A to Z Exams

The equation of the common tangent to x2+ y2 = 8 and y2 = 16x is

A mapping is selected at random from the set of all mappings from the set A={1,2,3}in to B= {1,2,3,4}.The probability that the mapping selected is many to one is

If the difference of the roots of x2-bx+c=0 is equal to the difference of the roots of x2-cx+b=0 and b≠c,then b+c=

If (2i+4j+2k)x(2i-xj+5k)=16i-6j+2xk then the value of x is

If the rate of change in the radius of a circle is 0.02 cm/sec, then the rate of change in the area of the circle when the radius is 5 cm is

The length of the latus rectum of the hyperbola 9x2-16y2+72x-32y-16=0 is

If m tan(θ-300)= n tan(θ+1200), then cos 2θ=

100 tickets are numbered as 00, 01, 02,...,09, 10, 11,...99. When a ticket is drawn at random from them and if A is the event of getting 9 as the sum of the numbers on the ticket, then P(A)=

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

Middle term in the expansion of (2x-3/x)15is

In ΔABC , cos(A+2B+3C/2)+cos(A-C/2) =

If 4x2+4xy-ky2-12x-12y+8 can be written as the product of two linear factors then the factors are

If (1+ cos θ+ i sin θ)(1+ cos 2θ+i sin2θ)= x+iy, then y=

Express (2+3i/ 2-3i)-(2-3i/ 2+3i) in the form of a+ib

y = Aex + Be2x + Ce3x satisfies the differential equation :

If xy=c2 then dy/dx=

Aqueous solution of an organic compound, 'A' on electrolysis liberates acetylene and CO2 at anode. 'A' is

The length of the direct common tangent of the circles x2+y2-4x-10y+28=0 and x2+y2+4x-6y+4=0 is

CaCl2+C2H5OH→CaCl2xC2H5OH,in this ‘x’ is

A complex compound of CO3+ with molecular formula COClx. yNH3 gives a total of 3 ions when dissolved in water. How many Cl- ions satisfy both primary and secondary valencies in this complex

Two tuning forks A and B give 6 beats per second .A resonates with a closed column of air 15 cm long and B with an open column 30.5 cm long in their fundamental harmonics.Their frequencies are

To generate power of 3.2 MW, the number of fissions of U235 per minute is : (Energy released per fission =200 MeV; 1eV=1.6x10-19J)

The locus of the centre of the circles which touch the lines 6x – 8y + 5=0 and 6x – 8y + 13=0 is 6x – 8y+k=0 then k is

The vectors a+2b+3c, 2a+b-2c, 3a-7c are

A box contains 40 balls of the same shape and weight. Among the balls 10 are white, 16 are red and the rest are black, the probability that a ball drawn from the box is not a black is

The equation of the normal to the curve x2=4y at (2, 1) is

2 sin θ. tan θ(1-tan θ)+2 sin θ sec2 θ / (1+tan θ)2

A 2 kg stone tied at the end of a string of 1 m length, is whirled along a vertical circle at a constant speed of 4 m/s. The tension in the string has a value of 52 N when the stone is :

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of K is given by the interval

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

A body is projected vertically upwards at time t = 0 and it is seen at a height 'H' at time t1 and t2 seconds during its flight. The maximum height attained is : (g is acceleration due to gravity)

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

Let f(x)=-2sinx, if x≤-π/2; f(x)=a sinx+b,if –π/2

The system of circle x2+y2+2λx-5=0 is

cos 240 cos 480 cos 960 cos 1680 =

The volume of a metal hollow sphere is constant. If the outer radius is increasing at the rate of ¼ cm per sec. the rate at which the inner radius is increasing when the radii are 8 cm and 4 cm respectively is

A train is travelling at 120kmph and blows a whistle of frequency 1000Hz.The frequency of the note heard by a stationary observer if the train is approaching him and moving away from him are(Velocity of sound in air=330ms-1)nearly

A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is

The four distinct points (0, 0), (2, 0), (0, - 2) and (k, - 2) are concylic, if k is equal to

If B,A, A+B are acute angles, sin(A+B)=12/13, sin B=5/13 then sin A=

The two curves x2+y2=25, 2x2-9y+18=0

d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

d/dx{sin2((1-x2)/(1+x2))}

If sin A= sin2 B and 2 cos2 A =3 cos2 B, then the ΔABC is

Let α,β be the roots of x2-x+p=0 and γ,δ be the roots of x2-4x+q=0.If α,β,γ,δ are in G.P then the integral values of p and q respectively,are

Midpoints of the sides AB and AC of triangle ABC are (-3,5) and (-3,-3) respectively, then the length of BC=

sin(π/2+θ). Cos(π-θ) cot(3π/2+θ)- sin(π/2-θ). sin(3π/2-θ) cot(π/2+θ) =

The equation of the hyperbola whose centre is (1,2), one focus is (6,2) and transverse axis 6 is

If the pairs of lines x2-2pxy-y2=0 and x2-4xy-y2=0 be such that each pair bisects the angle between the other pair, then p=

If P(-1,4), Q(11,-8) divides AB harmonically in the ratio 3:2 then A,B in order are

Which one of the following compounds liberates CO2 from aqueous NaHCO3

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

A tangent galvanometer properly adjusted gives a deflection of 300 when a certain current is passed through it. When the current is changed, then it gives a deflection of 450. The ratio of the current in the two cases is:

Mr. A is called for 3 interviews .There are 5 candidates at the first interview, 4 at the second and 6 at the third .If the selection of each candidates is equally likely then the probability that A will be selected for at least  one post is

Two unit negative charges are placed on a straight line. A positive charge q is placed exactly at the mid point between these unit charges. If the system of these three charges is in equilibrium, the value of q (inC) is

The midpoint of the line segment joining (2,3,-1), (4,5,3) is

If A, B, C, D are the lengths of normals to the curves 1.y=4x2 at (-1, 4) 2. Y=x3+1 at (1, 2) 3. Y=x3/2-x at (1,1) 4. 2x2+3xy-2y2=8 at (2, 3) then the ascending order of A,B,C,D is

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

If (n+1)P5:nP6= 2: 7 then n =

The length of the tangent of the curves x=a cos 3θ, y= a sin3θ (a>0) is

sin 120 sin 240 sin 480 sin 840 =

What is the correct order of spin only magnetic moment (in BM) of Mn2+, Cr2+ and V2+ ?

The maximum value of a2-abx-b2x2 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 angle between a pair-of tangents drawn from a point P to the circle x2+y2+4x-6y+9sin2α+13cos2 α=0 is 2α.The  equation of the locus of the point P is

Three faradays of electricity are passed through molten Al2O3, aqueous solution of CuSO4 and molten NaCl taken in three different electrolytic cells. The amount of Al,Cu and Na deposited at the cathodes will be in the ratio of

The angle between the lines 4x-y+9=0, 25x+15y+27=0 is

Which of the following compounds is soluble in benzene but almost insoluble in water

If (1 + cos θ + i sin θ)(1 + cos 2θ + i sin 2θ)=x+iy then y=

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

In ΔABC, if cos A cos B +sin A sin B sin C =1, then a:b:c =

If for a binomial distribution n=4 and 6P(X=4)=P(X=2), the probability of success is

In ABC where A(4,5,6), B(3,2,1), C(5,4,3), if p,q,r are lengths of the medians through A,B,C then ascending order of p,q,r is

The equation of the line parallel to 2x+3y-5=0 and forming an area 4/3sq.unit with the coordinate axes is

The length of the subnormal of the curves y=a/2(ex/a+e-x/a) at any point is

The equation of the latus rectum  of the parbola x2 – 12x – 8y + 52 = 0 is

If 4,5 are two sides of a triangle and the included angle is 600, then is area is

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

When a monochromatic light of frequency v is incident on a metal, stopping potential is V0. Frequency of the incident light for which stopping potential becomes 2V0 is

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 is

The value of k such that the straight line 2x+3y+4+k (6x-y+12) =0 is perpendicular to the line7x+5y=c

In a committee consisting of 25 members,  everyone is  proficient in Mathematics or Physics or both .Among them 19memers are proficient in mathematics and 16 are proficient in Physics. If a person is chosen at random from the commitee, the probability that he is proficient both in Mathematics and Physics is

If the equation of the parabola whose axis is parallel to x – axis and passing through (2,-1) (6,1) (3, -2) is ay2 + bx + cy + d = 0 then the ascending order of a,b,c,d is

When an unknown 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 4 Ω resistance is now connected in parallel to the right gap is

The area (in square units) of the triangle formed by the lines x = 0,y = 0 and 3x + 4y = 12, is

The charge required to reduce 1 mole Cr2O7-2 to Cr+3 ions is

The incentre of the triangle formed by the points (0,0), (5,12), (16,12) is

A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If α is the angle which the pole subtends at the midpoint of the opposite side, the length of each side of the park is

If α,β,γ are the roots of the equation x3-7x+7=0,then the value of α-4+β-4+γ-4 is

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that at least one letter may be placed in wrongly addressed envelope is

A sonometer consists of two wires of same material whose radii are in the ratio2:3.The tension in thick wire is 4 times the tension in thin wire.If V is velocity of transverse were in thin wire,then the velocity of transverse wave in thick wire is

Which of the following is not an air pollutant

The value of sin[(1/2)cot-1(3/4)] is equal to

The tangents X2+Y2=r2 having inclinations α and β intersect at P. If cotα+cotβ=0, then the locus of P is given by

If Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

If a circle passes through the point (a, b) and cuts the circle x2+y2=k2 orthogonally, the equation of the locus of its centre is

The frequency of a tuning fork A is 2% greater than that of standard fork K.The frequency of another tuning fork B is 3% less than K.When A and B are vibrated together 6 beats per second are heard per second. The frequencies of A and B are

The line x cosα+y sinα=p touches the circle x2+y2-2axcosα-2aysinα=0, then p=

If f(x,y)=xy+(1/x)+(1/y) then fxx?fyy-fxy2 at (1,1) is

The greatest negative integer satisfying x2+4x-774 is