dx+(1-ex)sec2ydy=0 is

A 4Ω resistor in series with 8Ωresistance are connected to 12 V supply.If another resistor of 8Ω is connected across the 8Ω resistor the current drawn from source would be

When cold junction is at 00C variation of thermo emf(e) of Fe-Cu thermo couple with temperature of hot junction t is given as e=14t-0.02t2.Its neutral temperature is

The equation of the tangent to the curve y2=4ax at (at2, 2at) is

If α,β,γ,δ are the roots of x4+px3+qx2+rx+s=0 then Σα2 β=

If a, b and c are mutually perpendicular unit vectors, then [a b c]2=

sin θ+ sin (1200+ θ)+sin (θ - 1200)=

If the area of the triangle formed by the pair of lines 8x2-6xy+y2=0 and the line 2x + 3y = a is 7 then

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to

Circum centre of the ?le formed by the points (2, -5), (2, 7), (4, 7) is

A piece of metal weighs 45gms in air and 25gms in a liquid  of density 1.5 X 103 kg-m-3 kept at 300 C . When the temperature of the liquid is raised to 400 C the metal piece weighs 27gms . The density of the liquid at 400 C is 1.25 X 103 kg-m-3 . The coefficient of linear expansion of metal is

The angle between the normals at (1,3),(-3,1) to the circle x2+y2=10 is

The locus of the middle points of portions of the tangents to the circle x2+y2=a2 terminated by the axes is

The vector equation of the plane passing through the point 2i+2j-3k and parallel to the vectors 3i+3j-5k, i+2j+k is

In Sun, the important source of energy is

The angle between the curve y2=4x+4 and y2=36(9-x) is

If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x2/3+y2/3=a2/3, then 4p2+q2 =

The equation whose roots are squares of the roots of x3-2x2-2x+3=0 is

On passing a current through molten KCl 19.5 of K is deposited. The amount of aluminium deposited by the same quantity of electricity if passed through molten AlCl3 is

If cot θ=-3/4 and θ is not in the second quadrant then 5 sin θ+10 cos θ+9 sec θ-16 cosecθ- 4cot θ=

The equation of the circle passing through the point (1, 2) cutting the circle x2+y2-2x+8y+7=0 orthogonally and bisects the circumference of the circle x2+y2=9 is

If  O(0,0), A(3,4), B(4,3) are the vertices of a triangle then the length of the altitude from O is

A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is

The polars of two points A(1, 3) and B(2, -1) w.r.to the circle x2+y2=9 intersect at C. Then the polar of C w.r.to the circle is

If the pair of lines 3x2+hxy+5y2=0 bisects the angles between the coordinate axes then h=

The first three terms in the expansion of (1+x+x2)10 are

The domain of Cos-1 (4x-9) is

The solution of dy/dx +1  = e x+y is

If the points (0,0), (3,√3), (x,y) form an equilateral triangle, then (x,y)=

Two sources A and B are sending notes of frequency 680 Hz. A listener moves from A to B with a constant velocity V. If the speed of sound in air is 340 ms-1, what must be the value of V so that he hears 10 beats per second

If a=2i-j+3k, b=-i+4j-2k, c=i+j+7k and xa+yb=c then (x, y)=

If f(x) =2x2+3x-5, x=3, δx=0.02, then  δf=

A maximum current 0.5mA can be passed through a galvanometer of resistance 20Ω.The resistance to be connected in series to convert it into voltmeter of range 0-5V is

A bullet of mass 10 g is fired horizontally with a velocity 1000ms-1 from a rifle situated at a height 50 m above the ground. If the bullet reaches the ground with a velocity 500ms-1, the work done against air resistance in the trajectory of the bullet is : (g=10ms-2)

(1+ω-ω2) (1-ω+ω2)=

d/dx{Tan-1(x/1-√1-x2)}=

(3+5ω+3ω2)6=

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

One junction of thermo couple is at 00C and the other junction is heated .Maximum current in the thermo couple is observed when hot junction is at 2400C.The temperature of the hot junction at which the direction of current reverses is

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 area bounded by the curve y2=4x and the lines x=1,x=9 is

The equation of the normal to the curve 2y=3-x2 at (1, 1) is

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

The condition that the lines joining the origin to the points of intersection of y=mx+c, x2+y2=a2are at right angles is

Two solid spheres A and B made of the same material have radii rA and rB respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of A and B is :

If O is the origin and if A(x1,y1), B(x2,y2) are two points then OA.OB.cos

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

A prism of refractive index μ and angle A is placed in the minimum deviation position. If the angle of minimum deviation Is A, then the value of A in terms of μ is

P and Q are two points on the line x-y+1=0. If OP=OQ=6 then length of median of Δ OPQ through O is

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 300. After walking 120 metres towards it on level ground the elevation is found to be 600. Then the height of the object (in metres) is :

The locus of the midpoint of the chord of the circle x2+y2-2x-2y-2=0, which makes an angle of 1200 at the centre is

The diameter and altitude of a right circular cylinder are found at a certain instant to be 20 cm and 40 cm respectively. If the diameter is increasing at the rate of 2 cm/sec then the rate of the change in the altitude will keep the volume constant is

Dipole moment of HC1 = 1.03 D, HI = 0.38 D. Bond length of HC1 = 1.3 and HI = 1.6A .The ratio of fraction of an electric charge, δ, existing on each atom in HC1 and HI is

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

Sin-1(24/25) +Tan-1(5/12) =

If cos x+ cos y=4/5, cos x- cos y=2/7, then 14 tan(x-y/2)+ 5 cot (x+y/2)=

If radii of two circles are 4 and 3 and distance between centres is √37 then the angle between the circles is

A stone is thrown vertically up and height s reached in time t is given by the formula s=2t2+3t+1. The stone reaches the maximum height in time t =

The orthocentre of the triangle formed by(2,-1/2), (1/2,-1/2)and (2,√3-1/2) is

If x2-3x+2 is a factor of x4-px2+q=0,then(p,q)=

If A+B+C=1800, then (sin 2A- sin 2B- sin 2C)/(sin 2B- sin 2A- sin 2C)=

The locus of the point [(et+e-t)/2,(et+e-t)/2] is a hyperbola of eccentricity

The distances between the objective and the eye lens of an astronomical telescope when adjusted for parallel light is 100cm.The measured value of the magnification is 19.The focal length of objective and eye piece are

For the circle x2+y2-2x-4y-4=0 the lines 2x+3y-1=0, 2x+y+5=0 are

Two bodies of 6 kg and 4 kg masses have their velocity   5i^-2j^+10k^   and   10i^-2j^+5k^ respectively. Then the velocity of their centre of mass is

Assertion (A) : NaCl is less soluble in heavy water than in ordinary water,Reason (R) : Dielectric constant of ordinary water is more than that of heavy waterThe correct answer is

The least distance of the line 8x-4y+73=0 from the circle 16x2+16y2+48x-8y-43=0 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 ?

A thin prism of 40 angle gives a deviation of 2.40. The value of refractive index of the material of the prism is

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

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

If the position of vectors of P, Q are respectively 5a+4b and 3a-2b then QP=

The circle with centre on the line 2x-2y+9=0 and cutting the circles x2+y2=4 orthogonally, passes through the fixed points

If x4-6x3+3x2+26x-24 is divide by x-4 then the quotient is

If the roots of a2x2+2bx+c2=0 are imaginary,then the roots of b(x2+1)+2acx=0 are

If N denotes the set of all positive integers and if f:N->N is defined by f(n) = thesum of positive divisors of n then, f (2k, 3), where k is a positive integers is

If y={sin x/2 sin x2/2. Sin x3/23...sin xn/2n}then dy/dx=

The equation of the parabola whose axis is parallel to y –axis and passing through (4, 5) (-2, 11), (-4, 21) is

For x є IR, 3cos(4x-5) + 4 lies in the interval :

If the coefficients of 2nd, 3rd, 4th terms in the expansion of (1+x)2n are in A.P. then

A flint glass prism is of refracting angle 50.Its refractive index for C line is 1.790 and for F line is 1.805.The angular dispersion of C and F lines is

The 1st  and  2nd points of trisection of the join of (-2, 11), (-5, 2) are

If the normal at (1,2) on the parabola again at the point (l2,2t), then the value of t is

The following phenomenon which is not explained by Huygens construction of wave front is

The equation ax2+8xy+2y2+2gx+13y+c=0 represents a pair of parallel straight lines then ascending order a,g,c is

The locus of  the point of intersection of two tangents of the hyperbola x2/a2+y2/b2=1 which  make an angle 300 with one another is

If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

The centres of similitude of the circles x2+y2-2x-6y+9=0, x2+y2=1 is

Particles and their anti-particles have

The number of ways in which the following prizes be given to a class of 20 boys, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English is

In the reaction AlCl3+Cl-→[AlCl4]-,AlCl3 acts as

If the line 3x-y =k is a hyperbola 3x2-y2=3, then k=

The equation of the circle with centre (-1, 1) and touching the circle x2+y2-4x+6y-3=0 externally is