A to Z Exams

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

The point on the curve x2=2y which is closest to the point (0, 5) is

If the lines 2x + 3y + 12 = 0,x – y + 4k = 0 are conjugate with respect to the parabola y2 = 8x then k =

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) 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

A bar magnet of 10 cm long is kept with its north (N)-pole pointing North. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earth's field is 0.4 Gauss, the pole strength of the magnet is

3√1003 -3√997

Equation of the tangent line at y=a/4 to the curve y(x2+a2)=ax2 is

If the lengths of the tangent from P(h,k) to the circles x2+y2-4x-5=0 and x2+y2+6x-2y+6=0 are equal then

The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

The length of the intercept made by the circle x2+y2+10x-12y-13=0 on y-axis is

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

The quantum number which explains the line spectra observed as doublets in case of hydrogen and alkali metals and doublets and triplets in case of alkaline earth metals is

The probabilities of problem being solved by two students are 1/2 and 1/3.Find the probability of the problem being solved.

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

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

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

A small square loop of wire of side l is placed inside a large square loop of side L(L>>1). If the loops are coplanar and their centres coincide, the mutual induction of the system is directlv proportional to :

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

Calculate the hydrolysis constant of a salt of a weak acid(Ka=2x10-6) and of a weak base(Kb=5x10-7)

There are 10 stations between two cities A and B. A train is to stop at three of these 10 stations. The probability that no two of these three stations are consecutive is

The length of the transverse axis of the hyperbola 4x2-9y2+8x+40=0 is

The vectors (1, 2, 3), (4, 5, 6), (6, 7, 8) are

Two lenses of focal lengths +10cm, and -15cm when put in contact behave like a convex lens .They will have zero longitudinal chromatic aberration if their dispersive powers are in the ratio

A plane π makes intercepts 3 and 4 respectively on z-axis.If π is parallel to y-axis,then its equation is

The ratio of surface areas of the two spheres is 9:16.They are put in contact and a charge of 7μC is given to the system and they are separated. Then the intensity of the electric field at a distance of 100m from the centre of smaller sphere is

If α,β,γ are the roots of the equation x3+qx+c=0 the equation whose roots are -α-1,-β-1,-γ-1 is

Equation to the pair of tangents drawn from (2,-1) to the ellipse x2+3y2=3 is

If C0, C1, C2,...... are binomial coefficients , then C1+C2+C3+C4+....+Cr+....+Cn is equal to :

If a= sin θ+ cos θ, b= sin3 θ+ cos3θ then

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

sin5θ/sinθ is equal to

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

If x is an acute angle and sin(x+280) =cos (3x-780), then x=

Ify=ae-bx cos(cx+d) then y2+2by1+(b2+c2)y=

The quadratic equation for which the sum of the roots is 12 and the sum of the cubes of the roots is 468 is

The equation of the circle belonging to the coaxal system of which (2, -3)(0, -4) are the limiting points and passing through the point (2, -1) is

Observe the following statements A: f'(x) = 2x3 - 9x2  + 12x - 3 is increasing outside the interval (1, 2)R: f'(x) < 0 for x belongs to (1,2).Then which of the following is true

If one ticket is randomly selected from, tickets numbered from 1to 30 then the probabilitythat the numbered on the tickets i a multiple of 5 or 7 is

The distance between the origin and the normal to the curve y=e2x+x2 at x=0 is

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

If π is Peltier coefficient,heat evolved at a junction when a current of 10 mA passes for 10 seconds in joules is

The area of the triangle formed by the tangent and normal at (2,4) on the circle x2+y2=20 and X-axis (in sq.units) is

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

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

The equation of the common tangent to y2= 8x and x2+y2 – 12x + 4 = 0

The slopes of the lines passing through A(2,0) and making an angle of 450 with the tangent at A to the circle x2+y2+4x-6y-12=0 is

sin2 θ+ sin2 (600+ θ)+ sin2 (600-θ)=

If the equation of the hyperbola whose focus is (2, 4), eccentricity is 5 and directrix is 4x-3y+1=0 is 15x2-24xy+8y2+ax+by+c=0 then the ascending order of a, b, c is

Which one of the following compounds liberates CO2 from aqueous NaHCO3

If the cold junction is held at 00C, the same thermo emf V of a thermocouple varies as V = 10 x 10 6t - * x 10 bt2, where t is the 40 temperature of the hot junction in 0C. The neutral temperature and the maximum value of thermo emf are respectively:

The equation of the tangent to the  curve y2=4x+5 and which is parallel to0 y=2x+7 is

32cos4 θ.sin2 θ=

The chords of contact of the pair of tangents to the circle x2+y2=1 drawn from any point on the line 2x+y=4 pass through the point

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

The equation of the sphere concentric with the sphere x2 + y2 + z2 – 2x – 4y – 6z – 11=0 and radius double of it is:

To obtain p-type extrinsic semi- conductor, the impurity element to be added to Germanium should be of valency :

If one root of the quadratic equation ax2+bx+c=0 is 3-4i, then a+b+c is :

(l1,m1,n1) and (l2,m2,n2) are D’rs of two lines inclined at an angle 1200 then D.C’s of the line bisecting the angle between them are

The parametric equations of circle (x-3)2+(y-2)2=100 are

A body of mass m1 moving with a velocity 10 ms-1 collides with another body at rest of mass m2 After collision the velocities of the two bodies are 2 ms-1 and 5 ms-1respectively, along the direction of motion of m1.The ratio m1/ m2

The image of the point (3,2,1) in the plane 2x - y + 3z= 7 is

From any point on the circle x2+y2+2gx+2fy+c=0 tangents are drawn to the circle x2+y2+2gx+2fy+c sin2α+(g2+f2) 13cos2 α =0

A long straight wire carries an electric current of 2A.The magnetic induction at a perpendicular distance of 5m from the wire is (μ0=4πx10-7 Hm-1)

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

Tan-1 2+ Tan-1 3 =

CCl3COCH3+Ca(OH)2→X+Y. Here X and Y are

The acute angle between the lines x2-2xycotθ+ y2=0 is

If tan(π/4+θ)+tan(π/4- θ)=3, then tan2 (π/4+θ)+ tan2 (π/4-θ)=

The molarity of pure water is:

The vertex and focus of a parabola are (2, 1), (1, -1). Then the equation of the tangent at the vertex is

If the locus of mid points of the chords of the parabola y2=4ax which passes through a fixed point (h, k) is also a parabola then its length of latusrectum is

A mixture of Boran trichloride and hydrogen is subjected to silent electric discharge to form ’A’ and HCl. ’A’ is mixed with NH3 and heated to 2000 C to form B. The formula of B is

 If x -y+ 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

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

The locus of poles of tangents to the hyperbola x2-y2=a2 w. r. t the parabola y2=4ax is

A proton, a deuteron (nucleus of 1H2) and an α-particle with same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular  paths is :

An organic compound containing C and H has 92.3% of carbon, Its empirical formula is:

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

If the third term in the expansion of (1/x+ xlog10 x)5 is 1, then x=

(tan α+ cosec β)2-(cot β- sec α)2 =

The length of the sub tangent to the curve x2y2=a4 at the point (-a, a) is

sin 200.sin 400.sin 600 sin800=

The angle between the lines joining the origin to the points of intersection of y-3x+2=0, 7x2-4xy+8y2+2x-4y-8=0 is

The maximum value of x4+3x3-2x2-9x+6 is

The parametric equation of the circle x2+y2+x+√3y=0 is

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)=

A train is travelling at 120 Kmph 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 =330 ms-1)nearly

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is :

One mole of N2H4 loses 10 moles of electrons to form a new compound Z.Assuming that all the nitrogens appear in the new compound, what is the oxidation state of nitrogen in Z? (There is no change in the oxidation state of hydrogen)

If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=

C2+C4+C6+……….. =

The equation to the parabola having focus (-1,-1) and directrix 2x -3y +6 = 0 is

If three points A, B, C have position vectors (1, x, 3) and (y, -2, -5) respectively and if they are collinear, then (x, y)=

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear then (x, y) is equal to

The amplitude of 1+cos θ+ i sin θ is

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

If two lines represented by ax3+bx2y+cxy2+dy3=0 are mutually perpendicular, then the slope of third line is

Counters numbered 1, 2, 3 are placed in a bag and one is drawn at random and replaced. The operation is being repeated three times. The probability of obtaining a total of 6 is